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(Integral(0)))~p0 4 ~Hs(Integral(e^(-?a*?x)*sin(?x)*d*?x)):(e^(-?a*~ ?x)/(?a^2+1)*(-?a*sin(?x)-cos(?x))+(Integral(0)))~p0 4 ~Hs(Integral(e^(-?a*?x)*sin(?b*?x)*d*?x)):(e^(-~ ?a*?x)/(?a^2+?b^2)*(-?a*sin(?b*?x)-?b*cos(?b*?x))+~ (Integral(0)))~p0 4 ~Hs(Integral(e^(-?a*?x)*cos(?x)*d*?x)):(e^(-?a*~ ?x)/(?a^2+1)*(-?a*cos(?x)+sin(?x))+(Integral(0)))~p0 4 ~Hs(Integral(e^(-?a*?x)*cos(?b*?x)*d*?x)):(e^(-~ ?a*?x)/(?a^2+?b^2)*(-?a*cos(?b*?x)+?b*sin(?b*?x))+~ (Integral(0)))~p0 4 ~Hs(Integral(?x*ln(?x)*d*?x)):((?x^2/2*ln(?x)-~ ?x^2/4)+(Integral(0)))~p0 4 ~Hs(Integral(?x^?n*ln(?x)*d*?x)):(?x^(?n+1)*((~ ln(?x))/(?n+1)-1/(?n+1)^2)+(Integral(0)))~p0 4 ~Hs(Integral(?x*ln(?a*?x)*d*?x)):(?x^2*((ln(?a*~ ?x))/2-1/4)+(Integral(0)))~p0 4 ~Hs(Integral(?x^?n*ln(?a*?x)*d*?x)):(?x^(?n+1)*~ ((ln(?a*?x))/(?n+1)-1/(?n+1)^2)+(Integral(0)))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b!^" Helvetica~: ;bP5&c55*trigonometric| | functions}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(Integral(?x*sin(?x)*d*?x)):(sin(?x)-?x*cos(~ ?x)+(Integral(0)))~p0 4 ~Hs(Integral(?x*sin(?a*?x)*d*?x)):(1/?a^2*sin(~ ?a*?x)-?x/?a*cos(?a*?x)+(Integral(0)))~p0 4 ~Hs(Integral(?x*cos(?x)*d*?x)):(cos(?x)+?x*sin(~ ?x)+(Integral(0)))~p0 4 ~Hs(Integral(?x*cos(?a*?x)*d*?x)):(1/?a^2*cos(~ ?a*?x)+1/?a*?x*sin(?a*?x)+(Integral(0)))~p0 4 ~Hs(Integral(?x^?m*sin(?x)*d*?x)):(-?x^?m*cos(~ ?x)+?m*(Integral(?x^(?m-1)*cos(?x)*d*?x)))~p0 4 ~Hs(Integral(?x^?m*sin(?a*?x)*d*?x)):(-1/?a*?x^~ ?m*cos(?a*?x)+?m/?a*(Integral(?x^(?m-1)*cos(?a*~ ?x)*d*?x)))~p0 4 ~Hs(Integral(?x^?m*cos(?x)*d*?x)):(?x^?m*sin(?x)-~ ?m*(Integral(?x^(?m-1)*sin(?x)*d*?x)))~p0 4 ~Hs(Integral(?x^?m*cos(?a*?x)*d*?x)):(1/?a*?x^~ ?m*sin(?a*?x)-?m/?a*(Integral(?x^(?m-1)*sin(?a*~ ?x)*d*?x)))~p0 4 ~Hs(Integral((sin(?x))^?n*d*?x)):(-((sin(?x))^~ (?n-1)*cos(?x))/?n+(?n-1)/?n*(Integral((sin(?x))^~ (?n-2)*d*?x)))~p0 4 ~Hs(Integral((cos(?x))^?n*d*?x)):((sin(?x)*(cos(~ ?x))^(?n-1))/?n+(?n-1)/?n*(Integral((cos(?x))^~ (?n-2)*d*?x)))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b!U" Helvetica~: ;bP5&c55*Other Integration| | Rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_}))# b#J" Helvetica~: ;bP5&c55*after Partial| | Fraction Decomposition integration}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(ln(?x+?b*i)):((-i*arctan(?x/?b)+1/2*ln(?x^~ 2+?b^2))+1/2*?*i)~p0 4 ~Hs(ln(?x+i)):((-i*arctan(?x)+1/2*ln(?x^2+1))+~ 1/2*?*i)~p0 4 ~Hs(ln(?x-?b*i)):((i*arctan(?x/?b)+1/2*ln(?x^2+~ ?b^2))+1/2*?*i)~p0 4 ~Hs(ln(?x-i)):((i*arctan(?x)+1/2*ln(?x^2+1))+1/~ 2*?*i)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})b @# b$R" Helvetica~: ;bP5&c55*substituting| | ;bP7&c552z;bP5&c55* ,] tan,H<2^;bP7&c552x^&c55*2};bP5,I into| | a rational function in sin,H;bP7&c552x;bP5&c55*,I and cos,H;bP7&c552x| |;bP5&c55*,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~He(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0 4 ~He(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b"0" Helvetica~: ;bP5&c55*Unifying| | arbitrary constants}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(?c*c_?n):(Integral(0))~p0 4 ~Hs(c_?n+0):(c_?n)~p0 4 ~Hs(c_?n+?c):(Integral(0))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b!L" Helvetica~: ;bP5&c55*Exponential| | Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(Integral(?x*?a^?x*d*?x)):(((?x*?a^?x)/(ln(~ ?a))-?a^?x/(ln(?a))^2)+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*?x*d*?x)):(e^?x*(?x-1)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*?x*d*?x)):(e^(?a*?x)/?a^~ 2*(?a*?x-1)+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*?x*d*?x)):((-?x-1)*e^(-?x)+~ (Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*?x*d*?x)):((-e^(-?a*?x)/~ ?a^2-(e^(-?a*?x)*?x)/?a)+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*?x^?n*d*?x)):(?x^?n*e^?x-?n*~ (Integral(?x^(?n-1)*e^?x*d*?x)))~p0 3 ~Hs(Integral(e^(-?x)*?x^?n*d*?x)):((-1)*?x^?n*~ e^?x-(-?n)*(Integral(e^(-?x)*?x^(?n-1)*d*?x)))~p0 3 ~Hs(Integral(?x^?n*e^(?a*?x)*d*?x)):(1/?a*?x^?n*~ e^(?a*?x)-?n/?a*(Integral(?x^(?n-1)*e^(?a*?x)*~ d*?x)))~p0 3 ~Hs(Integral(?x^?n*e^(-?a*?x)*d*?x)):(1/(-?a)*~ ?x^?n*e^(-?a*?x)-?n/(-?a)*(Integral(?x^(?n-1)*~ e^(-?a*?x)*d*?x)))~p0 3 ~Hs(Integral((?a+?x)*e^?x*d*?x)):(e^?x*(?a+?x)-~ e^?x)~p0 3 ~Hs(Integral((?a+?x)*e^(?c*?x)*d*?x)):((1/?c*e^~ (?c*?x)*(?x+?a)-(1/?c)^2*e^(?c*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a+?x)*e^(-?x)*d*?x)):((-(?x+?a)*~ e^(-?x)-e^(-?x))+(Integral(0)))~p0 3 ~Hs(Integral((?a+?x)*e^(-?c*?x)*d*?x)):((1/(-?c)*~ e^(-?c*?x)*(?a+?x)-1/?c^2*e^(-?c*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a+?b*?x)*e^?x*d*?x)):((e^?x*(?a+~ ?b*?x)-?b*e^?x)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)*e^(?c*?x)*d*?x)):((e^(~ ?c*?x)*(?a+?b*?x-?b/?c))/?c+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)*e^(-?x)*d*?x)):(-(?b*?x+~ ?a+?b)*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)*e^(-?c*?x)*d*?x)):((e^~ (-?c*?x)*(?a+?b*?x+?b/?c))/(-?c)+(Integral(0)))~p0 3 ~Hs(Integral((?a-?x)*e^?x*d*?x)):((e^?x*(?a-?x+~ 1))/1+(Integral(0)))~p0 3 ~Hs(Integral((?a-?x)*e^(?c*?x)*d*?x)):((e^(?c*~ ?x)*(?a-?x+1/?c))/?c+(Integral(0)))~p0 3 ~Hs(Integral((?a-?x)*e^(-?x)*d*?x)):(-(-?x+?a-~ 1)*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral((?a-?x)*e^(-?c*?x)*d*?x)):((e^(-?c*~ ?x)*(?a-?x-1/?c))/(-?c)+(Integral(0)))~p0 3 ~Hs(Integral((?a-?b*?x)*e^?x*d*?x)):(e^?x*(?a-~ ?b*?x+?b)+(Integral(0)))~p0 3 ~Hs(Integral((?a-?b*?x)*e^(?c*?x)*d*?x)):((e^(~ ?c*?x)*(?a-?b*?x+?b/?c))/?c+(Integral(0)))~p0 3 ~Hs(Integral((?a-?b*?x)*e^(-?x)*d*?x)):(-(-?b*~ ?x+?a-?b)*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral((?a-?b*?x)*e^(-?c*?x)*d*?x)):((e^~ (-?c*?x)*(?a-?b*?x+?b/(-?c)))/(-?c)+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a+?x)^2*e^?x*d*?x)):(((?x+?a)^2-~ 2*(?x+?a)+2)*e^?x+(Integral(0)))~p0 3 ~Hs(Integral((?a+?x)^2*e^(?c*?x)*d*?x)):((((?x+~ ?a)^2-2*(?x+?a)/?c+2*1/?c^2)*e^(?c*?x))/?c+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a+?x)^2*e^(-?x)*d*?x)):(-((?x+?a)^~ 2+2*(?x+?a)+2)*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?x)^2*e^(-?c*?x)*d*?x)):((((?x+~ ?a)^2-2*(?x+?a)/(-?c)+2*1/(-?c)^2)*e^((-?c)*?x))/~ (-?c)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)^2*e^?x*d*?x)):(((?a+?b*~ ?x)^2-2*?b*(?a+?b*?x)+2*?b^2)*e^?x+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)^2*e^(?c*?x)*d*?x)):(((~ ?a+?b*?x)^2-2*?b*(?a+?b*?x)/?c+2*?b^2/?c^2)*(1/~ ?c*e^(?c*?x))+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)^2*e^(-?x)*d*?x)):(-((?b*~ ?x+?a)^2+2*?b*(?b*?x+?a)+2*?b^2)*e^(-?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a+?b*?x)^2*e^(-?c*?x)*d*?x)):((~ (?a+?b*?x)^2-2*?b*(?a+?b*?x)/(-?c)+2*?b^2/(-?c)^~ 2)*(1/(-?c)*e^(-?c*?x))+(Integral(0)))~p0 3 ~Hs(Integral((?a-?x)^2*e^?x*d*?x)):(((-?x+?a)^~ 2+2*(-?x+?a)+2)*e^?x+(Integral(0)))~p0 3 ~Hs(Integral((?a-?x)^2*e^(?c*?x)*d*?x)):(((-?x+~ ?a)^2+2*(-?x+?a)/?c+2*1/?c^2)*(1/?c*e^(?c*?x))+~ (Integral(0)))~p0 3 ~Hs(Integral((?a-?x)^2*e^(-?x)*d*?x)):(((-?x+?a)^~ 2-2*(-?x+?a)+2)*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral((?a-?x)^2*e^(-?c*?x)*d*?x)):(((-?x+~ ?a)^2+2*(-?x+?a)/(-?c)+2*1/(-?c)^2)*(1/?c*e^(-~ ?c*?x))+(Integral(0)))~p0 3 ~Hs(Integral((?a-?b*?x)^2*e^?x*d*?x)):(((-?b*?x+~ ?a)^2+2*?b*(-?b*?x+?a)+2*(-?b)^2)*e^?x+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a-?b*?x)^2*e^(?c*?x)*d*?x)):(((~ ?a-?b*?x)^2-2*(-?b)*(?a+(-?b)*?x)/?c+2*(-?b)^2/~ ?c^2)*(1/?c*e^(?c*?x))+(Integral(0)))~p0 3 ~Hs(Integral((?a-?b*?x)^2*e^(-?x)*d*?x)):(-(((~ -?b*?x+?a)^2-2*?b*(-?b*?x+?a)+2*?b^2)*e^(-?x))/~ ?c+(Integral(0)))~p0 3 ~Hs(Integral((?a-?b*?x)^2*e^(-?c*?x)*d*?x)):(-~ (((-?b*?x+?a)^2-2*(?b*(-?b*?x+?a))/?c+2*?b^2/?c^~ 2)*e^(-?c*?x))/?c+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)^3*e^?x*d*?x)):(e^?x*((~ ?a+?b*?x)^3-3*?b*(?a+?b*?x)^2+6*?b^2*(?a+?b*?x)-~ 6*?b^3)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)^3*e^(?c*?x)*d*?x)):(1/~ ?c*e^(?c*?x)*((?a+?b*?x)^3-3*?b*(?a+?b*?x)^2/?c+~ 6*?b^2*(?a+?b*?x)/?c^2-6*?b^3/?c^3)+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a+?b*?x)^3*e^(-?c*?x)*d*?x)):(1/~ (-?c)*e^(-?c*?x)*((?a+?b*?x)^3-3*?b*(?a+?b*?x)^~ 2/(-?c)+6*?b^2*(?a+?b*?x)/(-?c)^2-6*?b^3/(-?c)^~ 3)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)^4*e^?x*d*?x)):(e^?x*((~ ?a+?b*?x)^4-4*?b*(?a+?b*?x)^3+12*?b^2*(?a+?b*?x)^~ 2-24*(?b*?x+?a)*?b^3+24*?b^4)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)^4*e^(?c*?x)*d*?x)):(1/~ ?c*e^(?c*?x)*((?a+?b*?x)^4-4*?b*(?a+?b*?x)^3/?c+~ 12*?b^2*(?a+?b*?x)^2/?c^2-24*(?b*?x+?a)/?c^3*?b^~ 3+24*?b^4/?c^4)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?x)^?n*e^?x*d*?x)):(e^?x*(?a+~ ?x)^?n-?n*(Integral((?a+?x)^(?n-1)*e^?x*d*?x)))~p0 3 ~Hs(Integral((?a+?x)^?n*e^(?c*?x)*d*?x)):(1/?c*~ e^(?c*?x)*(?a+?x)^?n-(?n*1/?c)*(Integral((?a+?x)^~ (?n-1)*e^(?c*?x)*d*?x)))~p0 3 ~Hs(Integral((?a+?x)^?n*e^(-?x)*d*?x)):(-(?x+?a)^~ ?n*e^(-?x)+?n*(Integral((?x+?a)^(?n-1)*e^(-?x)*~ d*?x)))~p0 3 ~Hs(Integral((?a+?x)^?n*e^(-?c*?x)*d*?x)):(-((~ ?x+?a)^?n*e^(-?c*?x))/?c+(?n*(Integral((?x+?a)^~ (?n-1)*e^(-?c*?x)*d*?x)))/?c)~p0 3 ~Hs(Integral((?a+?b*?x)^?n*e^?x*d*?x)):(e^?x*(~ ?a+?b*?x)^?n-(?n*?b)*(Integral((?a+?b*?x)^(?n-~ 1)*e^?x*d*?x)))~p0 3 ~Hs(Integral((?a+?b*?x)^?n*e^(?c*?x)*d*?x)):(1/~ ?c*e^(?c*?x)*(?a+?b*?x)^?n-(?n*?b/?c)*(Integral(~ (?a+?b*?x)^(?n-1)*e^(?c*?x)*d*?x)))~p0 3 ~Hs(Integral((?a+?b*?x)^?n*e^(-?x)*d*?x)):((-e)^~ (-?x)*(?a+?b*?x)^?n+?b*?n*(Integral((?b*?x+?a)^~ (?n-1)*e^(-?x)*d*?x)))~p0 3 ~Hs(Integral((?a+?b*?x)^?n*e^(-?c*?x)*d*?x)):(~ 1/(-?c)*e^(-?c*?x)*(?a+?b*?x)^?n-(?n*?b/(-?c))*~ (Integral((?a+?b*?x)^(?n-1)*e^(-?c*?x)*d*?x)))~p0 3 ~Hs(Integral((?a-?x)^?n*e^?x*d*?x)):((-?x+?a)^~ ?n*e^?x+?n*(Integral((-?x+?a)^(?n-1)*e^?x*d*?x)))~p0 3 ~Hs(Integral((?a-?x)^?n*e^(?c*?x)*d*?x)):(((-?x+~ ?a)^?n*e^(?c*?x))/?c+(?n*(Integral((-?x+?a)^(?n-~ 1)*e^(?c*?x)*d*?x)))/?c)~p0 3 ~Hs(Integral((?a-?x)^?n*e^(-?x)*d*?x)):(-(-?x+~ ?a)^?n*e^(-?x)-?n*(Integral((-?x+?a)^(?n-1)*e^~ (-?x)*d*?x)))~p0 3 ~Hs(Integral((?a-?x)^?n*e^(-?c*?x)*d*?x)):(((-~ ?x+?a)^?n*e^(-?c*?x))/(-?c)+(?n*(Integral((-?x+~ ?a)^(?n-1)*e^(-?c*?x)*d*?x)))/(-?c))~p0 3 ~Hs(Integral((?a-?b*?x)^?n*e^?x*d*?x)):((-?b*?x+~ ?a)^?n*e^?x+?b*?n*(Integral((-?b*?x+?a)^(?n-1)*~ e^?x*d*?x)))~p0 3 ~Hs(Integral((?a-?b*?x)^?n*e^(?c*?x)*d*?x)):(1/~ ?c*e^(?c*?x)*(?a-?b*?x)^?n-(?n*(-?b)/?c)*(Integral(~ (?a-?b*?x)^(?n-1)*e^(?c*?x)*d*?x)))~p0 3 ~Hs(Integral((?a-?b*?x)^?n*e^(-?x)*d*?x)):(-(-~ ?b*?x+?a)^?n*e^(-?x)-?b*?n*(Integral((-?b*?x+?a)^~ (?n-1)*e^(-?x)*d*?x)))~p0 3 ~Hs(Integral((?a-?b*?x)^?n*e^(-?c*?x)*d*?x)):(~ 1/(-?c)*e^(-?c*?x)*(?a-?b*?x)^?n-(?n*(-?b)/(-?c))*~ (Integral((?a-?b*?x)^(?n-1)*e^(-?c*?x)*d*?x)))~p0 3 ~Hs(Integral(1/(e^?x+?a)*d*?x)):(1/?a*(?x-ln(abs(~ e^?x+?a)))+(Integral(0)))~p0 3 ~Hs(Integral(1/(e^(?c*?x)+?a)*d*?x)):(1/(-?a*?c)*~ ln(abs(?a*e^(-?c*?x)+1))+(Integral(0)))~p0 3 ~Hs(Integral(1/(e^(-?x)+?a)*d*?x)):((ln(abs(?a*~ e^?x+1)))/?a+(Integral(0)))~p0 3 ~Hs(Integral(1/(e^(-?c*?x)+?a)*d*?x)):(1/(?a*?c)*~ ln(abs(?a*e^(?c*?x)+1))+(Integral(0)))~p0 3 ~Hs(Integral(1/(?b*e^?x+?a)*d*?x)):((?x/?a-1/?a*~ ln(abs(?a+?b*e^?x)))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-e^?x+?a)*d*?x)):(-(ln(abs(?a*~ e^(-?x)-1)))/?a+(Integral(0)))~p0 3 ~Hs(Integral(1/(-e^(?c*?x)+?a)*d*?x)):(1/((-?c)*~ ?a)*ln(abs(?a*e^(-?c*?x)-1))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-e^(-?x)+?a)*d*?x)):(1/?a*ln(abs(~ ?a*e^?x-1))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-e^(-?c*?x)+?a)*d*?x)):(1/(?c*~ ?a)*ln(abs(?a*e^(?c*?x)-1))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-?b*e^?x+?a)*d*?x)):((?x/?a-1/~ ?a*ln(abs(-?b*e^?x+?a)))+(Integral(0)))~p0 3 ~Hs(Integral(1/(e^(-?x)+e^?x)*d*?x)):(arctan(e^~ ?x)+(Integral(0)))~p0 3 ~Hs(Integral(1/(e^(-?x)+?a*e^?x)*d*?x)):(1/sqrt(~ ?a)*arctan(e^?x*sqrt(?a))+(Integral(0)))~p0 3 ~Hs(Integral(1/(?b*e^(-?x)+e^?x)*d*?x)):(1/sqrt(~ ?b)*arctan(e^?x*sqrt(1/?b))+(Integral(0)))~p0 3 ~Hs(Integral(1/(?b*e^(-?x)+?a*e^?x)*d*?x)):(1/~ sqrt(?a*?b)*arctan(e^?x*sqrt(?a/?b))+(Integral(~ 0)))~p0 3 ~Hs(Integral(1/(e^(-?c*?x)+e^(?c*?x))*d*?x)):(~ 1/?c*arctan(e^(?c*?x))+(Integral(0)))~p0 3 ~Hs(Integral(1/(e^(-?c*?x)+?a*e^(?c*?x))*d*?x)):(~ 1/(?c*sqrt(?a))*arctan(e^(?c*?x)*sqrt(?a))+(Integral(~ 0)))~p0 3 ~Hs(Integral(1/(?b*e^(-?c*?x)+e^(?c*?x))*d*?x)):(~ 1/(?c*sqrt(?b))*arctan(e^(?c*?x)*sqrt(1/?b))+(Integral(~ 0)))~p0 3 ~Hs(Integral(1/(?b*e^(-?c*?x)+?a*e^(?c*?x))*d*~ ?x)):(1/(?c*sqrt(?a*?b))*arctan(e^(?c*?x)*sqrt(~ ?a/?b))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-e^(-?x)+e^?x)*d*?x)):(1/2*ln(~ abs((1-e^?x)/(1+e^?x)))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-e^(-?x)-?a*e^?x)*d*?x)):((-1)/~ sqrt(?a)*arctan(e^?x*sqrt(?a))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-?b*e^(-?x)-e^?x)*d*?x)):((-1)/~ sqrt(?b)*arctan(e^?x*sqrt(1/?b))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-?b*e^(-?x)-?a*e^?x)*d*?x)):((-~ 1)/sqrt(?a*?b)*arctan(e^?x*sqrt(?a/?b))+(Integral(~ 0)))~p0 3 ~Hs(Integral(1/(-e^(-?c*?x)-e^(?c*?x))*d*?x)):(~ -(arctan(e^(?c*?x)))/?c+(Integral(0)))~p0 3 ~Hs(Integral(1/(-e^(-?c*?x)-?a*e^(?c*?x))*d*?x)):(~ (-1)/(?c*sqrt(?a))*arctan(e^(?c*?x)*sqrt(?a))+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(-?b*e^(-?c*?x)-e^(?c*?x))*d*?x)):(~ (-1)/(?c*sqrt(?b))*arctan(e^(?c*?x)*sqrt(1/?b))+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(-?b*e^(-?c*?x)-?a*e^(?c*?x))*d*~ ?x)):((-1)/(?c*sqrt(?a*?b))*arctan(e^(?c*?x)*sqrt(~ ?a/?b))+(Integral(0)))~p0 3 ~Hs(Integral((e^?x+?a)/(e^?x-?a)*d*?x)):(2*ln(~ abs(?a-e^?x))-?x+(Integral(0)))~p0 3 ~Hs(Integral((e^(?c*?x)+?a)/(e^(?c*?x)-?a)*d*?x)):(~ 2/?c*ln(abs(?a-e^(?c*?x)))-?x+(Integral(0)))~p0 3 ~Hs(Integral((e^(-?x)+?a)/(e^(-?x)-?a)*d*?x)):(~ (-2)*ln(abs(?a-e^(-?x)))-?x+(Integral(0)))~p0 3 ~Hs(Integral((e^(-?c*?x)+?a)/(e^(-?c*?x)-?a)*d*~ ?x)):(2/(-?c)*ln(abs(?a-e^(-?c*?x)))-?x+(Integral(~ 0)))~p0 3 ~Hs(Integral((e^?x*?x)/(?x+1)^2*d*?x)):(e^?x/(~ 1+?x)+(Integral(0)))~p0 3 ~Hs(Integral((e^(?a*?x)*?x)/(?a*?x+1)^2*d*?x)):(~ e^(?a*?x)/(?a^2*(1+?a*?x))+(Integral(0)))~p0 3 ~Hs(Integral((e^(-?x)*?x)/(-?x+1)^2*d*?x)):(e^~ (-?x)/(-?x+1)+(Integral(0)))~p0 3 ~Hs(Integral((e^(-?a*?x)*?x)/(-?a*?x+1)^2*d*?x)):(~ e^(-?a*?x)/(?a^2*(1-?a*?x))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(e^?x+?a)*e^?x*d*?x)):(2/(3*1*~ 1)*(?a+1*e^(1*?x))^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(e^(?c*?x)+?a)*e^(?c*?x)*d*?x)):(~ 2/(3*?c)*(?a+e^(?c*?x))^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(e^(-?x)+?a)*e^(-?x)*d*?x)):(~ -2/3*(e^(-?x)+?a)^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(e^(-?c*?x)+?a)*e^(-?c*?x)*d*~ ?x)):(-2/3*(e^(-?c*?x)+?a)^(3/2)/?c+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(?b*e^?x+?a)*e^?x*d*?x)):(2/(~ 3*?b)*(?a+?b*e^?x)^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?b*e^(?c*?x)+?a)*e^(?c*?x)*d*~ ?x)):(2/(3*?b*?c)*(?a+?b*e^(?c*?x))^(3/2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(?b*e^(-?x)+?a)*e^(-?x)*d*?x)):(~ 2/(-3*?b)*(?a+?b*e^(-?x))^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?b*e^(-?c*?x)+?a)*e^(-?c*?x)*~ d*?x)):(2/(3*?b*(-?c))*(?a+?b*e^(-?c*?x))^(3/2)+~ (Integral(0)))~p0 3 ~Hs(Integral(sqrt(-e^?x+?a)*e^?x*d*?x)):(-2/3*~ (-e^?x+?a)^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-e^(?c*?x)+?a)*e^(?c*?x)*d*?x)):(~ -2/3*(-e^(?c*?x)+?a)^(3/2)/?c+(Integral(0)))~p0 3 ~Hs(Integral((sqrt(-e^(-?x)+?a)*e^(-?x))*d*?x)):(~ -2/3*(-(-e^(-?x)+?a)^(3/2))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-e^(-?c*?x)+?a)*e^(-?c*?x)*d*~ ?x)):(-2/3*(-e^(-?c*?x)+?a)^(3/2)/(-?c)+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(-?b*e^?x+?a)*e^?x*d*?x)):(2/~ (-3*?b)*(?a+(-?b)*e^?x)^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?b*e^(?c*?x)+?a)*e^(?c*?x)*~ d*?x)):(2/(3*(-?b)*?c)*(?a+(-?b)*e^(?c*?x))^(3/~ 2)+(Integral(0)))~p0 3 ~Hs(Integral((sqrt(-?b*e^(-?x)+?a)*e^(-?x))*d*~ ?x)):(2/3*(-?b*e^(-?x)+?a)^(3/2)/?b+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(-?b*e^(-?c*?x)+?a)*e^(-?c*?x)*~ d*?x)):(2/(3*?b*?c)*(?a-?b*e^(-?c*?x))^(3/2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^?x/sqrt(e^?x+?a)*d*?x)):(2*sqrt(~ e^?x+?a)/?c+(Integral(0)))~p0 3 ~Hs(Integral(e^(?c*?x)/sqrt(e^(?c*?x)+?a)*d*?x)):(~ 2*sqrt(e^(?c*?x)+?a)/?c+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)/sqrt(e^(-?x)+?a)*d*?x)):(~ (-2)*sqrt(?a+e^(-?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?c*?x)/sqrt(e^(-?c*?x)+?a)*d*~ ?x)):(2/(-?c)*sqrt(?a+e^(-?c*?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x/sqrt(?b*e^?x+?a)*d*?x)):(2/?b*~ sqrt(?a+?b*e^?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(?c*?x)/sqrt(?b*e^(?c*?x)+?a)*d*~ ?x)):(2/(?b*?c)*sqrt(?a+?b*e^(?c*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?x)/sqrt(?b*e^(-?x)+?a)*d*?x)):(~ 2/(-?b)*sqrt(?a+?b*e^(-?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?c*?x)/sqrt(?b*e^(-?c*?x)+?a)*~ d*?x)):(2/(-?b*?c)*sqrt(?a+?b*e^(-?c*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?c*?x)/sqrt(-?b*e^(?c*?x)+?a)*~ d*?x)):(2/(-?b*?c)*sqrt(?a+(-?b)*e^(?c*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?x)/sqrt(-?b*e^(-?x)+?a)*d*?x)):(~ (2*1/?b)*sqrt(?a+(-?b)*e^(-?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?c*?x)/sqrt(-?b*e^(-?c*?x)+?a)*~ d*?x)):(2/(?b*?c)*sqrt(?a+(-?b)*e^(-?c*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt((e^?x-1)/(e^?x+1))*d*?x)):((~ -arccos(1/e^?x)+arccosh(e^?x))*1+(Integral(0)))~p0 3 ~Hs(Integral(sqrt((e^(?c*?x)-1)/(e^(?c*?x)+1))*~ d*?x)):((-arccos(1/e^(?c*?x))+arccosh(e^(?c*?x)))*~ 1/?c+(Integral(0)))~p0 3 ~Hs(Integral(((-?x^2+2)*e^?x)/((-?x+1)^(3/2)*sqrt(~ ?x+1))*d*?x)):(e^?x*sqrt((1+?x)/(1-?x))+(Integral(~ 0)))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b"1" Helvetica~: ;bP5&c55*Exponential| | Trig Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(Integral(e^?x*sin(?x)*d*?x)):(1/2*e^?x*(sin(~ ?x)-cos(?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*sin(?x)*d*?x)):(1/?a^2*~ e^(?a*?x)*(?a*sin(?x)-cos(?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*sin(?x)*d*?x)):(1/1*e^(-?x)*~ (-sin(?x)-cos(?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*sin(?x)*d*?x)):(1/(-?a)^~ 2*e^(-?a*?x)*((-?a)*sin(?x)-cos(?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^?x*sin(?x+?c)*d*?x)):(1/2*e^?x*~ (sin(?x+?c)-cos(?x+?c))+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*sin(?x+?c)*d*?x)):(1/?a^~ 2*e^(?a*?x)*(?a*sin(?x+?c)-cos(?x+?c))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?x)*sin(?x+?c)*d*?x)):((-cos(~ ?x+?c)-sin(?x+?c))*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*sin(?x+?c)*d*?x)):(1/(-~ ?a)^2*e^(-?a*?x)*((-?a)*sin(?x+?c)-cos(?x+?c))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^?x*sin(?b*?x+?c)*d*?x)):(1/?b^2*~ e^?x*(sin(?b*?x+?c)-?b*cos(?b*?x+?c))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*sin(?b*?x+?c)*d*?x)):(1/~ (?a^2+?b^2)*e^(?a*?x)*(?a*sin(?b*?x+?c)-?b*cos(~ ?b*?x+?c))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*sin(?b*?x+?c)*d*?x)):(((-~ ?b*cos(?b*?x+?c)-sin(?b*?x+?c))*e^(-?x))/(?b^2+~ 1)+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*sin(?b*?x+?c)*d*?x)):(~ 1/(?a^2+?b^2)*e^(-?a*?x)*((-?a)*sin(?b*?x+?c)-~ ?b*cos(?b*?x+?c))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*sin(-?x+?c)*d*?x)):(1/2*(cos(~ -?x+?c)+sin(-?x+?c))*e^?x+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*sin(-?x+?c)*d*?x)):(1/(~ ?a^2+1)*e^(?a*?x)*(cos(-?x+?c)+?a*sin(-?x+?c))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*sin(-?x+?c)*d*?x)):(1/2*(~ cos(-?x+?c)-sin(-?x+?c))*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*sin(-?x+?c)*d*?x)):(1/~ (?a^2+1)*e^(-?a*?x)*(cos(-?x+?c)-?a*sin(-?x+?c))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^?x*sin(-?b*?x+?c)*d*?x)):(((?b*~ cos(-?b*?x+?c)+sin(-?b*?x+?c))*e^?x)/(?b^2+1)+~ (Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*sin(-?b*?x+?c)*d*?x)):(~ 1/(?a^2+?b^2)*e^(?a*?x)*(?a*sin(-?b*?x+?c)-(-?b)*~ cos(-?b*?x+?c))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*sin(-?b*?x+?c)*d*?x)):(1/~ (1+?b^2)*e^(-?x)*(-sin(-?b*?x+?c)-(-?b)*cos(-?b*~ ?x+?c))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*sin(-?b*?x+?c)*d*?x)):(~ 1/(?a^2+?b^2)*e^(-?a*?x)*((-?a)*sin(-?b*?x+?c)-~ (-?b)*cos(-?b*?x+?c))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*(sin(?x))^2*d*?x)):((-1/10*(~ cos(2*?x)+2*sin(2*?x))*e^?x+1/2*e^?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(sin(?x))^2*d*?x)):(e^(~ ?a*?x)/(?a^2+4)*(?a*(sin(?x))^2-2*sin(?x)*cos(~ ?x)+2/?a)+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*(sin(?x))^2*d*?x)):(e^(-?x)/~ 5*(-(sin(?x))^2-2*sin(?x)*cos(?x)-2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(sin(?x))^2*d*?x)):(e^~ (-?a*?x)/(?a^2+4)*((-?a)*(sin(?x))^2-2*sin(?x)*~ cos(?x)+2/(-?a))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*(sin(?b*?x))^2*d*?x)):((-1/2*~ ((cos(2*?b*?x)+2*?b*sin(2*?b*?x))*e^?x)/(4*?b^~ 2+1)+1/2*e^?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(sin(?b*?x))^2*d*?x)):(~ (e^(?a*?x)/(2*?a)-e^(?a*?x)/(?a^2+4*?b^2)*(?a/~ 2*cos(2*?b*?x)+?b*sin(2*?b*?x)))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*(sin(?b*?x))^2*d*?x)):((e^~ (-?x)/(-2)-e^(-?x)/(1+4*?b^2)*((-1/2)*cos(2*?b*~ ?x)+?b*sin(2*?b*?x)))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(sin(?b*?x))^2*d*?x)):(~ (e^(-?a*?x)/(2*(-?a))-e^(-?a*?x)/(?a^2+4*?b^2)*~ ((-?a)/2*cos(2*?b*?x)+?b*sin(2*?b*?x)))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^?x*(sin(-?x))^2*d*?x)):((-1/5*(~ 1/2*cos(-2*?x)-sin(-2*?x))*e^?x+1/2*e^?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(sin(-?x))^2*d*?x)):((1/~ 2*e^(?a*?x)/?a-((1/2*?a*cos(-2*?x)-sin(-2*?x))*~ e^(?a*?x))/(?a^2+4))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*(sin(-?x))^2*d*?x)):((-1/~ 5*(-1/2*cos(-2*?x)-sin(-2*?x))*e^(-?x)-1/2*e^(-~ ?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(sin(-?x))^2*d*?x)):((~ -1/2*e^(-?a*?x)/?a-((-1/2*?a*cos(-2*?x)-sin(-2*~ ?x))*e^(-?a*?x))/(?a^2+4))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*(sin(-?b*?x))^2*d*?x)):((-((~ 1/2*cos(-2*?b*?x)-?b*sin(-2*?b*?x))*e^?x)/(4*?b^~ 2+1)+1/2*e^?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(sin(-?b*?x))^2*d*?x)):(~ (e^(?a*?x)/(2*?a)-e^(?a*?x)/(?a^2+4*?b^2)*(?a/~ 2*cos(2*(-?b)*?x)+(-?b)*sin(2*(-?b)*?x)))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?x)*(sin(-?b*?x))^2*d*?x)):((~ -((-1/2*cos(-2*?b*?x)-?b*sin(-2*?b*?x))*e^(-?x))/~ (4*?b^2+1)-1/2*e^(-?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(sin(-?b*?x))^2*d*?x)):(~ (e^(-?a*?x)/(2*(-?a))-e^(-?a*?x)/(?a^2+4*?b^2)*~ ((-?a)/2*cos(2*(-?b)*?x)+(-?b)*sin(2*(-?b)*?x)))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^?x*(sin(?x))^3*d*?x)):(e^?x/10*~ (?a*(sin(?x))^3-3*(sin(?x))^2*cos(?x)+6*(-cos(~ ?x)+sin(?x))/2)+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(sin(?x))^3*d*?x)):(e^(~ ?a*?x)/(?a^2+9)*(?a*(sin(?x))^3-3*(sin(?x))^2*~ cos(?x)+6*(?a*sin(?x)-cos(?x))/(?a^2+1))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?x)*(sin(?x))^3*d*?x)):(1/10*~ (3*(-cos(?x)-sin(?x))-(sin(?x))^3-3*cos(?x)*(sin(~ ?x))^2)*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(sin(?x))^3*d*?x)):(e^~ (-?a*?x)/(?a^2+9)*((-?a)*(sin(?x))^3-3*(sin(?x))^~ 2*cos(?x)+6*((-?a)*sin(?x)-cos(?x))/((-?a)^2+1))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^?x*(cos(?x))^2*d*?x)):((1/5*(cos(~ ?x)+2*sin(?x))*e^?x*cos(?x)+2/5*e^?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(cos(?x))^2*d*?x)):((2*~ e^(?a*?x)/((?a^2+4)*?a)+((?a*cos(?x)+2*sin(?x))*~ e^(?a*?x)*cos(?x))/(?a^2+4))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*(cos(?x))^2*d*?x)):((1/5*~ (-cos(?x)+2*sin(?x))*e^(-?x)*cos(?x)-2/5*e^(-?x))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(cos(?x))^2*d*?x)):((2*~ e^(-?a*?x)/((?a^2+4)*(-?a))+(((-?a)*cos(?x)+2*~ sin(?x))*e^((-?a)*?x)*cos(?x))/(?a^2+4))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^?x*(cos(?b*?x))^2*d*?x)):((2*(?b^~ 2*e^?x)/(4*?b^2+1)+((cos(?b*?x)+2*?b*sin(?b*?x))*~ e^?x*cos(?b*?x))/(4*?b^2+1))+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(cos(?b*?x))^2*d*?x)):(~ (((e^(?a*?x)*cos(?b*?x))*(?a*cos(?b*?x)+2*?b*sin(~ ?b*?x)))/(4*?b^2+?a^2)+(2*?b^2*e^(?a*?x))/((4*~ ?b^2+?a^2)*?a))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*(cos(?b*?x))^2*d*?x)):((-~ 2*(?b^2*e^(-?x))/(4*?b^2+1)+((-cos(?b*?x)+2*?b*~ sin(?b*?x))*e^(-?x)*cos(?b*?x))/(4*?b^2+1))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(cos(?b*?x))^2*d*?x)):(~ (((e^(-?a*?x)*cos(?b*?x))*((-?a)*cos(?b*?x)+2*~ ?b*sin(?b*?x)))/(4*?b^2+?a^2)+(2*?b^2*e^(-?a*?x))/~ ((?a^2+4*?b^2)*(-?a)))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*(cos(-?x))^2*d*?x)):((1/5*(cos(~ -?x)+2*sin(-?x))*e^?x*cos(-?x)+2/5*e^?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(cos(-?x))^2*d*?x)):((2*~ e^(?a*?x)/((?a^2+4)*?a)+((?a*cos(-?x)-2*sin(-?x))*~ e^(?a*?x)*cos(-?x))/(?a^2+4))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*(cos(-?x))^2*d*?x)):((1/5*~ (-cos(-?x)-2*sin(-?x))*e^(-?x)*cos(-?x)+2/5*e^~ (-?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(cos(-?x))^2*d*?x)):((~ 2*e^(-?a*?x)/((?a^2+4)*?a)+(((-?a)*cos(-?x)-2*~ sin(-?x))*e^(-?a*?x)*cos(-?x))/(?a^2+4))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^?x*(cos(-?b*?x))^2*d*?x)):((2*(~ ?b^2*e^?x)/(4*?b^2+1)+((cos(-?b*?x)-2*?b*sin(-~ ?b*?x))*e^?x*cos(-?b*?x))/(4*?b^2+1))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(cos(-?b*?x))^2*d*?x)):(~ (((e^(?a*?x)*cos(-?b*?x))*(?a*cos(-?b*?x)+2*(-~ ?b)*sin(-?b*?x)))/(4*?b^2+?a^2)+(2*?b^2*e^(?a*~ ?x))/((4*?b^2+?a^2)*?a))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*(cos(-?b*?x))^2*d*?x)):((~ -2*(?b^2*e^(-?x))/(4*?b^2+1)+((-cos(-?b*?x)-2*~ ?b*sin(-?b*?x))*e^(-?x)*cos(-?b*?x))/(4*?b^2+1))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(cos(-?b*?x))^2*d*?x)):(~ (((e^(-?a*?x)*cos(-?b*?x))*((-?a)*cos(-?b*?x)+~ 2*(-?b)*sin(-?b*?x)))/(?a^2+4*?b^2)+(2*(-?b)^2*~ e^(-?a*?x))/((?a^2+4*?b^2)*(-?a)))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*(cos(?x))^3*d*?x)):(1/10*(3*~ (cos(?x)+sin(?x))+(cos(?x))^3+3*(cos(?x))^2*sin(~ ?x))*e^?x+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(cos(?x))^3*d*?x)):(e^(~ ?a*?x)/(?a^2+9)*(?a*(cos(?x))^3+3*sin(?x)*(cos(~ ?x))^2+(6*(?a*cos(?x)+sin(?x)))/(?a^2+1))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?x)*(cos(?x))^3*d*?x)):(1/10*~ (3*(-cos(?x)+sin(?x))-(cos(?x))^3+3*(cos(?x))^~ 2*sin(?x))*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(cos(?x))^3*d*?x)):(e^~ (-?a*?x)/(?a^2+9)*((-?a)*(cos(?x))^3+3*sin(?x)*~ (cos(?x))^2+(6*((-?a)*cos(?x)+sin(?x)))/(?a^2+~ 1))+(Integral(0)))~p0 3 ~Hs(Integral(e^(cos(?x))*sin(?x)*d*?x)):(-e^(cos(~ ?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*?x*sin(?x)*d*?x)):(1/2*(-(?x-~ 1)*cos(?x)+?x*sin(?x))*e^?x+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*?x*sin(?x)*d*?x)):(((-(~ ?x-2*?a/(?a^2+1))*cos(?x)+(?a*?x-(?a^2-1)/(?a^~ 2+1))*sin(?x))*e^(?a*?x))/(?a^2+1)+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*?x*sin(?x)*d*?x)):(1/2*(-~ (?x+1)*cos(?x)-?x*sin(?x))*e^(-?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*?x*sin(?x)*d*?x)):(((-~ (?x-2*(-?a)/(?a^2+1))*cos(?x)+((-?a)*?x-(?a^2-~ 1)/(?a^2+1))*sin(?x))*e^((-?a)*?x))/((-?a)^2+1)+~ (Integral(0)))~p0 3 ~Hs(Integral(e^?x*?x*sin(?b*?x)*d*?x)):(((-(?b*~ ?x-2*?b/(?b^2+1))*cos(?b*?x)+(?x-(-?b^2+1)/(?b^~ 2+1))*sin(?b*?x))*e^?x)/(?b^2+1)+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*?x*sin(?b*?x)*d*?x)):(1/~ (?a^2+?b^2)*e^(?a*?x)*((?a*?x-(?a^2-?b^2)/(?a^~ 2+?b^2))*sin(?b*?x)-(?b*?x-(2*?a*?b)/(?a^2+?b^~ 2))*cos(?b*?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*?x*sin(?b*?x)*d*?x)):(((-~ (?b*?x+2*?b/(?b^2+1))*cos(?b*?x)+(-?x-(-?b^2+1)/~ (?b^2+1))*sin(?b*?x))*e^(-?x))/(?b^2+1)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*?x*sin(?b*?x)*d*?x)):(~ 1/((-?a)^2+?b^2)*e^(-?a*?x)*(((-?a)*?x-(?a^2-?b^~ 2)/(?a^2+?b^2))*sin(?b*?x)-(?b*?x-(-2*?a*?b)/(~ ?a^2+?b^2))*cos(?b*?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*?x*sin(?b*?x)*d*?x)):(1/~ (?a^2+?b^2)*e^(?a*?x)*((?a*?x-(?a^2-?b^2)/(?a^~ 2+?b^2))*sin(?b*?x)-(?b*?x-(2*?a*?b)/(?a^2+?b^~ 2))*cos(?b*?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*?x*sin(-?x)*d*?x)):(1/2*(-(-~ ?x+1)*cos(-?x)+?x*sin(-?x))*e^?x+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*?x*sin(-?x)*d*?x)):(((-~ (-?x+2*?a/(?a^2+1))*cos(-?x)+(?a*?x-(?a^2-1)/(~ ?a^2+1))*sin(-?x))*e^(?a*?x))/(?a^2+1)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?x)*?x*sin(-?x)*d*?x)):(1/2*(~ -(-?x-1)*cos(-?x)-?x*sin(-?x))*e^(-?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*?x*sin(-?x)*d*?x)):(((~ -(-?x+2*(-?a)/(?a^2+1))*cos(-?x)+(-?a*?x-(?a^2-~ 1)/(?a^2+1))*sin(-?x))*e^(-?a*?x))/(?a^2+1)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^?x*?x*sin(-?b*?x)*d*?x)):(((-(-~ ?b*?x+2*?b/(?b^2+1))*cos(-?b*?x)+(?x-(-?b^2+1)/~ (?b^2+1))*sin(-?b*?x))*e^?x)/(?b^2+1)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*?x*sin(-?b*?x)*d*?x)):(~ 1/(?a^2+(-?b)^2)*e^(?a*?x)*((?a*?x-(?a^2-?b^2)/~ (?a^2+?b^2))*sin(-?b*?x)-(-?b*?x-(2*?a*(-?b))/~ (?a^2+?b^2))*cos(-?b*?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*?x*sin(-?b*?x)*d*?x)):(((~ -(-?b*?x-2*?b/(?b^2+1))*cos(-?b*?x)+(-?x-(-?b^~ 2+1)/(?b^2+1))*sin(-?b*?x))*e^(-?x))/(?b^2+1)+~ (Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*?x*sin(-?b*?x)*d*?x)):(~ 1/((-?a)^2+(-?b)^2)*e^(-?a*?x)*((-?a*?x-(?a^2-~ ?b^2)/(?a^2+?b^2))*sin(-?b*?x)-(-?b*?x-(2*(?a*~ ?b))/(?a^2+?b^2))*cos(-?b*?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*sin(?x)*sin(?x+?c)*d*?x)):((~ -1/10*(cos(2*?x+?c)+2*sin(2*?x+?c))*e^?x+1/2*cos(~ ?c)*e^?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*sin(?x)*sin(?x+?c)*d*?x)):(~ ((e^(?a*?x)*cos(?c))/(2*?a)-1/2*((?a*cos(2*?x+~ ?c)+2*sin(2*?x+?c))*e^(?a*?x))/(?a^2+4))+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(-?x)*sin(?x)*sin(?x+?c)*d*?x)):(~ (-1/10*(-cos(2*?x+?c)+2*sin(2*?x+?c))*e^(-?x)-~ 1/2*cos(?c)*e^(-?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*sin(?x)*sin(?x+?c)*d*?x)):(~ ((e^(-?a*?x)*cos(?c))/(2*(-?a))-1/2*(((-?a)*cos(~ 2*?x+?c)+2*sin(2*?x+?c))*e^(-?a*?x))/(?a^2+4))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^?x*sin(?b*?x)*sin(?b*?x+?c)*d*?x)):(~ (-1/2*((cos(2*?b*?x+?c)+2*?b*sin(2*?b*?x+?c))*~ e^?x)/(?a^2+4*?b^2)+1/2*cos(?c)*e^?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*sin(?b*?x)*sin(?b*?x+?c)*~ d*?x)):(((e^(?a*?x)*cos(?c))/(2*?a)-(e^(?a*?x)*~ (?a*cos(2*?b*?x+?c)+2*?b*sin(2*?b*?x+?c)))/(2*~ (?a^2+4*?b^2)))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*sin(?b*?x)*sin(?b*?x+?c)*~ d*?x)):((-1/2*((-cos(2*?b*?x+?c)+2*?b*sin(2*?b*~ ?x+?c))*e^(-?x))/(4*?b^2+1)-1/2*cos(?c)*e^(-?x))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*sin(?b*?x)*sin(?b*?x+?c)*~ d*?x)):(((e^(-?a*?x)*cos(?c))/(-2*?a)-(e^(-?a*~ ?x)*((-?a)*cos(2*?b*?x+?c)+2*?b*sin(2*?b*?x+?c)))/~ (2*(?a^2+4*?b^2)))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*(sin(-?x+?c)*sin(-?x))*d*?x)):(~ (-1/10*(cos(-2*?x+?c)-2*sin(-2*?x+?c))*e^?x+1/~ 2*cos(?c)*e^?x)+(Integral(0)))~p0 3 ~Hs(Integral(e^(?a*?x)*(sin(-?x+?c)*sin(-?x))*~ d*?x)):((1/2*(cos(?c)*e^(?a*?x))/?a-1/2*((?a*cos(~ -2*?x+?c)-2*sin(-2*?x+?c))*e^(?a*?x))/(?a^2+4))+~ (Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*(sin(-?x+?c)*sin(-?x))*d*~ ?x)):((-1/10*(-cos(-2*?x+?c)-2*sin(-2*?x+?c))*~ e^(-?x)-1/2*cos(?c)*e^(-?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*(sin(-?x+?c)*sin(-?x))*~ d*?x)):((-1/2*(cos(?c)*e^(-?a*?x))/?a-1/2*((-?a*~ cos(-2*?x+?c)-2*?b*sin(-2*?x+?c))*e^(-?a*?x))/~ (?a^2+4))+(Integral(0)))~p0 3 ~Hs(Integral(e^?x*sin(-?b*?x)*sin(-?b*?x+?c)*d*~ ?x)):((-1/2*((cos(-2*?b*?x+?c)-2*?b*sin(-2*?b*~ ?x+?c))*e^?x)/(4*?b^2+1)+1/2*cos(?c)*e^?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(e^(?a*?x)*sin(-?b*?x)*sin(-?b*?x+~ ?c)*d*?x)):(((e^(?a*?x)*cos(?c))/(2*?a)-(e^(?a*~ ?x)*(?a*cos(2*(-?b*?x)+?c)+2*(-?b)*sin(2*(-?b*~ ?x)+?c)))/(2*(?a^2+4*?b^2)))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?x)*sin(-?b*?x)*sin(-?b*?x+?c)*~ d*?x)):((-1/2*((-cos(-2*?b*?x+?c)-2*?b*sin(-2*~ ?b*?x+?c))*e^(-?x))/(4*?b^2+1)-1/2*cos(?c)*e^(-~ ?x))+(Integral(0)))~p0 3 ~Hs(Integral(e^(-?a*?x)*sin(-?b*?x)*sin(-?b*?x+~ ?c)*d*?x)):(((e^(-?a*?x)*cos(?c))/(2*(-?a))-(e^~ (-?a*?x)*((-?a)*cos(2*(-?b*?x)+?c)+2*(-?b)*sin(~ 2*(-?b*?x)+?c)))/(2*(?a^2+4*?b^2)))+(Integral(~ 0)))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b!L" Helvetica~: ;bP5&c55*Hyperbolic| | Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(Integral(?x*sinh(?x)*d*?x)):((?x*cosh(?x)-~ sinh(?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sinh(?c*?x)*d*?x)):((-(sinh(?c*~ ?x))/?c^2+(?x*cosh(?c*?x))/?c)+(Integral(0)))~p0 3 ~Hs(Integral(?x*sinh(-?x)*d*?x)):((-?x*cosh(-?x)-~ sinh(-?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sinh(-?c*?x)*d*?x)):((-(sinh(-~ ?c*?x))/?c^2-(?x*cosh(-?c*?x))/?c)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)*sinh(?c*?x)*d*?x)):((1/~ ?c*(?a+?b*?x)*cosh(?c*?x)-?b/?c^2*sinh(?c*?x))+~ (Integral(0)))~p0 3 ~Hs(Integral(sinh(?x)*sinh(?x)*d*?x)):((1/4*sinh(~ 2*?x)-1/2*?x)+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?a*?x)*sinh(?a*?x)*d*?x)):((~ 1/4*(sinh(2*?a*?x))/?a-1/2*?x)+(Integral(0)))~p0 3 ~Hs(Integral(sinh(-?x)*sinh(-?x)*d*?x)):((-1/4*~ sinh(-2*?x)-1/2*?x)+(Integral(0)))~p0 3 ~Hs(Integral(sinh(-?a*?x)*sinh(-?a*?x)*d*?x)):(~ (-1/4*(sinh(-2*?a*?x))/?a-1/2*?x)+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?x+?b)*sinh(?x)*d*?x)):((-?x/~ 2*cosh(?b)+1/4*sinh(2*?x+?b))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?a*?x+?b)*sinh(?a*?x)*d*?x)):(~ (-?x/2*cosh(?b)+1/(4*?a)*sinh(2*?a*?x+?b))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sinh(-?a*?x+?b)*sinh(-?a*?x)*d*?x)):(~ (-?x/2*cosh(?b)+1/(-4*?a)*sinh(-2*?a*?x+?b))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sinh(-?a*?x+?b)*sinh(-?a*?x)*d*?x)):(~ (-?x/2*cosh(?b)+1/(-4*?a)*sinh(-2*?a*?x+?b))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sinh(?x+?b)*sinh(?x+?c)*d*?x)):((~ -?x/2*cosh(?b-?c)+1/4*sinh(2*?x+?b+?c))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sinh(?a*?x+?b)*sinh(?a*?x+?c)*d*?x)):(~ (-?x/2*cosh(?b-?c)+1/(4*?a)*sinh(2*?a*?x+?b+?c))+~ (Integral(0)))~p0 3 ~Hs(Integral(sinh(-?x+?b)*sinh(-?x+?c)*d*?x)):(~ (-1/4*sinh(-2*?x+?b+?c)-1/2*cosh(?b-?c)*?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(sinh(-?a*?x+?b)*sinh(-?a*?x+?c)*d*~ ?x)):((-?x/2*cosh(?b-?c)+(-1/(4*?a))*sinh(-2*?a*~ ?x+?b+?c))+(Integral(0)))~p0 3 ~Hs(Integral(?x*(sinh(?x))^2*d*?x)):((1/4*?x*sinh(~ 2*?x)-1/8*cosh(2*?x)-?x^2/4)+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*(sinh(?x))^2*d*?x)):((1/4*(?x^~ 2+1/2)*sinh(2*?x)-1/4*?x*cosh(2*?x)-1/6*?x^3)+~ (Integral(0)))~p0 3 ~Hs(Integral(?x*(sinh(?x))^3*d*?x)):((3/4*sinh(~ ?x)-1/36*sinh(3*?x)-3/4*?x*cosh(?x)+1/12*?x*cosh(~ 3*?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*(sinh(?x))^3*d*?x)):((-(3/4*~ ?x^2+3/2)*cosh(?x)+(1/12*?x^2+1/54)*cosh(3*?x)+~ 3/2*?x*sinh(?x)-1/18*?x*sinh(3*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x*cosh(?x)*d*?x)):((?x*sinh(?x)-~ cosh(?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x*cosh(?c*?x)*d*?x)):((1/?c*?x*sinh(~ ?c*?x)-1/?c^2*cosh(?c*?x))+(Integral(0)))~p0 3 ~Hs(Integral((?a+?x)*cosh(?x)*d*?x)):(((?a+?x)*~ sinh(?x)-cosh(?x))+(Integral(0)))~p0 3 ~Hs(Integral((?a+?x)*cosh(?c*?x)*d*?x)):((1/?c*~ (?a+?x)*sinh(?c*?x)-1/?c^2*cosh(?c*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a+?b*?x)*cosh(?c*?x)*d*?x)):((1/~ ?c*(?a+?x*?b)*sinh(?c*?x)-?b/?c^2*cosh(?c*?x))+~ (Integral(0)))~p0 3 ~Hs(Integral(?x*cosh(-?x)*d*?x)):((cosh(-?x)-?x*~ sinh(-?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x*cosh(-?c*?x)*d*?x)):(((-1/?c)*~ ?x*sinh(-?c*?x)-(-1/?c^2)*cosh(-?c*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x^2*cosh(?x)*d*?x)):(((?x^2+2)*sinh(~ ?x)-2*?x*cosh(?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*cosh(?c*?x)*d*?x)):((-2*(?x*~ cosh(?c*?x))/?c^2+((?x^2+2*1/?c^2)*sinh(?c*?x))/~ ?c)+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*cosh(-?x)*d*?x)):((-2*?x*cosh(~ -?x)-(?x^2+2)*sinh(-?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*cosh(-?c*?x)*d*?x)):((-2*(?x*~ cosh(-?c*?x))/?c^2-((?x^2+2*1/?c^2)*sinh(-?c*?x))/~ ?c)+(Integral(0)))~p0 3 ~Hs(Integral((?x+?a)^2*cosh(?x)*d*?x)):((-2*(?x+~ ?a)*cosh(?x)+((?x+?a)^2+2)*sinh(?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral((?x+?a)^2*cosh(?c*?x)*d*?x)):((1/~ ?c*((?a+?x)^2+2*1/?c^2)*sinh(?c*?x)-(2*(?x+?a)*~ cosh(?c*?x))/?c^2)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)^2*cosh(?c*?x)*d*?x)):(~ (1/?c*((?a+?b*?x)^2+2*?b^2/?c^2)*sinh(?c*?x)-(~ 2*?b*(?a+?b*?x)*cosh(?c*?x))/?c^2)+(Integral(0)))~p0 3 ~Hs(Integral((?a-?b*?x)^2*cosh(?c*?x)*d*?x)):(~ (2*(?b*(-?b*?x+?a)*cosh(?c*?x))/?c^2+(((-?b*?x+~ ?a)^2+2*?b^2/?c^2)*sinh(?c*?x))/?c)+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x*(cosh(?x))^2*d*?x)):((1/4*?x*sinh(~ 2*?x)-1/8*cosh(2*?x)+1/4*?x^2)+(Integral(0)))~p0 3 ~Hs(Integral(?x*(cosh(?x))^3*d*?x)):((-3/4*cosh(~ ?x)-1/36*cosh(3*?x)+3/4*?x*sinh(?x)+1/12*?x*sinh(~ 3*?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*(cosh(?x))^2*d*?x)):(((?x^2/~ 4+1/8)*sinh(2*?x)-1/4*cosh(2*?x)*?x+?x^3/6)+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x^2*(cosh(?x))^3*d*?x)):(((3/4*?x^~ 2+3/2)*sinh(?x)+(?x^2/12+1/54)*sinh(3*?x)-3/2*~ ?x*cosh(?x)-1/18*?x*cosh(3*?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x^5*cosh(?x)*d*?x)):(((?x^5+20*?x^~ 3+120*?x)*sinh(?x)-(5*?x^4+60*?x^2+120)*cosh(?x))+~ (Integral(0)))~p0 3 ~Hs(Integral(sinh(?x)*cosh(?x)*d*?x)):(1/4*cosh(~ 2*?x)+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?a*?x)*cosh(?x)*d*?x)):(((cosh(~ (?a+1)*?x))/(2*(?a+1))+(cosh((?a-1)*?x))/(2*(?a-~ 1)))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?x)*cosh(?b*?x)*d*?x)):(((cosh(~ (?b+1)*?x))/(2*(?b+1))+(cosh((-?b+1)*?x))/(2*(~ -?b+1)))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?a*?x)*cosh(?b*?x)*d*?x)):((~ (cosh((?a+?b)*?x))/(2*(?a+?b))+(cosh((?a-?b)*?x))/~ (2*(?a-?b)))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(-?x)*cosh(-?x)*d*?x)):((-1/4)*~ cosh(-2*?x)+(Integral(0)))~p0 3 ~Hs(Integral(sinh(-?a*?x)*cosh(?x)*d*?x)):(((cosh(~ (-?a+1)*?x))/(2*(-?a+1))+(cosh((-?a-1)*?x))/(2*~ (-?a-1)))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?x)*cosh(-?b*?x)*d*?x)):(((cosh(~ (-?b+1)*?x))/(2*(-?b+1))+(cosh((?b+1)*?x))/(2*~ (?b+1)))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(-?a*?x)*cosh(-?b*?x)*d*?x)):(~ ((cosh((-?a-?b)*?x))/(2*(-?a-?b))+(cosh((-?a+?b)*~ ?x))/(2*(-?a+?b)))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?x+?b)*cosh(?c*?x+?d)*d*?x)):(~ (1/(2*(?c+1))*cosh((?c+1)*?x+?b+?d)+1/(2*(-?c+~ 1))*cosh((-?c+1)*?x+?b-?d))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?a*?x+?b)*cosh(?x+?d)*d*?x)):(~ (1/(2*(?a+1))*cosh((?a+1)*?x+?b+?d)+1/(2*(?a-1))*~ cosh((?a-1)*?x+?b-?d))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?a*?x+?b)*cosh(?a*?x+?d)*d*?x)):(~ (?x/2*sinh(?b-?d)+1/(4*?a)*cosh(2*?a*?x+?b+?d))+~ (Integral(0)))~p0 3 ~Hs(Integral(sinh(-?a*?x+?b)*cosh(-?a*?x+?d)*d*~ ?x)):((?x/2*sinh(?b-?d)+(-1/(4*?a))*cosh(-2*?a*~ ?x+?b+?d))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(?a*?x+?b)*cosh(?c*?x+?d)*d*?x)):(~ (1/(2*(?c+?a))*cosh((?a+?c)*?x+?b+?d)+1/(2*(?a-~ ?c))*cosh((?a-?c)*?x+?b-?d))+(Integral(0)))~p0 3 ~Hs(Integral(sinh(-?a*?x+?b)*cosh(-?c*?x+?d)*d*~ ?x)):((1/(2*(-?c-?a))*cosh((-?a-?c)*?x+?b+?d)+~ 1/(2*(-?a+?c))*cosh((-?a+?c)*?x+?b-?d))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sinh(?x)*(cosh(?x))^2*d*?x)):(1/3*~ (cosh(?x))^3+(Integral(0)))~p0 3 ~Hs(Integral((cosh(?x))^2*sinh(4*?x)*d*?x)):(1/~ 3*(cosh(?x))^3*cosh(3*?x)+(Integral(0)))~p0 3 ~Hs(Integral((cosh(?x))^2*(sinh(?x))^2*d*?x)):(~ (-1/8*?x+1/32*sinh(4*?x))+(Integral(0)))~p0 3 ~Hs(Integral((sinh(?x))^3*(cosh(?x))^3*d*?x)):(~ (1/48*(cosh(2*?x))^3-1/16*cosh(2*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral((sinh(?x))^?n*cosh(?x)*d*?x)):(1/~ (?n+1)*(sinh(?x))^(?n+1)+(Integral(0)))~p0 3 ~Hs(Integral(1/(?b*sinh(?x)+?a)*d*?x)):(2/sqrt(~ ?a^2+?b^2)*arctanh((?a*tanh(?x/2)-?b)/sqrt(?a^~ 2+?b^2))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-?b*sinh(?x)+?a)*d*?x)):(2/sqrt(~ ?a^2+?b^2)*arctanh((?a*tanh(?x/2)+?b)/sqrt(?a^~ 2+?b^2))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-(sinh(?x))^2+1)*d*?x)):(Conditional(~ 1/sqrt(2)*arccoth(sqrt(2)*tanh(?x))+(Integral(~ 0)),(abs(?x)>0.88139999999999996);1/sqrt(2)*arctanh(~ sqrt(2)*tanh(?x))+(Integral(0)),(abs(?x)<0.88139999999999996)))~p0 3 ~Hs(Integral(1/((sinh(?x))^2+1)*d*?x)):(tanh(?x)+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(cosh(?x)-1)*d*?x)):(-coth(?x/2)+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(cosh(?x)+1)*d*?x)):(tanh(?x/2)+~ (Integral(0)))~p0 3 ~Hs(Integral(1/((cosh(?x))^2+1)*d*?x)):(sqrt(1/~ 2)*arccoth(sqrt(2)*coth(?x))+(Integral(0)))~p0 3 ~Hs(Integral(1/(cos(?a)+cosh(?x))*d*?x)):(2*csc(~ ?a)*arctan(tanh(?x/2)*tan(?a/2))+(Integral(0)))~p0 3 ~Hs(Integral(1/(cosh(?a)+cosh(?x))*d*?x)):(arccsch(~ ?a)*(-ln(cosh(1/2*(-?a+?x)))+ln(cosh(1/2*(?a+?x))))+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(cosh(?x)+sinh(?x))*d*?x)):(-e^~ (-?x)+(Integral(0)))~p0 3 ~Hs(Integral(1/(cosh(?x)+?b*sinh(?x))*d*?x)):(~ 1/sqrt(?b^2-1)*ln(abs(tanh(?x/2+1/2*arctanh(1/~ ?b))))+(Integral(0)))~p0 3 ~Hs(Integral(1/(?a*cosh(?x)+sinh(?x))*d*?x)):(~ 1/sqrt(?a^2-1)*arctan(sinh(?x+arctanh(1/?a)))+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(?a*cosh(?x)+?b*sinh(?x))*d*?x)):(~ Conditional(1/sqrt(?b^2-?a^2)*ln(abs(tanh(?x/2+~ 1/2*arctanh(?a/?b))))+(Integral(0)),(?a?b)))~p0 3 ~Hs(Integral(1/(cosh(?x)-sinh(?x))*d*?x)):(e^?x+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(-cosh(?x)+sinh(?x))*d*?x)):(-e^~ ?x+(Integral(0)))~p0 3 ~Hs(Integral(1/(cosh(?x)-?b*sinh(?x))*d*?x)):(~ (arctan(sinh(?x-arctanh(?b))))/sqrt(-?b^2+1)+(Integral(~ 0)))~p0 3 ~Hs(Integral(1/(?a*cosh(?x)-sinh(?x))*d*?x)):(~ 1/sqrt(?a^2-1)*arctan(sinh(?x-arctanh(1/?a)))+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(?a*cosh(?x)-?b*sinh(?x))*d*?x)):(~ 1/sqrt(?a^2-?b^2)*arctan(sinh(?x-arctanh(?b/?a)))+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(-cosh(?x)+?b*sinh(?x))*d*?x)):(~ 1/sqrt(?b^2-1)*ln(abs(tanh(?x/2+1/2*arctanh(-1/~ ?b))))+(Integral(0)))~p0 3 ~Hs(Integral(1/(-?a*cosh(?x)+sinh(?x))*d*?x)):(~ 1/sqrt(1-?a^2)*ln(abs(tanh(?x/2+1/2*arctanh(-?a))))+~ (Integral(0)))~p0 3 ~Hs(Integral(1/(-?a*cosh(?x)+?b*sinh(?x))*d*?x)):(~ 1/sqrt(?b^2-?a^2)*ln(abs(tanh(?x/2+1/2*arctanh(~ ?a/(-?b)))))+(Integral(0)))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b"/" Helvetica~: ;bP5&c55*Inverse| | Hyperbolic Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(Integral((arcsinh(?x))^2*d*?x)):(?x*(arcsinh(~ ?x))^2-2*sqrt(?x^2+1)*arcsinh(?x)+2*?x+(Integral(~ 0)))~p0 3 ~Hs(Integral((arccosh(?x))^2*d*?x)):(?x*(arccosh(~ ?x))^2-2*sqrt(?x^2-1)*arccosh(?x)+2*?x+(Integral(~ 0)))~p0 3 ~Hs(Integral((arccosh(?x/?a))^2*d*?x)):(?x*(arccosh(~ ?x/?a))^2-2*sqrt(?x^2-?a^2)*arccosh(?x/?a)+2*?x+~ (Integral(0)))~p0 3 ~Hs(Integral(?x*arcsinh(?x)*d*?x)):(((2*?x^2+1)/~ 4*arcsinh(?x)-?x/4*(?x^2+1)^(1/2))+(Integral(0)))~p0 3 ~Hs(Integral(?x*arcsinh(?x/?a)*d*?x)):(((2*?x^~ 2+?a^2)/4*arcsinh(?x/?a)-?x/4*(?x^2+?a^2)^(1/2))+~ (Integral(0)))~p0 3 ~Hs(Integral(?x*arccosh(?x)*d*?x)):(((2*?x^2-1)/~ 4*arccosh(?x)-?x/4*(?x^2-1)^(1/2))+(Integral(0)))~p0 3 ~Hs(Integral(?x*arccosh(?x/?a)*d*?x)):(((2*?x^~ 2-?a^2)/4*arccosh(?x/?a)-?x/4*(?x^2-?a^2)^(1/2))+~ (Integral(0)))~p0 3 ~Hs(Integral(?x*arctanh(?x)*d*?x)):((?x^2-1)/2*~ arctanh(?x)+?x/2+(Integral(0)))~p0 3 ~Hs(Integral(?x*arctanh(?x/?a)*d*?x)):((?x^2-?a^~ 2)/2*arctanh(?x/?a)+(?a*?x)/2+(Integral(0)))~p0 3 ~Hs(Integral(?x*arccoth(?x)*d*?x)):((?x^2-1)/2*~ arccoth(?x)+?x/2+(Integral(0)))~p0 3 ~Hs(Integral(?x*arccoth(?x/?a)*d*?x)):((?x^2-?a^~ 2)/2*arccoth(?x/?a)+(?a*?x)/2+(Integral(0)))~p0 3 ~Hs(Integral(?x*arcsech(?x)*d*?x)):(?x^2/2*arcsech(~ ?x)-1/2*sqrt(1-?x^2)+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*arccosh(?x)*d*?x)):((-1/9*(?x^~ 2+2)*sqrt(?x^2-1)+1/3*?x^3*arccosh(?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x^2*arccosh(?x/?a)*d*?x)):((?x^3/~ 3*arccosh(?x/?a)-1/9*(2*?a^2+?x^2)*(?x^2-?a^2)^~ (1/2))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*arctanh(?x)*d*?x)):(?x^3/3*arctanh(~ ?x)+1/6*ln(1-?x^2)+?x^2/6+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*arctanh(?x/?a)*d*?x)):(?x^3/~ 3*arctanh(?x/?a)+?a^3/6*ln(?a^2-?x^2)+(?a*?x^2)/~ 6+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*arccoth(?x)*d*?x)):(?x^3/3*arccoth(~ ?x)+1/6*ln(?x^2-1)+?x^2/6+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*arccoth(?x/?a)*d*?x)):(?x^3/~ 3*arccoth(?x/?a)+?a^3/6*ln(?a^2-?x^2)+(?a*?x^2)/~ 6+(Integral(0)))~p0 3 ~Hs(Integral((arccosh(?x))/?x^2*d*?x)):(-1/?x*~ arccosh(?x)-arcsin(1/?x)+(Integral(0)))~p0 3 ~Hs(Integral((arccosh(?x/?a))/?x^2*d*?x)):(-1/~ ?x*arccosh(?x/?a)-1/?a*arcsin(?a/?x)+(Integral(~ 0)))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b"B" Helvetica~: ;bP5&c55*Inverse| | Trigonometric Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(Integral(arcsin(?a/?x)*d*?x)):((?x*arcsin(~ ?a/?x)+?a*arccosh(abs(?x/?a)))+(Integral(0)))~p0 3 ~Hs(Integral((arcsin(?x))^2*d*?x)):((?x*(arcsin(~ ?x))^2-2*?x+(2*sqrt(1-?x^2))*arcsin(?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(arccos(?a/?x)*d*?x)):((?x*arccos(~ ?a/?x)-?a*arccosh(abs(?x/?a)))+(Integral(0)))~p0 3 ~Hs(Integral((arccos(?x))^2*d*?x)):((?x*(arccos(~ ?x))^2-2*?x-(2*sqrt(1-?x^2))*arccos(?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x*arcsin(?x)*d*?x)):(1/4*((2*?x^~ 2-1)*arcsin(?x)+?x*sqrt(1-?x^2))+(Integral(0)))~p0 3 ~Hs(Integral(?x*arcsin(?a*?x)*d*?x)):(1/(4*?a^~ 2)*((2*?a^2*?x^2-1)*arcsin(?a*?x)+?a*?x*sqrt(1-~ ?a^2*?x^2))+(Integral(0)))~p0 3 ~Hs(Integral(?x*arccos(?x)*d*?x)):(1/4*((2*?x^~ 2-1)*arccos(?x)-?x*sqrt(1-?x^2))+(Integral(0)))~p0 3 ~Hs(Integral(?x*arccos(?a*?x)*d*?x)):(1/(4*?a^~ 2)*((2*?a^2*?x^2-1)*arccos(?a*?x)-?a*?x*sqrt(1-~ ?a^2*?x^2))+(Integral(0)))~p0 3 ~Hs(Integral(?x*arctan(?x)*d*?x)):((1/2*(1+?x^~ 2)*arctan(?x)-?x/2)+(Integral(0)))~p0 3 ~Hs(Integral(?x*arctan(?a*?x)*d*?x)):((1/2*(1/~ ?a^2+?x^2)*arctan(?a*?x)-?x/(2*?a))+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x*arctan(?x/?a)*d*?x)):((1/2*(?a^~ 2+?x^2)*arctan(?x/?a)-1/2*?x*?a)+(Integral(0)))~p0 3 ~Hs(Integral(?x*arccot(?x)*d*?x)):((1/2*(1+?x^~ 2)*arccot(?x)+?x/2)+(Integral(0)))~p0 3 ~Hs(Integral(?x*arccot(?a*?x)*d*?x)):((1/2*(1/~ ?a^2+?x^2)*arccot(?a*?x)+?x/(2*?a))+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x*arccot(?x/?a)*d*?x)):((1/2*(?a^~ 2+?x^2)*arccot(?x/?a)+(?x*?a)/2)+(Integral(0)))~p0 3 ~Hs(Integral(?x*arcsec(?x)*d*?x)):((?x^2/2*arcsec(~ ?x)-1/2*sqrt(?x^2-1))+(Integral(0)))~p0 3 ~Hs(Integral(?x*arccsc(?x)*d*?x)):((?x^2/2*arccsc(~ ?x)+1/2*sqrt(?x^2-1))+(Integral(0)))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b"/" Helvetica~: ;bP5&c55*Irrational| | Algebraic Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(Integral(?x*sqrt(?x+?b)*d*?x)):((2*(3*?x-2*~ ?b)*(?x+?b)^(3/2))/15+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?x+?b)*?x*d*?x)):((2*(3*?x-2*~ ?b)*(?x+?b)^(3/2))/15+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?a*?x+?b)*d*?x)):((2*(3*?a*~ ?x-2*?b)*(?a*?x+?b)^(3/2))/(15*?a^2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(?a*?x+?b)*?x*d*?x)):((2*(3*?a*~ ?x-2*?b)*(?a*?x+?b)^(3/2))/(15*?a^2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x*sqrt(-?x+?b)*d*?x)):((2*(-3*?x-~ 2*?b)*(-?x+?b)^(3/2))/15+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?x+?b)*?x*d*?x)):((2*(-3*?x-~ 2*?b)*(-?x+?b)^(3/2))/15+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(-?a*?x+?b)*d*?x)):((2*(-3*~ ?a*?x-2*?b)*(-?a*?x+?b)^(3/2))/(15*?a^2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(-?a*?x+?b)*?x*d*?x)):((2*(-3*~ ?a*?x-2*?b)*(-?a*?x+?b)^(3/2))/(15*?a^2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x^2*sqrt(?x+?b)*d*?x)):(2*((?x+?b)^~ 2/7-(2*?b*(?x+?b))/5+?b^2/3)*(?x+?b)^(3/2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(?x+?b)*?x^2*d*?x)):(2*((?x+?b)^~ 2/7-(2*?b*(?x+?b))/5+?b^2/3)*(?x+?b)^(3/2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x^2*sqrt(?a*?x+?b)*d*?x)):(2/?a^~ 3*((?a*?x+?b)^2/7-(2*?b*(?a*?x+?b))/5+?b^2/3)*~ (?a*?x+?b)^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*sqrt(-?x+?b)*d*?x)):((-2)*((~ -?x+?b)^2/7-(2*?b*(-?x+?b))/5+?b^2/3)*(-?x+?b)^~ (3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?x+?b)*?x^2*d*?x)):((-2)*((~ -?x+?b)^2/7-(2*?b*(-?x+?b))/5+?b^2/3)*(-?x+?b)^~ (3/2)+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*sqrt(-?a*?x+?b)*d*?x)):(2/(-~ ?a^3)*((-?a*?x+?b)^2/7-(2*?b*(-?a*?x+?b))/5+?b^~ 2/3)*(-?a*?x+?b)^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?a*?x+?b)*?x^2*d*?x)):(2/(-~ ?a^3)*((-?a*?x+?b)^2/7-(2*?b*(-?a*?x+?b))/5+?b^~ 2/3)*(-?a*?x+?b)^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?x^2+?a)*d*?x)):(1/2*(?x*sqrt(~ ?x^2+?a)+?a*ln(abs(?x+sqrt(?x^2+?a))))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(-?x^2+?a)*d*?x)):(1/2*(?x*sqrt(~ ?a-?x^2)+?a*arcsin(?x/sqrt(abs(?a))))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(?a*?x^2+?c)*d*?x)):((?x/2*sqrt(~ ?a*?x^2+?c)+(?c*ln(abs(?x*sqrt(?a)+sqrt(?a*?x^~ 2+?c))))/(2*sqrt(?a)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?a*?x^2+?c)*d*?x)):((?x/2*sqrt(~ ?c-?a*?x^2)+(?c*arcsin(?x*sqrt(?a/?c)))/(2*sqrt(~ ?a)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?x^2+?x)*d*?x)):((1/4*sqrt(?x^~ 2+?x)*(2*?x+1)-1/8*ln(abs(2*sqrt(?x^2+?x)+2*?x+~ 1)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?a*?x^2+?x)*d*?x)):((-1/8*(ln(~ abs(2*sqrt(?a*(?a*?x^2+?x))+2*?a*?x+1)))/?a^(3/~ 2)+1/4*((2*?a*?x+1)*sqrt(?a*?x^2+?x))/?a)+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(?x^2+?b*?x)*d*?x)):((1/4*sqrt(~ ?x^2+?b*?x)*(2*?x+?b)-1/8*?b^2*ln(abs(2*sqrt(?x^~ 2+?b*?x)+2*?x+?b)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?a*?x^2+?b*?x)*d*?x)):((1/4*~ ((2*?a*?x+?b)*sqrt(?a*?x^2+?b*?x))/?a-1/8*(?b^~ 2*ln(abs(2*sqrt(?a*(?a*?x^2+?b*?x))+2*?a*?x+?b)))/~ ?a^(3/2))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?x^2-?x)*d*?x)):((1/4*sqrt(?x^~ 2-?x)*(2*?x-1)-1/8*ln(abs(2*sqrt(?x^2-?x)-2*?x-~ 1)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?x^2-?b*?x)*d*?x)):((1/4*sqrt(~ ?x^2-?b*?x)*(2*?x-?b)-1/8*?b^2*ln(abs(2*sqrt(?x^~ 2-?b*?x)-2*?x-?b)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?a*?x^2-?x)*d*?x)):((-1/8*(ln(~ abs(2*sqrt(?a*(?a*?x^2-?x))-2*?a*?x-1)))/?a^(3/~ 2)+1/4*((2*?a*?x-1)*sqrt(?a*?x^2-?x))/?a)+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(?a*?x^2-?b*?x)*d*?x)):((1/4*~ ((2*?a*?x-?b)*sqrt(?a*?x^2-?b*?x))/?a-1/8*(?b^~ 2*ln(abs(2*sqrt(?a*(?a*?x^2-?b*?x))-2*?a*?x-?b)))/~ ?a^(3/2))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?x^2+?x+?c)*d*?x)):((1/4*sqrt(~ ?x^2+?x+?c)*(2*?x+1)+1/8*(4*?c-1)*ln(abs(2*sqrt(~ ?x^2+?x+?c)+2*?x+1)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?a*?x^2+?b*?x+?c)*d*?x)):(((~ 2*?a*?x+?b)/(4*?a)*sqrt(?a*?x^2+?b*?x+?c)+(4*?c*~ ?a-?b^2)/(8*?a^(3/2))*ln(abs(2*sqrt(?a*(?a*?x^~ 2+?b*?x+?c))+2*?a*?x+?b)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?x^2-?x+?c)*d*?x)):((1/4*sqrt(~ ?x^2-?x+?c)*(2*?x-1)+1/8*(4*?c-1)*ln(abs(2*sqrt(~ ?x^2-?x+?c)+2*?x-1)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?a*?x^2-?b*?x+?c)*d*?x)):(((~ 2*?a*?x-?b)/(4*?a)*sqrt(?a*?x^2-?b*?x+?c)+(4*?c*~ ?a-?b^2)/(8*?a^(3/2))*ln(abs(2*sqrt(?a*(?a*?x^~ 2-?b*?x+?c))+2*?a*?x-?b)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?x^2+?x)*d*?x)):(1/2*((?x-1/~ 2)*sqrt(?x-?x^2)+1/4*arcsin(2*(?x-1/2)))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt(-?x^2+?a*?x)*d*?x)):(1/2*((?x-~ ?a/2)*sqrt(?a*?x-?x^2)+(?a/2)^2*arcsin(2*(?x-1/~ 2*?a)/?a))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?x^2-?x)*d*?x)):(1/2*((?x+1/~ 2)*sqrt(-?x-?x^2)+1/4*arcsin(2*(?x+1/2)/(-1)))+~ (Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?x^2-?a*?x)*d*?x)):(1/2*((?x-~ (-?a)/2)*sqrt(-?a*?x-?x^2)+(?a/2)^2*arcsin(2*(~ ?x+1/2*?a)/(-?a)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?a+?b*?x)*sqrt(?f+?g*?x)*d*?x)):(~ (((?a*?g-?b*?f)+2*?b*(?f+?g*?x))/(4*?b*?g)*sqrt(~ (?a+?b*?x)*(?f+?g*?x))-(?a*?g-?b*?f)^2/(8*?b*?g)*~ 2/sqrt(?b*?g)*ln(sqrt(?b*?g*(?a+?b*?x))+?b*sqrt(~ ?f+?g*?x)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt((?x+?a)*(?x+?f))*d*?x)):((-1/~ 4*(?a-?f)^2*ln(sqrt(?x+?a)+sqrt(?x+?f))+1/4*(2*~ (?x+?f)+?a-?f)*sqrt((?x+?a)*(?x+?f)))+(Integral(~ 0)))~p0 3 ~Hs(Integral(sqrt((?x+?a)*(?g*?x+?f))*d*?x)):(~ (-1/4*((-?f+?a*?g)^2*ln(sqrt(?g*?x+?f)+sqrt(?g*~ (?x+?a))))/?g^(3/2)+1/4*(2*(?g*?x+?f)-?f+?a*?g)/~ ?g*sqrt((?x+?a)*(?g*?x+?f)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt((?a+?b*?x)*(?f+?g*?x))*d*?x)):(~ (((?a*?g-?b*?f)+2*?b*(?f+?g*?x))/(4*?b*?g)*sqrt(~ (?a+?b*?x)*(?f+?g*?x))-(?a*?g-?b*?f)^2/(8*?b*?g)*~ 2/sqrt(?b*?g)*ln(sqrt(?b*?g*(?a+?b*?x))+?b*sqrt(~ ?f+?g*?x)))+(Integral(0)))~p0 3 ~Hs(Integral(sqrt((?a-?b*?x)*(?f-?g*?x))*d*?x)):(~ (-1/4*(?b*?f-?a*?g)^2/(?b*?g)*1/sqrt(?b*?g)*ln(~ -?b*sqrt(-?g*?x+?f)+sqrt(?b*?g*(-?b*?x+?a)))+1/~ 4*(-2*?b*(-?g*?x+?f)+?b*?f-?a*?g)/(?b*?g)*sqrt(~ (-?b*?x+?a)*(-?g*?x+?f)))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?x^2+?a)*d*?x)):(1/3*sqrt(~ (?x^2+?a)^3)+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?a-?x^2)*d*?x)):(-1/3*sqrt(~ (?a-?x^2)^3)+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?x^2+?x)*d*?x)):((1/3*(?x^~ 2+?x)^(3/2)-1/8*sqrt(?x^2+?x)*(2*?x+1)+1/16*ln(~ abs(2*sqrt(?x^2+?x)+2*?x+1)))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?x^2+?x+?c)*d*?x)):((1/3*~ (?x^2+?x+?c)^(3/2)-1/8*sqrt(?x^2+?x+?c)*(2*?x+~ 1)-1/16*(4*?c-1)*ln(abs(2*sqrt(?x^2+?x+?c)+2*?x+~ 1)))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?x^2+?b*?x+?c)*d*?x)):((1/~ 3*(?x^2+?b*?x+?c)^(3/2)-1/8*?b*sqrt(?x^2+?b*?x+~ ?c)*(2*?x+?b)-1/16*(-?b^2+4*?c)*?b*ln(abs(2*sqrt(~ ?x^2+?b*?x+?c)+2*?x+?b)))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?a*?x^2+?b*?x+?c)*d*?x)):(~ ((?a*?x^2+?b*?x+?c)^(3/2)/(3*?a)-?b*(2*?a*?x+?b)/~ (8*?a^2)*(?c+?a*?x^2+?b*?x)^(1/2)-?b*(4*?a*?c-~ ?b^2)/(16*?a^(5/2))*ln(abs(2*(?a*(?a*?x^2+?b*?x+~ ?c))^(1/2)+2*?a*?x+?b)))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?x^2-?x)*d*?x)):((1/3*(?x^~ 2-?x)^(3/2)+1/8*sqrt(?x^2-?x)*(2*?x-1)-1/16*ln(~ abs(2*sqrt(?x^2-?x)+2*?x-1)))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?x^2-?x+?c)*d*?x)):((1/3*~ (?x^2-?x+?c)^(3/2)+1/8*sqrt(?x^2-?x+?c)*(2*?x-~ 1)+1/16*(4*?c-1)*ln(abs(2*sqrt(?x^2-?x+?c)+2*?x-~ 1)))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?x^2-?b*?x+?c)*d*?x)):((1/~ 3*(?x^2-?b*?x+?c)^(3/2)+1/8*?b*sqrt(?x^2-?b*?x+~ ?c)*(2*?x-?b)+1/16*(-?b^2+4*?c)*?b*ln(abs(2*sqrt(~ ?x^2-?b*?x+?c)+2*?x-?b)))+(Integral(0)))~p0 3 ~Hs(Integral(?x*sqrt(?a*?x^2-?b*?x+?c)*d*?x)):(~ ((?a*?x^2-?b*?x+?c)^(3/2)/(3*?a)-(-?b)*(2*?a*?x-~ ?b)/(8*?a^2)*(?c+?a*?x^2+(-?b)*?x)^(1/2)-(-?b)*~ (4*?a*?c-?b^2)/(16*?a^(5/2))*ln(abs(2*(?a*(?a*~ ?x^2-?b*?x+?c))^(1/2)+2*?a*?x-?b)))+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x^2*sqrt(?a-?x^2)*d*?x)):((-?x/4*~ sqrt((?a-?x^2)^3)+?a*?x/8*sqrt(?a-?x^2)+?a^2/8*~ arcsin(?x/sqrt(abs(?a))))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*sqrt(?x^2+?a)*d*?x)):((?x/4*~ sqrt((?x^2+?a)^3)-?a*?x/8*sqrt(?x^2+?a)-?a^2/8*~ ln(abs(?x+sqrt(?x^2+?a))))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*sqrt(?a*?x^2+?b*?x+?c)*d*?x)):(~ ((?x-5*?b/(6*?a))*(?a*?x^2+?b*?x+?c)^(3/2)/(4*~ ?a)+(5*?b^2-4*?a*?c)/(16*?a^2)*((2*?a*?x+?b)/(~ 4*?a)*(?a*?x^2+?b*?x+?c)^(1/2)+(4*?a*?c-?b^2)/~ (8*?a)*1/sqrt(?a)*ln(abs(2*(?a*(?a*?x^2+?b*?x+~ ?c))^(1/2)+2*?a*?x+?b))))+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*sqrt(?x^2+?a)*d*?x)):((1/5*?x^~ 2-(2*?a)/15)*sqrt((?x^2+?a)^3)+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*sqrt(?a-?x^2)*d*?x)):((-1/5*~ ?x^2-(2*?a)/15)*sqrt((?a-?x^2)^3)+(Integral(0)))~p0 3 ~Hs(Integral(?x^4*sqrt(?x^2+?a)*d*?x)):((1/16*~ ?a^3*ln(abs(sqrt(?x^2+?a)+?x))+1/6*(?x^2+?a)^(~ 3/2)*?x^3-1/8*?a*(?x^2+?a)^(3/2)*?x+1/16*?a^2*~ ?x*sqrt(?x^2+?a))+(Integral(0)))~p0 3 ~Hs(Integral(?x^4*sqrt(?a+?c*?x^2)*d*?x)):(((1/~ 6*?x^3*sqrt(?a+?c*?x^2)^3)/?c-(?a*?x*sqrt(?a+?c*~ ?x^2)^3)/(8*?c^2)+?a^2*?x*sqrt(?a+?c*?x^2)/(16*~ ?c^2)+?a^3/(16*?c^2)*(1/sqrt(?c)*ln(abs(?x*sqrt(~ ?c)+sqrt(?a+?c*?x^2)))))+(Integral(0)))~p0 3 ~Hs(Integral(?x^5*sqrt(?x^2+?a)*d*?x)):((((?x^~ 2+?a)^(7/2)/7-(2*?a*(?x^2+?a)^(5/2))/5)+(?a^2*~ (?x^2+?a)^(3/2))/3)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?x^2+?b)/?x^4*d*?x)):(-(?x^2+~ ?b)^(3/2)/(3*?b*?x^3)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?x^2+?b)/?x^4*d*?x)):(-(-?x^~ 2+?b)^(3/2)/(3*?b*?x)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(?a*?x^2+?b)/?x^4*d*?x)):(-(?a*~ ?x^2+?b)^(3/2)/(3*?b*?x^3)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(-?a*?x^2+?b)/?x^4*d*?x)):(-(~ -?a*?x^2+?b)^(3/2)/(3*?b*?x^3)+(Integral(0)))~p0 3 ~Hs(Integral(1/sqrt(?a+?b*?x)*d*?x)):((2*sqrt(~ ?a+?b*?x))/?b+(Integral(0)))~p0 3 ~Hs(Integral(1/(sqrt(?x+?b)*?x^2)*d*?x)):(Conditional(~ -(sqrt(?x+?b)/(?b*?x)+1/(2*?b*sqrt(?b))*ln(abs(~ (sqrt(?x+?b)-sqrt(?b))/(sqrt(?x+?b)+sqrt(?b)))))+~ (Integral(0)),(?b>0);-sqrt(?x+?b)/(?b*?x)-1/2*~ (arctan(sqrt((?x+?b)/abs(?b))))/(sqrt(abs(?b))*~ ?b)+(Integral(0)),(?b<0)))~p0 3 ~Hs(Integral(1/(sqrt(?a*?x+?b)*?x^2)*d*?x)):(Conditional(~ -(sqrt(?a*?x+?b)/(?b*?x)+?a/(2*?b*sqrt(?b))*ln(~ (sqrt(?a*?x+?b)-sqrt(?b))/(sqrt(?a*?x+?b)+sqrt(~ ?b))))+(Integral(0)),(?b>0);-sqrt(?a*?x+?b)/(?b*~ ?x)-?a*(arctan(sqrt((?a*?x+?b)/abs(?b))))/(sqrt(~ abs(?b))*?b)+(Integral(0)),(?b<0)))~p0 3 ~Hs(Integral(1/sqrt(?x^2+?a)*d*?x)):(ln(abs(?x+~ sqrt(?x^2+?a)))+(Integral(0)))~p0 3 ~Hs(Integral(1/sqrt(-?x^2+?a)*d*?x)):(arctan(?x/~ sqrt(?a-?x^2))+(Integral(0)))~p0 3 ~Hs(Integral(1/sqrt(?a+?b*?x^2)*d*?x)):(1/sqrt(~ ?b)*ln(abs(sqrt(?b)*?x+sqrt(?a+?b*?x^2)))+(Integral(~ 0)))~p0 3 ~Hs(Integral(1/sqrt(?a-?b*?x^2)*d*?x)):(1/sqrt(~ ?b)*arcsin(sqrt(?b/?a)*?x)+(Integral(0)))~p0 3 ~Hs(Integral(1/sqrt(-?x^2+?a*?x)*d*?x)):(arccos(~ (?a/2-?x)/abs(?a/2))+(Integral(0)))~p0 3 ~Hs(Integral(?x/sqrt(?x^2+?b)*d*?x)):(sqrt(?x^~ 2+?b)+(Integral(0)))~p0 3 ~Hs(Integral(?x/sqrt(?a*?x^2+?b)*d*?x)):(sqrt(~ ?a*?x^2+?b)/?a+(Integral(0)))~p0 3 ~Hs(Integral(?x^2/sqrt(?x^2+?a)*d*?x)):(?x/2*sqrt(~ ?x^2+?a)-?a/2*ln(abs(?x+sqrt(?x^2+?a)))+(Integral(~ 0)))~p0 3 ~Hs(Integral(1/(sqrt(-?x^2+?a)*?x)*d*?x)):(1/sqrt(~ ?a)*ln(abs(?x)/(sqrt(-?x^2+?a)+sqrt(?a)))+(Integral(~ 0)))~p0 3 ~Hs(Integral(1/(sqrt(?x^2+?a)*?x)*d*?x)):(Conditional(~ -ln((sqrt(?a)+sqrt(?x^2+?a))/abs(?x))*1/sqrt(?a)+~ (Integral(0)),(?a>0);1/sqrt(abs(?a))*arccos(sqrt(~ abs(?a))/?x)+(Integral(0)),(?a<0)))~p0 3 ~Hs(Integral(1/(sqrt(?x^2+?b)*?x^2)*d*?x)):(-sqrt(~ ?x^2+?b)/(?b*?x)+(Integral(0)))~p0 3 ~Hs(Integral(1/(sqrt(-?x^2+?b)*?x^2)*d*?x)):(-~ sqrt(-?x^2+?b)/(?b*?x)+(Integral(0)))~p0 3 ~Hs(Integral(1/(sqrt(?a*?x^2+?b)*?x^2)*d*?x)):(~ -sqrt(?a*?x^2+?b)/(?b*?x)+(Integral(0)))~p0 3 ~Hs(Integral(1/(sqrt(-?a*?x^2+?b)*?x^2)*d*?x)):(~ -sqrt(-?a*?x^2+?b)/(?b*?x)+(Integral(0)))~p0 3 ~Hs(Integral((?a+?b*?x)^(3/2)*?x*d*?x)):((2*(?a+~ ?b*?x)^(5/2)*(5*?b*?x-2*?a))/(35*?b^2)+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a+?b*?x)^(3/2)*?x^2*d*?x)):(2/?b^~ 3*((?a+?b*?x)^2/9-2/7*?a*(?a+?b*?x)+?a^2/5)*(?a+~ ?b*?x)^(5/2)+(Integral(0)))~p0 3 ~Hs(Integral((?x^2+?a)^(3/2)*d*?x)):(1/4*(?x*sqrt(~ (?x^2+?a)^3)+3/2*?a*?x*sqrt(?x^2+?a)+(3/2*?a^2)*~ ln(abs(?x+sqrt(?x^2+?a))))+(Integral(0)))~p0 3 ~Hs(Integral((-?x^2+?a)^(3/2)*d*?x)):(1/4*(?x*~ sqrt((-?x^2+?a)^3)+3/2*?a*?x*sqrt(-?x^2+?a)+(3/~ 2*?a^2)*arcsin(?x/sqrt(abs(?a))))+(Integral(0)))~p0 3 ~Hs(Integral((?a+?c*?x^2)^(3/2)*d*?x)):((1/4*?x*~ (?a+?c*?x^2)^(3/2)+3/8*?a*?x*(?a+?c*?x^2)^(1/2)+~ 3/8*?a^2*(ln(abs(?x*sqrt(?c)+sqrt(?a+?c*?x^2))))/~ sqrt(?c))+(Integral(0)))~p0 3 ~Hs(Integral((?a+?x^2)^(3/2)*?x*d*?x)):(1/5*sqrt(~ ?x^2+?a)^5+(Integral(0)))~p0 3 ~Hs(Integral((-?x^2+?a)^(3/2)*?x*d*?x)):(-1/5*~ sqrt(?a-?x^2)^5+(Integral(0)))~p0 3 ~Hs(Integral((?x^2+?a)^(3/2)*?x^2*d*?x)):((?x/~ 6*sqrt(?x^2+?a)^5-?a*?x/24*sqrt((?x^2+?a)^3)-?a^~ 2*?x/16*sqrt(?x^2+?a)-?a^3/16*ln(abs(?x+sqrt(?x^~ 2+?a))))+(Integral(0)))~p0 3 ~Hs(Integral((-?x^2+?a)^(3/2)*?x^2*d*?x)):((-1/~ 6*?x*sqrt((?a-?x^2)^5)+?a*?x/24*sqrt((?a-?x^2)^~ 3)+?a^2*?x/16*sqrt(?a-?x^2)+?a^3/16*arcsin(?x/~ sqrt(abs(?a))))+(Integral(0)))~p0 3 ~Hs(Integral((?a+?x^2)^(3/2)*?x^3*d*?x)):((1/7*~ sqrt(?x^2+?a)^7-?a/5*sqrt(?x^2+?a)^5)+(Integral(~ 0)))~p0 3 ~Hs(Integral((-?x^2+?a)^(3/2)*?x^3*d*?x)):((1/~ 7*sqrt(?a-?x^2)^7-?a/5*sqrt((?a-?x^2)^5))+(Integral(~ 0)))~p0 3 ~Hs(Integral((?a+?x^2)^(3/2)*?x^4*d*?x)):(((1/~ 8*?x^3)*(?a+?x^2)^(5/2)-1/16*?a*?x*(?a+?x^2)^(~ 5/2)+1/64*?a^2*?x*(?a+?x^2)^(3/2)+3/128*?a^3*?x*~ (?a+?x^2)^(1/2)+3/256*?a^4*ln(abs((sqrt(?x^2+?a)+~ ?x)/(sqrt(?x^2+?a)-?x))))+(Integral(0)))~p0 3 ~Hs(Integral((?a+?c*?x^2)^(5/2)*d*?x)):(((1/6*~ ?x*(?a+?x^2*?c)^(5/2)+5/24*?a*?x*(?a+?x^2*?c)^~ (3/2))+5/16*?a^2*?x*(?a+?x^2*?c)^(1/2)+5/16*?a^~ 3/sqrt(?c)*ln(?x*sqrt(?c)+(?a+?x^2*?c)^(1/2)))+~ (Integral(0)))~p0 3 ~Hs(Integral(sqrt(sqrt(?x)+?c)*d*?x)):(4/15*(3*~ sqrt(?x)-2*?c)*(sqrt(?x)+?c)^(3/2)+(Integral(0)))~p0 3 ~Hs(Integral(sqrt(sqrt(?a*?x)+?c)*d*?x)):(4/(15*~ ?a)*(3*sqrt(?a*?x)-2*?c)*(sqrt(?a*?x)+?c)^(3/2)+~ (Integral(0)))~p0 3 ~Hs(Integral(sqrt(sqrt(?a*?x+?b)+?c)*d*?x)):(4/~ (15*?a)*(3*sqrt(?a*?x+?b)-2*?c)*(sqrt(?a*?x+?b)+~ ?c)^(3/2)+(Integral(0)))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b!L" Helvetica~: ;bP5&c55*Logarithmic| | Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(Integral(?x*ln(?x)*d*?x)):((?x^2/2*ln(?x)-~ ?x^2/4)+(Integral(0)))~p0 3 ~Hs(Integral(1/(?x*(ln(?x))^?n)*d*?x)):(1/(1-?n)*~ (ln(?x))^(1-?n)+(Integral(0)))~p0 3 ~Hs(Integral(1/(?x*ln(?x))*d*?x)):(ln(ln(?x))+~ (Integral(0)))~p0 3 ~Hs(Integral(-?x*ln(?x)*d*?x)):(-(?x^2/2*ln(?x)-~ ?x^2/4)+(Integral(0)))~p0 3 ~Hs(Integral(?x*ln(?x^2)*d*?x)):((1/2*?x^2*ln(~ ?x^2)-1/2*?x^2)+(Integral(0)))~p0 3 ~Hs(Integral(?x*ln(?x^2+?a)*d*?x)):((1/2*(?a+?x^~ 2)*ln(?a+?x^2)-1/2*?x^2)+(Integral(0)))~p0 3 ~Hs(Integral(ln(?x^2+?a)*d*?x)):(Conditional((~ ?x*ln(?a+?x^2)+2*sqrt(?a)*arctan(?x/?a)-2*?x)+~ (Integral(0)),(?a>0);(?x*ln(?a+?x^2)+2*sqrt(abs(~ ?a))*arctanh(?x/sqrt(abs(?a)))-2*?x)+(Integral(~ 0)),(?a<0)))~p0 3 ~Hs(Integral(ln(?x^3+?a)*d*?x)):((?x*ln(?x^3+?a)-~ ?a^(1/3)/2*ln((?a^(2/3)+?x^2-?a^(1/3)*?x)/(?x+~ ?a^(1/3))^2)+?a^(1/3)*sqrt(3)*arctan((2*?x-?a^~ (1/3))/(sqrt(3)*?a^(1/3)))-3*?x)+(Integral(0)))~p0 3 ~Hs(Integral(ln(?x^4-?a)*d*?x)):((?x*ln(?x^4-?a)+~ abs(?a)^(1/4)*ln(abs((?x+abs(?a)^(1/4))/(?x-abs(~ ?a)^(1/4))))+2*abs(?a)^(1/4)*arctan(?x/abs(?a)^~ (1/4))-4*?x)+(Integral(0)))~p0 3 ~Hs(Integral((ln(?x))^2*d*?x)):((?x*(ln(?x))^2-~ 2*?x*ln(?x)+2*?x)+(Integral(0)))~p0 3 ~Hs(Integral((ln(?x))^3*d*?x)):((?x*(ln(?x))^3-~ 3*?x*(ln(?x))^2+6*?x*ln(?x)-6*?x)+(Integral(0)))~p0 3 ~Hs(Integral((ln(?b*?x))^3*d*?x)):((?x*(ln(?b*~ ?x))^3-3*?x*(ln(?b*?x))^2+6*?x*ln(?b*?x))-6*?x+~ (Integral(0)))~p0 3 ~Hs(Integral((ln(-?x))^3*d*?x)):((?x*(ln(-?x))^~ 3-3*?x*(ln(-?x))^2+6*?x*ln(-?x))-6*?x+(Integral(~ 0)))~p0 3 ~Hs(Integral((ln(-?b*?x))^3*d*?x)):((?x*(ln(-?b*~ ?x))^3-3*?x*(ln(-?b*?x))^2+6*?x*ln(-?b*?x))-6*~ ?x+(Integral(0)))~p0 3 ~Hs(Integral((ln(?x))^3*d*?x)):((?x*(ln(?x))^3-~ 3*?x*(ln(?x))^2+6*?x*ln(?x))-6*?x+(Integral(0)))~p0 3 ~Hs(Integral((ln(?b*?x))^3*d*?x)):((?x*(ln(?b*~ ?x))^3-3*?x*(ln(?b*?x))^2+6*?x*ln(?b*?x))-6*?x+~ (Integral(0)))~p0 3 ~Hs(Integral((ln(-?x))^3*d*?x)):((?x*(ln(-?x))^~ 3-3*?x*(ln(-?x))^2+6*?x*ln(-?x))-6*?x+(Integral(~ 0)))~p0 3 ~Hs(Integral((ln(-?b*?x))^3*d*?x)):((?x*(ln(-?b*~ ?x))^3-3*?x*(ln(-?b*?x))^2+6*?x*ln(-?b*?x))-6*~ ?x+(Integral(0)))~p0 3 ~Hs(Integral((ln(?x+?a))^3*d*?x)):(((?x+?a)*(ln(~ ?x+?a))^3-3*(?x+?a)*(ln(?x+?a))^2+6*(?x+?a)*ln(~ ?x+?a))-6*?x+(Integral(0)))~p0 3 ~Hs(Integral((ln(?b*?x+?a))^3*d*?x)):(((?a+?b*~ ?x)/?b*(ln(?a+?b*?x))^3-(3*(?a+?b*?x)*(ln(?a+?b*~ ?x))^2)/?b+(6*(?a+?b*?x)*ln(?a+?b*?x))/?b)-6*?x+~ (Integral(0)))~p0 3 ~Hs(Integral((ln(-?x+?a))^3*d*?x)):((-(-?x+?a)*~ (ln(-?x+?a))^3+3*(-?x+?a)*(ln(-?x+?a))^2-6*(-?x+~ ?a)*ln(-?x+?a))-6*?x+(Integral(0)))~p0 3 ~Hs(Integral((ln(-?b*?x+?a))^3*d*?x)):(((?a-?b*~ ?x)/(-?b)*(ln(?a-?b*?x))^3-(3*(?a-?b*?x)*(ln(?a-~ ?b*?x))^2)/(-?b)+(6*(?a-?b*?x)*ln(?a-?b*?x))/(-~ ?b))-6*?x+(Integral(0)))~p0 3 ~Hs(Integral((?x+?a)*ln(?x)*d*?x)):(((1/2*(?x+~ ?a)^2-1/2*?a^2)*ln(?x)-1/4*?x^2-?a*?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral((?b*?x+?a)*ln(?x)*d*?x)):((((?a+?b*~ ?x)^2/(2*?b)-?a^2/(2*?b))*ln(?x)-?a*?x-1/4*?b*~ ?x^2)+(Integral(0)))~p0 3 ~Hs(Integral((-?x+?a)*ln(?x)*d*?x)):(((-1/2*(-~ ?x+?a)^2+1/2*?a^2)*ln(?x)+1/4*?x^2-?a*?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral((-?b*?x+?a)*ln(?x)*d*?x)):((((?a-~ ?b*?x)^2/(-2*?b)-?a^2/(-2*?b))*ln(?x)-?a*?x+1/~ 4*?b*?x^2)+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*ln(?x)*d*?x)):((1/4*?x^4*ln(~ ?x)-1/16*?x^4)+(Integral(0)))~p0 3 ~Hs(Integral((-?x)^3*ln(?x)*d*?x)):((-1/4*(-?x)^~ 4*ln(?x)+1/16*?x^4)+(Integral(0)))~p0 3 ~Hs(Integral((?x+?a)^3*ln(?x)*d*?x)):((1/4*((?x+~ ?a)^4-?a^4)*ln(?x)-1/16*?x^4-1/3*?a*?x^3-3/4*?a^~ 2*?x^2-?a^3*?x)+(Integral(0)))~p0 3 ~Hs(Integral((?b*?x+?a)^3*ln(?x)*d*?x)):((1/(4*~ ?b)*((?a+?b*?x)^4-?a^4)*ln(?x)-(?a^3*?x+3/4*?a^~ 2*?b*?x^2+1/3*?a*?b^2*?x^3+1/16*?x^4*?b^3))+(Integral(~ 0)))~p0 3 ~Hs(Integral((-?x+?a)^3*ln(?x)*d*?x)):((-1/4*(~ (-?x+?a)^4-?a^4)*ln(?x)+1/16*?x^4-1/3*?a*?x^3+~ 3/4*?a^2*?x^2-?a^3*?x)+(Integral(0)))~p0 3 ~Hs(Integral((-?b*?x+?a)^3*ln(?x)*d*?x)):((-1/~ 4*(((-?b*?x+?a)^4-?a^4)*ln(abs(?x)))/?b+1/16*?b^~ 3*?x^4-1/3*?a*?b^2*?x^3+3/4*?a^2*?b*?x^2-?a^3*~ ?x)+(Integral(0)))~p0 3 ~Hs(Integral(?x*ln(?b*?x)*d*?x)):((1/2*?x^2*ln(~ ?b*?x)-1/4*?x^2)+(Integral(0)))~p0 3 ~Hs(Integral(?x*ln(-?x)*d*?x)):((1/2*?x^2*ln(abs(~ ?x))-1/4*?x^2)+(Integral(0)))~p0 3 ~Hs(Integral(?x*ln(-?b*?x)*d*?x)):((1/2*?x^2*ln(~ abs(?b*?x))-1/4*?x^2)+(Integral(0)))~p0 3 ~Hs(Integral(?x*ln(?x+?a)*d*?x)):((1/2*(?x^2-?a^~ 2)*ln(?x+?a)-1/4*?x^2+1/2*?a*?x)+(Integral(0)))~p0 3 ~Hs(Integral(?x*ln(?b*?x+?a)*d*?x)):(((?a*?x)/~ (2*?b)-?x^2/4+((?b^2*?x^2-?a^2)*ln(?a+?b*?x))/~ (2*?b^2))+(Integral(0)))~p0 3 ~Hs(Integral(?x*ln(-?x+?a)*d*?x)):((1/2*(?x^2-~ ?a^2)*ln(abs(-?x+?a))-1/4*?x^2-1/2*?a*?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x*ln(-?b*?x+?a)*d*?x)):((-1/2*(?a*~ ?x)/?b-?x^2/4+((?b^2*?x^2-?a^2)*ln(abs(-?b*?x+~ ?a)))/(2*?b^2))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(?x^2-1)*d*?x)):((1/3*?x^3*~ ln(?x^2-1)-2/3*?x-2/9*?x^3-1/3*ln((?x-1)/(?x+1)))+~ (Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(?x)*d*?x)):((1/3*?x^2*ln(~ abs(?x))-1/9*?x^2)*?x+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(?b*?x)*d*?x)):(((1/3*?b^2*~ ?x^2*ln(abs(?b*?x))-1/9*?b^2*?x^2)*?x)/?b^2+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x^2*ln(-?x)*d*?x)):((1/3*?x^2*ln(~ abs(?x))-1/9*?x^2)*?x+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(-?b*?x)*d*?x)):(-(?b*(1/3*~ ?b^2*?x^2*ln(abs(?b*?x))-1/9*?b^2*?x^2)*?x)/(-~ ?b)^3+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(?x+?a)*d*?x)):((1/18*(-2*~ ?x^2+5*?a*?x-11*?a^2)+1/3*(?x^2-?a*?x+?a^2)*ln(~ abs(?x+?a)))*(?x+?a)+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(?b*?x+?a)*d*?x)):(((1/3*(~ ?b^2*?x^2-?a*?b*?x+?a^2))*ln(abs(?a+?b*?x))+1/~ 18*(-2*?b^2*?x^2+5*?a*?b*?x-11*?a^2))*(?a+?b*?x)/~ ?b^3+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(-?x+?a)*d*?x)):((1/18*(-2*~ ?x^2-5*?a*?x+7*?a^2)+1/3*(?x^2+?a*?x+?a^2)*ln(~ abs(-?x+?a))-?a^2)*(?x-?a)+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(-?b*?x+?a)*d*?x)):((1/18*~ (-2*?b^2*?x^2-5*?a*?b*?x+7*?a^2)+(1/3*(?b^2*?x^~ 2+?a*?b*?x+?a^2))*ln(abs(-?b*?x+?a))-?a^2)*(?a-~ ?b*?x)/(-?b)^3+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*ln(?x)*d*?x)):((1/4*?x^4*ln(~ abs(?x))-1/16*?x^4)+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*ln(?b*?x)*d*?x)):((1/4*?x^4*~ ln(abs(?b*?x))-1/16*?x^4)+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*ln(-?x)*d*?x)):((1/4*?x^4*ln(~ abs(?x))-1/16*?x^4)+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*ln(-?b*?x)*d*?x)):((1/4*?x^4*~ ln(abs(?b*?x))-1/16*?x^4)+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*ln(?x+?a)*d*?x)):((-1/4*(1/4*~ ?x^4-1/3*?a*?x^3+1/2*?a^2*?x^2-?a^3*?x)+1/4*(?x^~ 4-?a^4)*ln(abs(?x+?a)))+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*ln(?b*?x+?a)*d*?x)):((1/4*(?x^~ 4-?a^4/?b^4)*ln(abs(?a+?b*?x))-1/4*(?x^4/4-(?a*~ ?x^3)/(3*?b)+(?a^2*?x^2)/(2*?b^2)-(?a^3*?x)/?b^~ 3))+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*ln(-?x+?a)*d*?x)):((-1/4*(1/~ 4*?x^4+1/3*?a*?x^3+1/2*?a^2*?x^2+?a^3*?x)+1/4*~ (?x^4-?a^4)*ln(abs(-?x+?a)))+(Integral(0)))~p0 3 ~Hs(Integral(?x^3*ln(-?b*?x+?a)*d*?x)):((-1/4*~ ((?a^3*?x)/?b^3+1/3*(?a*?x^3)/?b+1/2*(?a^2*?x^~ 2)/?b^2+1/4*?x^4)+1/4*(?x^4-?a^4/?b^4)*ln(abs(~ -?b*?x+?a)))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(?x^2)*d*?x)):(1/3*(?x^3*ln(~ ?x^2)-2/3*?x^3)+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*ln(?x^2+?a)*d*?x)):(Conditional(~ 1/3*(?x^3*ln(?x^2+?a)-2/3*?x^3+2*?x*?a-2*?a^(3/~ 2)*arctan(?x/sqrt(?a)))+(Integral(0)),(?a>0);1/~ 3*(?x^3*ln(?x^2+?a)-2/3*?x^3+2*?x*?a+abs(?a)^(~ 3/2)*ln(abs((?x+sqrt(abs(?a)))/(?x-sqrt(abs(?a))))))+~ (Integral(0)),(?a<0)))~p0 3 ~Hs(Integral(?x^5*ln(?x^2)*d*?x)):(1/6*(?x^6*ln(~ ?x^2)-?x^6/3)+(Integral(0)))~p0 3 ~Hs(Integral(?x^5*ln(?x^2+?a)*d*?x)):(1/6*((?x^~ 6+?a^3)*ln(?x^2+?a)-?x^6/3+(?x^4*?a)/2-?x^2*?a^~ 2)+(Integral(0)))~p0 3 ~Hs(Integral(?x^?n*ln(?x)*d*?x)):(?x^(?n+1)/(?n+~ 1)*(ln(?x)-1/(?n+1))+(Integral(0)))~p0 3 ~Hs(Integral(?x^?n*ln(?a*?x)*d*?x)):((ln(?a*?x)*~ ?x^(?n+1)/(?n+1)-?x^(?n+1)/(?n+1)^2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x^?n*ln(-?x)*d*?x)):((ln(abs(-?x))*~ ?x^(?n+1)/(?n+1)-?x^(?n+1)/(?n+1)^2)+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x^?n*ln(-?a*?x)*d*?x)):((ln(abs(~ -?a*?x))*?x^(?n+1)/(?n+1)-?x^(?n+1)/(?n+1)^2)+~ (Integral(0)))~p0 3 ~Hs(Integral((ln(?x))/?x*d*?x)):(1/2*(ln(?x))^~ 2+(Integral(0)))~p0 3 ~Hs(Integral((ln(?x))/?x^?n*d*?x)):(-((ln(?x)+~ 1/(?n-1))/((?n-1)*?x^(?n-1))+(Integral(0))))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b!U" Helvetica~: ;bP5&c55*Trigonometric| | Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(Integral(sin(?x/?a)*d*?x)):(-?a*cos(?x/?a)+~ (Integral(0)))~p0 3 ~Hs(Integral(sin(-?x/?a)*d*?x)):(?a*cos(-?x/?a)+~ (Integral(0)))~p0 3 ~Hs(Integral((sin(?x))^2*d*?x)):((-1/2*cos(?x)*~ sin(?x)+1/2*?x)+(Integral(0)))~p0 3 ~Hs(Integral((sin(?a*?x))^2*d*?x)):((1/2*?x-1/~ (4*?a)*sin(2*?a*?x))+(Integral(0)))~p0 3 ~Hs(Integral((sin(-?a*?x))^2*d*?x)):((1/4*(sin(~ -2*?a*?x))/?a+1/2*?x)+(Integral(0)))~p0 3 ~Hs(Integral((sin(?x))^3*d*?x)):(-1/3*cos(?x)*~ ((sin(?x))^2+2)+(Integral(0)))~p0 3 ~Hs(Integral((sin(?x))^4*d*?x)):((-3/8*cos(?x)*~ sin(?x)+3/8*?x-1/4*(sin(?x))^3*cos(?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral((sin(?x))^5*d*?x)):((-5/8*cos(?x)+~ 5/48*cos(3*?x)-1/80*cos(5*?x))+(Integral(0)))~p0 3 ~Hs(Integral((sin(?x))^6*d*?x)):((-1/6*cos(?x)*~ (sin(?x))^5-5/24*cos(?x)*(sin(?x))^3-5/16*cos(~ ?x)*sin(?x))+(Integral(0))+5/16*?x)~p0 3 ~Hs(Integral((sin(?x))^7*d*?x)):((-35/64*cos(?x)+~ 7/64*cos(3*?x)-7/320*cos(5*?x)+1/448*cos(7*?x))+~ (Integral(0)))~p0 3 ~Hs(Integral((sin(?x))^?n*d*?x)):((-(sin(?x))^~ (?n-1)*cos(?x))/?n+(?n-1)/?n*(Integral((sin(?x))^~ (?n-2)*d*?x)))~p0 3 ~Hs(Integral((sin(?a*?x))^?n*d*?x)):((-(sin(?a*~ ?x))^(?n-1)*cos(?a*?x))/(?n*?a)+(?n-1)/?n*(Integral(~ (sin(?a*?x))^(?n-2)*d*?x)))~p0 3 ~Hs(Integral((cos(?x))^2*d*?x)):((1/2*?x+1/4*sin(~ 2*?x))+(Integral(0)))~p0 3 ~Hs(Integral((cos(?x))^3*d*?x)):(((3*sin(?x))/~ 4+1/12*sin(3*?x))+(Integral(0)))~p0 3 ~Hs(Integral((cos(?x))^4*d*?x)):((3/8*?x+1/4*sin(~ 2*?x)+1/32*sin(4*?x))+(Integral(0)))~p0 3 ~Hs(Integral((cos(?x))^5*d*?x)):((5/8*sin(?x)+~ 5/48*sin(3*?x)+1/80*sin(5*?x))+(Integral(0)))~p0 3 ~Hs(Integral((cos(?x))^6*d*?x)):((5/16*?x+15/64*~ sin(2*?x)+3/64*sin(4*?x)+1/192*sin(6*?x))+(Integral(~ 0)))~p0 3 ~Hs(Integral((cos(?x))^?n*d*?x)):((sin(?x)*(cos(~ ?x))^(?n-1))/?n+(?n-1)/?n*(Integral((cos(?x))^~ (?n-2)*d*?x)))~p0 3 ~Hs(Integral((cos(?a*?x))^?n*d*?x)):((sin(?a*?x)*~ (cos(?a*?x))^(?n-1))/(?n*?a)+(?n-1)/?n*(Integral(~ (cos(?a*?x))^(?n-2)*d*?x)))~p0 3 ~Hs(Integral((tan(?x))^2*d*?x)):((tan(?x)-?x)+~ (Integral(0)))~p0 3 ~Hs(Integral((tan(?x))^4*d*?x)):((1/3*(tan(?x))^~ 3-tan(?x)+?x)+(Integral(0)))~p0 3 ~Hs(Integral((tan(?x))^?n*d*?x)):((tan(?x))^(?n-~ 1)/(?n-1)-(Integral((tan(?x))^(?n-2)*d*?x)))~p0 3 ~Hs(Integral((tan(?a*?x))^?n*d*?x)):((tan(?a*?x))^~ (?n-1)/(?a*(?n-1))-(Integral((tan(?a*?x))^(?n-~ 2)*d*?x)))~p0 3 ~Hs(Integral(cot(?x)*d*?x)):(ln(abs(sin(?x)))+~ (Integral(0)))~p0 3 ~Hs(Integral((cot(?x))^2*d*?x)):((-cot(?x)-?x)+~ (Integral(0)))~p0 3 ~Hs(Integral((cot(?x))^4*d*x)):((-1/3*(cot(?x))^~ 3+cot(?x)+?x)+(Integral(0)))~p0 3 ~Hs(Integral((cot(?x))^?n*d*?x)):(-(cot(?x))^(~ ?n-1)/(?n-1)-(Integral((cot(?x))^(?n-2)*d*?x)))~p0 3 ~Hs(Integral((cot(?a*?x))^?n*d*?x)):(-(cot(?a*~ ?x))^(?n-1)/(?a*(?n-1))-(Integral((cot(?a*?x))^~ (?n-2)*d*?x)))~p0 3 ~Hs(Integral((sec(?x))^2*d*?x)):(tan(?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral((csc(?x))^2*d*?x)):(-cot(?x)+(Integral(~ 0)))~p0 3 ~Hs(Integral(?x*sin(?x)*d*?x)):((sin(?x)-?x*cos(~ ?x))+(Integral(0)))~p0 3 ~Hs(Integral(?x^2*sin(?x)*d*?x)):((2*?x*sin(?x)-~ (?x^2-2)*cos(?x))+(Integral(0)))~p0 3 ~Hs(Integral(1/(cos(?x)+?a)*d*?x)):(Conditional(~ 1/sqrt(?a^2-1)*arctan((sqrt(?a^2-1)*sin(?x))/(~ 1+?a*cos(?x)))+(Integral(0)),(abs(?a)>1);1/sqrt(~ 1-?a^2)*ln(abs((sqrt(1-?a^2)*tan(?x/2)+?a+1)/(~ sqrt(1-?a^2)*tan(?x/2)-?a-1)))+(Integral(0)),(~ abs(?a)<1);tan(?x/2)+(Integral(0)),(?a=1);cot(~ ?x/2)+(Integral(0)),(?a=-1)))~p0 3 ~Hs(Integral(1/(?b*cos(?x)+?a)*d*?x)):(Conditional(~ 1/sqrt(?a^2-?b^2)*arctan((sqrt(?a^2-?b^2)*sin(~ ?x))/(?b+?a*cos(?x)))+(Integral(0)),(abs(?a)>abs(~ ?b));1/sqrt(?b^2-?a^2)*ln(abs((sqrt(?b^2-?a^2)*~ tan(?x/2)+?a+?b)/(sqrt(?b^2-?a^2)*tan(?x/2)-?a-~ ?b)))+(Integral(0)),(abs(?a)1);1/sqrt(~ 1-?a^2)*ln(abs((sqrt(1-?a^2)*tan(?x/2)+?a-1)/(~ sqrt(1-?a^2)*tan(?x/2)-?a+1)))+(Integral(0)),(~ abs(?a)<1);-cot(?x/2)+(Integral(0)),(?a=1);-tan(~ ?x/2)+(Integral(0)),(?a=-1)))~p0 3 ~Hs(Integral(1/(sin(?x)+?a)*d*?x)):(Conditional(~ 1/sqrt(?a^2-1)*arcsin((1+?a*sin(?x))/(?a+sin(?x)))+~ (Integral(0)),(abs(?a)>1);1/sqrt(1-?a^2)*ln((1+~ ?a*tan(?x/2)-sqrt(1-?a^2))/(1+?a*tan(?x/2)+sqrt(~ 1-?a^2)))+(Integral(0)),(abs(?a)<1);tan(?x/2-?/~ 4)+(Integral(0)),(?a=1);-tan(?x/2-?/4)+(Integral(~ 0)),(?a=-1)))~p0 3 ~Hs(Integral(1/(?b*sin(?x)+?a)*d*?x)):(Conditional(~ 1/sqrt(?a^2-?b^2)*arcsin((?b+?a*sin(?x))/(?a+?b*~ sin(?x)))+(Integral(0)),(?babs(?a));1/?a*tan(?x/2-?/4)+(Integral(0)),~ (?b=?a);1/?a*tan(?x/2+?/4)+(Integral(0)),(?b=-~ ?a)))~p0 3 ~Hs(Integral(1/(-sin(?x)+?a)*d*?x)):(Conditional(~ 1/sqrt(?a^2-1)*arcsin((?a*sin(?x)-1)/(?a-sin(?x)))+~ (Integral(0)),(abs(?a)>1);1/sqrt(1-?a^2)*ln((-~ 1+?a*tan(?x/2)-sqrt((-1)^2-?a^2))/(-1+?a*tan(?x/~ 2)+sqrt((-1)^2-?a^2)))+(Integral(0)),(abs(?a)<~ 1);tan(?x/2+?/4)+(Integral(0)),(?a=-1);tan(-?x/~ 2+?/4)+(Integral(0)),(?a=1)))~p0 3 ~Hs(Integral((tan(?x))^?n*d*?x)):((1/(?n-1)*(tan(~ ?x))^(?n-1)-(Integral((tan(?x))^(?n-2)*d*?x)))+~ (Integral(0)))~p0 3 ~Hs(Integral(sin(?x)*cos(?x)*d*?x)):(1/2*(sin(~ ?x))^2+(Integral(0)))~p0 3 ~Hs(Integral(cos(?x)*(sin(?x))^?m*d*?x)):(1/(?m+~ 1)*(sin(?x))^(?m+1)+(Integral(0)))~p0 3 ~Hs(Integral((cos(?x))^?n*sin(?x)*d*?x)):(-(cos(~ ?x))^(?n+1)/(?n+1)+(Integral(0)))~p0 3 ~Hs(Integral((sin(?x))^?m*(cos(?x))^?n*d*?x)):(~ (((sin(?x))^(?m-1)*(cos(?x))^(?n-1))/(?m+?n)*(~ (sin(?x))^2-(?n-1)/(?m+?n-2))+((?m-1)*(?n-1))/~ ((?m+?n)*(?m+?n-2))*(Integral(((sin(?x))^(?m-2)*~ (cos(?x))^(?n-2))*d*?x)))+(Integral(0)))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP5&c55*u ,M Substitution| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP5&c55*Added Trig| | Simplifies}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'42);sqrt(~ ?o^?x)*?q,(1>=0)))~p0 3 ~He(sqrt(?a)*sqrt(?b)):(sqrt(?a*?b))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b'4" *~: ;bP6&c55*General Roots| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Ht(ReduceIt_4(?a^(?x/?y))):(ReduceIt_4((?a^?x)^~ (1/?y)))~p0 3 ~Hs(ReduceIt_4(?o*?p)):(ReduceIt_4(?o)*ReduceIt_~ 4(?p))~p0 3 ~Hs(ReduceIt_4(?a^(?x/?y))):(ReduceIt_3(?a,(?a^~ ?x)^(1/?y),?x,?y,1))~p0 3 ~Ht((?a^?x)^(1/?y)):(ReduceIt_3(?a,(?a^?x)^(1/~ ?y),?x,?y,1))~p0 3 ~Ht((?o^?x)^(1/?y)*?p):(ReduceIt_3(?o,(?o^?x)^~ (1/?y),?x,?y,1)*?p)~p0 3 ~Ht(?p*(?o^?x)^(1/?y)):(ReduceIt_3(?o,(?o^?x)^~ (1/?y),?x,?y,1)*?p)~p0 3 ~Hs(ReduceIt_4(?o)):(?o)~p0 3 ~Hs(ReduceIt_3(?o,?p,?x,?y,?q)):(Conditional(ReduceIt_~ 3(?o,?o*(?o^(?x-?y))^(1/?y),?x-?y,?y,?q*?o),(?x>~ ?y-1);?q*(?o^?x)^(1/?y),(1>=0)))~p0 3 ~He(?a^?x*?b^?x):((?a*?b)^?x)~p0 3 ~Ht((?o*?p)^?x):(ReduceIt_4(?o^?x*?p^?x))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b'4" Helvetica~: ;bP6&c55*Rationalizing| | Roots}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})-# b'4" Helvetica~: ;bP6&c55*Rationalizing| | Denominators with Roots,Z Use Expand| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~He(?c/(?a+sqrt(?b))):((?c*(?a-sqrt(?b)))/(?a^~ 2-?b))~p0 3 ~He(?c/(?a-sqrt(?b))):((?c*(?a+sqrt(?b)))/(?a^~ 2-?b))~p0 3 ~He(?c/(?a+?d*sqrt(?b))):((?c*(?a-?d*sqrt(?b)))/~ (?a^2-?d^2*?b))~p0 3 ~He(?c/(?a-?d*sqrt(?b))):((?c*(?a+?d+sqrt(?b)))/~ (?a^2-?d^2*?b))~p0 3 ~He((-?c)/(?a+sqrt(?b))):((-?c*(?a-sqrt(?b)))/~ (?a^2-?b))~p0 3 ~He((-?c)/(?a-sqrt(?b))):((-?c*(?a+sqrt(?b)))/~ (?a^2-?b))~p0 3 ~He((-?c)/(?a+?d*sqrt(?b))):((-?c*(?a-?d*sqrt(~ ?b)))/(?a^2-?d^2*?b))~p0 3 ~He((-?c)/(?a-?d*sqrt(?b))):((-?c*(?a+?d*sqrt(~ ?b)))/(?a^2-?d^2*?b))~p0 3 ~He(?c/(sqrt(?b)+?a)):((?c*(?a-sqrt(?b)))/(?a^~ 2-?b))~p0 3 ~He(?c/(-sqrt(?b)+?a)):((?c*(?a+sqrt(?b)))/(?a^~ 2-?b))~p0 3 ~He(?c/(?d*sqrt(?b)+?a)):((?c*(?a-?d*sqrt(?b)))/~ (?a^2-?d^2*?b))~p0 3 ~He(?c/(-?d*sqrt(?b)+?a)):((?c*(?a+?d+sqrt(?b)))/~ (?a^2-?d^2*?b))~p0 3 ~He((-?c)/(sqrt(?b)+?a)):((-?c*(?a-sqrt(?b)))/~ (?a^2-?b))~p0 3 ~He((-?c)/(-sqrt(?b)+?a)):((-?c*(?a+sqrt(?b)))/~ (?a^2-?b))~p0 3 ~He((-?c)/(?d*sqrt(?b)+?a)):((-?c*(?a-?d*sqrt(~ ?b)))/(?a^2-?d^2*?b))~p0 3 ~He((-?c)/(-?d*sqrt(?b)+?a)):((-?c*(?a+?d*sqrt(~ ?b)))/(?a^2-?d^2*?b))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})1# b'4" Helvetica~: ;bP6&c55*Rationalizing| | Denominators with Roots SEE STEPS,Z Use Transform| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Ht(?c/(?a+sqrt(?b))):((?c*(?a-sqrt(?b)))/((?a+~ sqrt(?b))*(?a-sqrt(?b))))~p0 3 ~Ht(?c/(?a-sqrt(?b))):((?c*(?a+sqrt(?b)))/((?a-~ sqrt(?b))*(?a+sqrt(?b))))~p0 3 ~Ht(?c/(?a+?d*sqrt(?b))):((?c*(?a-?d*sqrt(?b)))/~ ((?a+?d*sqrt(?b))*(?a-?d*sqrt(?b))))~p0 3 ~Ht(?c/(?a-?d*sqrt(?b))):((?c*(?a+?d*sqrt(?b)))/~ ((?a-?d*sqrt(?b))*(?a+?d*sqrt(?b))))~p0 3 ~Ht((-?c)/(?a+sqrt(?b))):((-?c*(?a-sqrt(?b)))/~ ((?a+sqrt(?b))*(?a-sqrt(?b))))~p0 3 ~Ht((-?c)/(?a-sqrt(?b))):((-?c*(?a+sqrt(?b)))/~ ((?a-sqrt(?b))*(?a+sqrt(?b))))~p0 3 ~Ht((-?c)/(?a+?d*sqrt(?b))):((-?c*(?a-?d*sqrt(~ ?b)))/((?a+?d*sqrt(?b))*(?a-?d*sqrt(?b))))~p0 3 ~Ht((-?c)/(?a-?d*sqrt(?b))):((-?c*(?a+?d*sqrt(~ ?b)))/((?a-?d*sqrt(?b))*(?a+?d*sqrt(?b))))~p0 3 ~Ht(?c/(sqrt(?b)+?a)):((?c*(?a-sqrt(?b)))/((?a+~ sqrt(?b))*(?a-sqrt(?b))))~p0 3 ~Ht(?c/(-sqrt(?b)+?a)):((?c*(?a+sqrt(?b)))/((?a-~ sqrt(?b))*(?a+sqrt(?b))))~p0 3 ~Ht(?c/(?d*sqrt(?b)+?a)):((?c*(?a-?d*sqrt(?b)))/~ ((?a+?d*sqrt(?b))*(?a-?d*sqrt(?b))))~p0 3 ~Ht(?c/(-?d*sqrt(?b)+?a)):((?c*(?a+?d*sqrt(?b)))/~ ((?a-?d*sqrt(?b))*(?a+?d*sqrt(?b))))~p0 3 ~Ht((-?c)/(sqrt(?b)+?a)):((-?c*(?a-sqrt(?b)))/~ ((?a+sqrt(?b))*(?a-sqrt(?b))))~p0 3 ~Ht((-?c)/(-sqrt(?b)+?a)):((-?c*(?a+sqrt(?b)))/~ ((?a-sqrt(?b))*(?a+sqrt(?b))))~p0 3 ~Ht((-?c)/(?d*sqrt(?b)+?a)):((-?c*(?a-?d*sqrt(~ ?b)))/((?a+?d*sqrt(?b))*(?a-?d*sqrt(?b))))~p0 3 ~Ht((-?c)/(-?d*sqrt(?b)+?a)):((-?c*(?a+?d*sqrt(~ ?b)))/((?a-?d*sqrt(?b))*(?a+?d*sqrt(?b))))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})-# b'4" Helvetica~: ;bP6&c55*Rationalizing| | Numerators with Roots,Z Use Expand}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~He((?a+sqrt(?b))/?c):((?a^2-?b)/(?c*(?a-sqrt(~ ?b))))~p0 3 ~He((?a-sqrt(?b))/?c):((?a^2-?b)/(?c*(?a+sqrt(~ ?b))))~p0 3 ~He((?a+?d*sqrt(?b))/?c):((?a^2-?d^2*?b)/(?c*(~ ?a-?d*sqrt(?b))))~p0 3 ~He((?a-?d*sqrt(?b))/?c):((?a^2-?d^2*?b)/(?c*(~ ?a+?d*sqrt(?b))))~p0 3 ~He((?a+sqrt(?b))/(-?c)):((?a^2-?b)/(-?c*(?a-sqrt(~ ?b))))~p0 3 ~He((?a-sqrt(?b))/(-?c)):((?a^2-?b)/(-?c*(?a+sqrt(~ ?b))))~p0 3 ~He((?a+?d*sqrt(?b))/(-?c)):((?a^2-?d^2*?b)/(-~ ?c*(?a-?d*sqrt(?b))))~p0 3 ~He((?a-?d*sqrt(?b))/(-?c)):((?a^2-?d^2*?b)/(-~ ?c*(?a+?d*sqrt(?b))))~p0 3 ~He((sqrt(?b)+?a)/?c):((?a^2-?b)/(?c*(?a-sqrt(~ ?b))))~p0 3 ~He((-sqrt(?b)+?a)/?c):((?a^2-?b)/(?c*(?a+sqrt(~ ?b))))~p0 3 ~He((?d*sqrt(?b)+?a)/?c):((?a^2-?d^2*?b)/(?c*(~ ?a-?d*sqrt(?b))))~p0 3 ~He((-?d*sqrt(?b)+?a)/?c):((?a^2-?d^2*?b)/(?c*~ (?a+?d*sqrt(?b))))~p0 3 ~He((sqrt(?b)+?a)/(-?c)):((?a^2-?b)/(-?c*(?a-sqrt(~ ?b))))~p0 3 ~He((-sqrt(?b)+?a)/(-?c)):((?a^2-?b)/(-?c*(?a+~ sqrt(?b))))~p0 3 ~He((?d*sqrt(?b)+?a)/(-?c)):((?a^2-?d^2*?b)/(-~ ?c*(?a-?d*sqrt(?b))))~p0 3 ~He((-?d*sqrt(?b)+?a)/(-?c)):((?a^2-?d^2*?b)/(-~ ?c*(?a+?d*sqrt(?b))))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})1# b'4" Helvetica~: ;bP6&c55*Rationalizing| | Numerators with Roots SEE STEPS,Z Use Transform| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Ht((?a+sqrt(?b))/?c):(((?a+sqrt(?b))*(?a-sqrt(~ ?b)))/(?c*(?a-sqrt(?b))))~p0 3 ~Ht((?a-sqrt(?b))/?c):(((?a-sqrt(?b))*(?a+sqrt(~ ?b)))/(?c*(?a+sqrt(?b))))~p0 3 ~Ht((?a+?d*sqrt(?b))/?c):(((?a+?d*sqrt(?b))*(?a-~ ?d*sqrt(?b)))/(?c*(?a-?d*sqrt(?b))))~p0 3 ~Ht((?a-?d*sqrt(?b))/?c):(((?a-?d*sqrt(?b))*(?a+~ ?d*sqrt(?b)))/(?c*(?a+?d*sqrt(?b))))~p0 3 ~Ht((?a+sqrt(?b))/(-?c)):(((?a+sqrt(?b))*(?a-sqrt(~ ?b)))/(-?c*(?a-sqrt(?b))))~p0 3 ~Ht((?a-sqrt(?b))/(-?c)):(((?a-sqrt(?b))*(?a+sqrt(~ ?b)))/(-?c*(?a+sqrt(?b))))~p0 3 ~Ht((?a+?d*sqrt(?b))/(-?c)):(((?a+?d*sqrt(?b))*~ (?a-?d*sqrt(?b)))/(-?c*(?a-?d*sqrt(?b))))~p0 3 ~Ht((?a-?d*sqrt(?b))/(-?c)):(((?a-?d*sqrt(?b))*~ (?a+?d*sqrt(?b)))/(-?c*(?a+?d*sqrt(?b))))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_}),# b'4" Helvetica~: ;bP6&c55*Rationalizing| | Denominators with i,Z Use Transform}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Ht(?c/(?a+?b*i)):((?c*(?a-?b*i))/(?a^2+?b^2))~p0 3 ~Ht(?c/(?b*i+?a)):((?c*(?a-?b*i))/(?a^2+?b^2))~p0 3 ~Ht(?c/(-?b*i+?a)):((?c*(?a+?b*i))/(?a^2+?b^2))~p0 3 ~Ht(?c/(?a-?b*i)):((?c*(?a+?b*i))/(?a^2+?b^2))~p0 3 ~Ht(?c/(?a+i)):((?c*(?a-?b*i))/(?a^2+1))~p0 3 ~Ht(?c/(?a-i)):((?c*(?a+i))/(?a^2+1^2))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_}))# b'4" Helvetica~: ;bP6&c55*Integer| | Factoring `fb#@}&c55),HiFactor`f }&c55*,I Package| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b'4" Helvetica~: ;bP5&c55*The Mechanism| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f0 (iFactor)~p0 3 ~Hs(iFactor(?o)):(EvaluateAt(?o):(x=xSV))~p0 3 ~Hs(N(?a/?b)):(?a)~p0 3 ~Hs(N(-?a/?b)):(-?a)~p0 3 ~Hs(D(?a/?b)):(?b)~p0 3 ~Hs(D(-?a/?b)):(?b)~p0 3 ~Hs(xSV+?a*i):(1/(D(?a))*(EvaluateAt(D(?a)*xSV+~ N(?a)*i):(xSV=x)))~p0 3 ~Hs(xSV-?a*i):(1/(D(?a))*(EvaluateAt(D(?a)*xSV-~ N(?a)*i):(xSV=x)))~p0 3 ~Hs(xSV+?a):(1/(D(?a))*(EvaluateAt(D(?a)*xSV+N(~ ?a)):(xSV=x)))~p0 3 ~Hs((1/(D(?a))*(EvaluateAt(D(?a)*xSV+N(?a)):(xSV=~ x)))^?n):((1/(D(?a)))^?n*(EvaluateAt(D(?a)*xSV+~ N(?a)):(xSV=x))^?n)~p0 3 ~Hs((1/(D(?a))*(EvaluateAt(D(?a)*xSV+N(?a)*i):(~ xSV=x)))^?n):((1/(D(?a)))^?n*(EvaluateAt(D(?a)*~ xSV+N(?a)*i):(xSV=x))^?n)~p0 3 ~Hs((1/(D(?a))*(EvaluateAt(D(?a)*xSV-N(?a)*i):(~ xSV=x)))^?n):((1/(D(?a)))^?n*(EvaluateAt(D(?a)*~ xSV-N(?a)*i):(xSV=x))^?n)~p0 3 ~Hs(N(?f)):(?f)~p0 3 ~Hs(D(?f)):(1)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})3# b'4" Helvetica~: ;bP5&c55*Completing| | the Square,Z Transform Command on a Quadratic Polynomial| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f0 (CompleteSquare)~p0 2 ~Ht(?a*?x^2+?b*?x+?c):(CompleteSquare(?a,?b,?c,~ ?x))~p1 2 ~Ht(?a*?x^2+?b*?x-?c):(CompleteSquare(?a,?b,-?c,~ ?x))~p0 3 ~Ht(?a*?x^2-?b*?x+?c):(CompleteSquare(?a,-?b,?c,~ ?x))~p0 3 ~Ht(?a*?x^2-?b*?x-?c):(CompleteSquare(?a,-?b,-~ ?c,?x))~p0 3 ~Ht(-?a*?x^2+?b*?x+?c):(CompleteSquare(-?a,?b,~ ?c,?x))~p1 2 ~Ht(-?a*?x^2+?b*?x-?c):(CompleteSquare(-?a,?b,~ -?c,?x))~p0 3 ~Ht(-?a*?x^2-?b*?x-?c):(CompleteSquare(-?a,-?b,~ -?c,?x))~p0 3 ~Ht(-?a*?x^2-?b*?x+?c):(CompleteSquare(-?a,-?b,~ ?c,?x))~p0 3 ~Ht(?x^2+?b*?x+?c):(CompleteSquare(1,?b,?c,?x))~p1 2 ~Ht(?x^2+?b*?x-?c):(CompleteSquare(1,?b,-?c,?x))~p0 3 ~Ht(?x^2-?b*?x+?c):(CompleteSquare(1,-?b,?c,?x))~p0 3 ~Ht(-?x^2+?b*?x+?c):(CompleteSquare(-1,?b,?c,?x))~p1 2 ~Ht(-?x^2+?b*?x-?c):(CompleteSquare(-1,?b,-?c,~ ?x))~p0 3 ~Ht(-?x^2-?b*?x-?c):(CompleteSquare(-1,-?b,-?c,~ ?x))~p0 3 ~Hs(CompleteSquare(?a,?b,?c,?x)):(?a*(?x+?b/(2*~ ?a))^2+?c-?b^2/(4*?a))~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_}))# b'4" Helvetica~: ;bP5&c55*Combine| | Rational Expressions,Z Transform}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Ht(?x/?y+?r/?s):((?x*?s+?y*?r)/(?y*?s))~p0 2 ~Ht(-?x/?y+?r/?s):((-?x*?s+?y*?r)/(?y*?s))~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55)Inequality| | Solving Package}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#@})%# b'4" Helvetica~: ;bP6&c55*Inequality| | Solving Package}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f0 (Xpoint)~p0 3 ~V?v0 (GraphIneq)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})"# b'4" Helvetica~: ;bP6&c55*Strict | |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(abs(?x)abs(?y)):((?x>?y);(-?x>?y);(?x>-?y);~ (-?x>-?y))~p0 4 ~Hs(abs(?x)?y):((?x>?y);(-?x>?y))~p0 4 ~Hs(?a*?x-?b?c):(?a*?x>?c+?b)~p0 4 ~Hs(-?a*?x-?b>?c):(-?a*?x>?c+?b)~p0 4 ~Hs(?a*?x+?b>?c):(?a*?x>?c-?b)~p0 4 ~Hs(-?a*?x+?b>?c):(-?a*?x>?c-?b)~p0 4 ~Hs(-?a*?x-?b<0):(-?a*?x0):(-?a*?x>?b)~p0 4 ~Hs(-?x-?b<0):(-?x0):(-?x>?b)~p0 4 ~Hs(?a*?x-?b<0):(?a*?x0):(?a*?x>?b)~p0 4 ~Hs(?x-?b<0):(?x0):(?x>?b)~p0 4 ~Hs(-?a*?x+?b<0):(-?a*?x>-?b)~p0 4 ~Hs(-?a*?x+?b>0):(-?a*?x>-?b)~p0 4 ~Hs(-?x+?b<0):(-?x>-?b)~p0 4 ~Hs(-?x+?b>0):(-?x>-?b)~p0 4 ~Hs(?a*?x+?b<0):(?a*?x<-?b)~p0 4 ~Hs(?a*?x+?b>0):(?a*?x>-?b)~p0 4 ~Hs(?x+?b<0):(?x<-?b)~p0 4 ~Hs(?x+?b>0):(?x>-?b)~p0 4 ~Hs(-?a*?x?b/(-?a))~p0 4 ~Hs(-?a*?x>?b):(?x?b):(?x?b/(-1))~p0 4 ~Hs(?a*?x?b):(?x>?b/?a)~p0 4 ~Hs(?x?a):(?x>?a)~p0 4 ~Hs(?x?y):(?x-?y>0)~p0 4 ~Hs(?x>?b):(?x-?b>0)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*Non,MStrict| | }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(abs(?x)<=abs(?y)):((?x<=?y);(-?x<=?y);(?x<=~ -?y);(-?x<=-?y))~p0 4 ~Hs(abs(?x)>=abs(?y)):((?x>=?y);(-?x>=?y);(?x>=~ -?y);(-?x>=-?y))~p0 4 ~Hs(abs(?x)<=?y):((?x<=?y);(-?x<=?y))~p0 4 ~Hs(abs(?x)>=?y):((?x>=?y);(-?x>=?y))~p0 4 ~Hs(?a*?x-?b<=?c):(?a*?x<=?c+?b)~p0 4 ~Hs(-?a*?x-?b<=?c):(-?a*?x<=?c+?b)~p0 4 ~Hs(?a*?x+?b<=?c):(?a*?x<=?c-?b)~p0 4 ~Hs(-?a*?x+?b<=?c):(-?a*?x<=?c-?b)~p0 4 ~Hs(?a*?x-?b>=?c):(?a*?x>=?c+?b)~p0 4 ~Hs(-?a*?x-?b>=?c):(-?a*?x>=?c+?b)~p0 4 ~Hs(?a*?x+?b>=?c):(?a*?x>=?c-?b)~p0 4 ~Hs(-?a*?x+?b>=?c):(-?a*?x>=?c-?b)~p0 4 ~Hs(-?a*?x-?b<=0):(-?a*?x<=?b)~p0 4 ~Hs(-?a*?x-?b>=0):(-?a*?x>=?b)~p0 4 ~Hs(-?x-?b<=0):(-?x<=?b)~p0 4 ~Hs(-?x-?b>=0):(-?x>=?b)~p0 4 ~Hs(?a*?x-?b<=0):(?a*?x<=?b)~p0 4 ~Hs(?a*?x-?b>=0):(?a*?x>=?b)~p0 4 ~Hs(?x-?b<=0):(?x<=?b)~p0 4 ~Hs(?x-?b>=0):(?x>=?b)~p0 4 ~Hs(-?a*?x+?b<=0):(-?a*?x>=-?b)~p0 4 ~Hs(-?a*?x+?b>=0):(-?a*?x>=-?b)~p0 4 ~Hs(-?x+?b<=0):(-?x>=-?b)~p0 4 ~Hs(-?x+?b>=0):(-?x>=-?b)~p0 4 ~Hs(?a*?x+?b<=0):(?a*?x<=-?b)~p0 4 ~Hs(?a*?x+?b>=0):(?a*?x>=-?b)~p0 4 ~Hs(?x+?b<=0):(?x<=-?b)~p0 4 ~Hs(?x+?b>=0):(?x>=-?b)~p0 4 ~Hs(-?a*?x<=?b):(?x>=?b/(-?a))~p0 4 ~Hs(-?a*?x>=?b):(?x<=?b/(-?a))~p0 4 ~Hs(-?x<=?b):(?x>=?b/(-1))~p0 4 ~Hs(-?x>=?b):(?x<=?b/(-1))~p0 4 ~Hs(?a*?x<=?b):(?x<=?b/?a)~p0 4 ~Hs(?a*?x>=?b):(?x>=?b/?a)~p0 4 ~Hs(?x<=?a):(?x<=?a)~p0 4 ~Hs(?x>=?a):(?x>=?a)~p0 4 ~Hs(?x<=?y):(?x-?y<=0)~p0 4 ~Hs(?x>=?y):(?x-?y>=0)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55*Row Operation| | Package}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f161 (min)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" Helvetica~: ;bP6&c55*Base and| | Defined Names}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(RowAdd(?a,?b,?c,?o)):(RowAdd_1(RowsOf(?o),~ ?a,?b,?c,?o))~p0 3 ~V?f146 (ColumnsOf)~p0 3 ~V?m0 (A)~p0 3 ~V?f0 (RowAdd)~p0 3 ~V?m0 (B)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b'4" Helvetica~: ;bP6&c55*RowReduction| | Package}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP6&c55*RowReduce| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(RowReduce(?o)):(RowReduce_1(?o,RowsOf(?o),~ ColumnsOf(?o)))~p0 4 ~Hs(RowReduce(?o)):(RowReduce_1(?o,RowsOf(?o),~ ColumnsOf(?o)))~p0 4 ~Hs(RowReduce_1(?o,?a,?b)):(RowReduce_2(?o,(Conditional(~ ?a,(?a=0)))))~p0 4 ~Hs(RowReduce_2(?o,?a)):(RowReduce_3(?o,MakeSubMatrix(~ ?o,?a)))~p0 4 ~Hs(RowReduce_3(?o,?p)):(RowReduce_4(?p^(-1)*?o))~p0 4 ~Hs(RowReduce_4(?o)):(?o)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP6&c55*MakeSubMatrix| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(MakeSubMatrix(?o,2)):(?o_(1,1),?o_(1,2);?o_~ (2,1),?o_(2,2))~p0 4 ~Hs(MakeSubMatrix(?o,3)):(?o_(1,1),?o_(1,2),?o_~ (1,3);?o_(2,1),?o_(2,2),?o_(2,3);?o_(3,1),?o_(~ 3,2),?o_(3,3))~p0 4 ~Hs(MakeSubMatrix(?o,4)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4);?o_(2,1),?o_(2,2),?o_(2,3),?o_(~ 2,4);?o_(3,1),?o_(3,2),?o_(3,3),?o_(3,4);?o_(4,~ 1),?o_(4,2),?o_(4,3),?o_(4,4))~p0 4 ~Hs(MakeSubMatrix(?o,5)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4),?o_(1,5);?o_(2,1),?o_(2,2),?o_(~ 2,3),?o_(2,4),?o_(2,5);?o_(3,1),?o_(3,2),?o_(3,~ 3),?o_(3,4),?o_(3,5);?o_(4,1),?o_(4,2),?o_(4,3),~ ?o_(4,4),?o_(4,5);?o_(5,1),?o_(5,2),?o_(5,3),?o_~ (5,4),?o_(5,5))~p0 4 ~Hs(MakeSubMatrix(?o,6)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4),?o_(1,5),?o_(1,6);?o_(2,1),?o_(~ 2,2),?o_(2,3),?o_(2,4),?o_(2,5),?o_(2,6);?o_(3,~ 1),?o_(3,2),?o_(3,3),?o_(3,4),?o_(3,5),?o_(3,6);~ ?o_(4,1),?o_(4,2),?o_(4,3),?o_(4,4),?o_(4,5),?o_~ (4,6);?o_(5,1),?o_(5,2),?o_(5,3),?o_(5,4),?o_(~ 5,5),?o_(5,6);?o_(6,1),?o_(6,2),?o_(6,3),?o_(6,~ 4),?o_(6,5),?o_(6,6))~p0 4 ~Hs(MakeSubMatrix(?o,7)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4),?o_(1,5),?o_(1,6),?o_(1,7);?o_(~ 2,1),?o_(2,2),?o_(2,3),?o_(2,4),?o_(2,5),?o_(2,~ 6),?o_(2,7);?o_(3,1),?o_(3,2),?o_(3,3),?o_(3,4),~ ?o_(3,5),?o_(3,6),?o_(3,7);?o_(4,1),?o_(4,2),?o_~ (4,3),?o_(4,4),?o_(4,5),?o_(4,6),?o_(4,7);?o_(~ 5,1),?o_(5,2),?o_(5,3),?o_(5,4),?o_(5,5),?o_(5,~ 6),?o_(5,7);?o_(6,1),?o_(6,2),?o_(6,3),?o_(6,4),~ ?o_(6,5),?o_(6,6),?o_(6,7);?o_(7,1),?o_(7,2),?o_~ (7,3),?o_(7,4),?o_(7,5),?o_(7,6),?o_(7,7))~p0 4 ~Hs(MakeSubMatrix(?o,8)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4),?o_(1,5),?o_(1,6),?o_(1,7),?o_(~ 1,8);?o_(2,1),?o_(2,2),?o_(2,3),?o_(2,4),?o_(2,~ 5),?o_(2,6),?o_(2,7),?o_(2,8);?o_(3,1),?o_(3,2),~ ?o_(3,3),?o_(3,4),?o_(3,5),?o_(3,6),?o_(3,7),?o_~ (3,8);?o_(4,1),?o_(4,2),?o_(4,3),?o_(4,4),?o_(~ 4,5),?o_(4,6),?o_(4,7),?o_(4,8);?o_(5,1),?o_(5,~ 2),?o_(5,3),?o_(5,4),?o_(5,5),?o_(5,6),?o_(5,7),~ ?o_(5,8);?o_(6,1),?o_(6,2),?o_(6,3),?o_(6,4),?o_~ (6,5),?o_(6,6),?o_(6,7),?o_(6,8);?o_(7,1),?o_(~ 7,2),?o_(7,3),?o_(7,4),?o_(7,5),?o_(7,6),?o_(7,~ 7),?o_(7,8);?o_(8,1),?o_(8,2),?o_(8,3),?o_(8,4),~ ?o_(8,5),?o_(8,6),?o_(8,7),?o_(8,8))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" Helvetica~: ;bP5&c55*dim ,] | |2 rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(RowAdd_1(2,1,2,?c,?o)):(RowAdd(?,?,?,(1,0;~ ?c,1)*?o))~p0 3 ~Hs(RowAdd_1(2,1,1,?c,?o)):(RowAdd(?,?,?,(?c,0;~ 0,1)*?o))~p0 3 ~Hs(RowAdd_1(2,2,2,?c,?o)):(RowAdd(?,?,?,(1,0;~ 0,?c)*?o))~p0 3 ~Hs(RowAdd_1(2,2,1,?c,?o)):(RowAdd(?,?,?,(1,?c;~ 0,1)*?o))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" Helvetica~: ;bP5&c55*dim ,] | |3 rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(RowAdd_1(3,1,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;?c,1,0;0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(3,1,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,1,0;?c,0,1)*?o))~p0 3 ~Hs(RowAdd_1(3,2,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,1,0;0,?c,1)*?o))~p0 3 ~Hs(RowAdd_1(3,1,1,?c,?o)):(RowAdd(?,?,?,(?c,0,~ 0;0,1,0;0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(3,2,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,?c,0;0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(3,3,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,1,0;0,0,?c)*?o))~p0 3 ~Hs(RowAdd_1(3,3,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,1,?c;0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(3,3,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ ?c;0,1,0;0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(3,2,1,?c,?o)):(RowAdd(?,?,?,(1,?c,~ 0;0,1,0;0,0,1)*?o))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" Helvetica~: ;bP5&c55*dim ,] | |4 rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(RowAdd_1(4,1,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;?c,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,1,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;?c,0,1,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,1,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,0;?c,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,2,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,?c,1,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,2,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,0;0,?c,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,3,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,0;0,0,?c,1)*?o))~p0 3 ~Hs(RowAdd_1(4,1,1,?c,?o)):(RowAdd(?,?,?,(?c,0,~ 0,0;0,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,2,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,?c,0,0;0,0,1,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,3,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,?c,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,4,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,0;0,0,0,?c)*?o))~p0 3 ~Hs(RowAdd_1(4,4,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,?c;0,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,4,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,?c;0,0,1,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,4,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,?c;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,3,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,?c,0;0,0,1,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,3,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ ?c,0;0,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 3 ~Hs(RowAdd_1(4,2,1,?c,?o)):(RowAdd(?,?,?,(1,?c,~ 0,0;0,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" Helvetica~: ;bP5&c55*dim ,] | |5 rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(RowAdd_1(5,1,1,?c,?o)):(RowAdd(?,?,?,(?c,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,2,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,?c,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,3,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,?c,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,4,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,?c,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,5,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,?c)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,1,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;?c,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,1,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;?c,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,1,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;?c,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,1,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;?c,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,2,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,?c,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,2,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,?c,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,2,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,?c,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,3,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,?c,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,3,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,?c,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,4,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,?c,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,5,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,?c;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,5,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,?c;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,5,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,?c;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,5,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,?c;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,4,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,?c,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,4,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,?c,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,4,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,?c,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,3,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ ?c,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,3,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,?c,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Hs(RowAdd_1(5,2,1,?c,?o)):(RowAdd(?,?,?,(1,?c,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP6&c55*Instructions| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4[%! `fb#@})%# b'4" Helvetica~: ;bP6&c54IIn| |,MPlace Calculations}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })<# b'4| |&c54JMAC&c55*,Z Use `f#}&c55)CTRL,MApple ,M1`f }&c55* on the| | right,Mhand,Mside to keep the}& b!( b"0 b#8 b$@ b%H b&P!WW})3# b'4| |calculations in place,N Do each `f#}&c55)CTRL,MApple,M1`f }&c55* | |Twice}& b!( b"0 b#8 b$@ b%H b&P!WW})b A# b'4&c54JWIN&c55*,Z | |Use `fb"#}&c55)CTRL,MALT,MOPT,M1`f }&c55* on the right ,M hand| | ,M side to keep the}& b!( b"0 b#8 b$@ b%H b&P!WW})6# b'4calculations| | in place,N Do each `fb"#}&c55)CTRL,MALT,MOPT,M1 `f }&c55*Twice| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 3 ~A(A=RowAdd(?,?,?,(3,2,1,4;3,-3,2,-4;7,0,-2,4)))~p0 3 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4[(! ) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})*# b'4" Helvetica~: ;bP7&c54JHow| | to Use RowAdd Function,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})/# b'4&c55*RowAdd,H X,L Y,L Z,L| | Matrix ,I}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})5# b'4`fb"#}&c55)Add`f } `f#},H| |Z times Row X,I`f } to `fb!D}Row Y`f,} in Matrix| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`fb!D})5# b'4if X ,] Y,L then | |multiply Row X by Z}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP6&c55*Example| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~A(A=(3,2,1,4;3,-3,2,-4;7,0,-2,4))~p0 3 ~A(B=RowAdd(1,2,-1,A))~p0 3 ~A(B=RowAdd_1(?,1,2,-1,A))~p0 4 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd_~ 1(?,1,2,-1,A))~p0 5 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd(~ 1,1,1/3,(3,2,1,4;0,-5,1,-8;7,0,-2,4)))~p0 5 ~A(B=RowAdd(?,?,?,(0.33333333333333331,0,0;0,1,~ 0;0,0,1)*(3,2,1,4;0,-5,1,-8;7,0,-2,4)))~p0 6 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd(~ ?,?,?,(1,0.66666666666666663,0.33333333333333331,~ 1.3333333333333333;0,-5,1,-8;7,0,-2,4)))~p0 7 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd(~ 1,3,-7,(1,0.66666666666666663,0.33333333333333331,~ 1.3333333333333333;0,-5,1,-8;7,0,-2,4)))~p0 7 ~A(B=RowAdd(?,?,?,(1,0,0;0,1,0;-7,0,1)*(1,0.66666666666666663,~ 0.33333333333333331,1.3333333333333333;0,-5,1,~ -8;7,0,-2,4)))~p0 8 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd(~ ?,?,?,(1,0.66666666666666663,0.33333333333333331,~ 1.3333333333333333;0,-5,1,-8;0,-4.6666666666666661,~ -4.333333333333333,-5.3333333333333321)))~p0 9 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4["! )## b'4" Helvetica~: ;bP6&c55*AutoReduce| | Package}& b!( b"0 b#8 b$@ b%H b&P!WW})'# b'4Modifications by| | Robert Tranquille}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b'4" Helvetica~: ;bP6&c55*Name Declarations| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP6&c55*Matrices| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~V?m0 (CM)~p0 4 ~V?m0 (EM)~p0 4 ~V?m0 (MM)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP6&c55*Variables| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~V?v0 (MatrixRowEqualsFourIsMax)~p1 4 ~A(MatrixRowEqualsFourIsMax=1893090932093)~p0 5 ~d~Hs(1893090932093):(MatrixRowEqualsFourIsMax)~p0 5 ~V?v0 (ThresholdOfZero)~p1 4 ~A(ThresholdOfZero=9.9999999999999995e-7)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})## b'4" Helvetica~: ;bP6&c55*Old functions| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~V?f0 (MakeSubMatrix)~p0 4 ~V?f0 (RowReduce)~p0 4 ~V?f0 (RowOp)~p0 4 ~V?f0 (Row)~p0 4 ~V?f0 (ClearAdd)~p0 4 ~V?f0 (MakeOne)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b'4" Helvetica~: ;bP6&c55*New functions| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~V?f0 (AutoReduce)~p0 4 ~V?f0 (ColOfPvtA)~p1 4 ~A(ColOfPvtA(?o,?y)=Conditional(?y,(?o_(1,?y)<>~ 0)*(abs(?o_(1,?y))>ThresholdOfZero);ColOfPvtA(~ ?o,?y+1),(?y~ 0)*(?y<>ColOfPvtA(?o,1))*(abs(?o_(2,?y))>ThresholdOfZero);~ ColOfPvtB(?o,?y+1),(?y~ 0)*(?y<>ColOfPvtA(?o,1))*(?y<>ColOfPvtB(?o,1))*~ (abs(?o_(3,?y))>ThresholdOfZero);ColOfPvtC(?o,~ ?y+1),(?y~ 0)*(?y<>ColOfPvtA(?o,1))*(?y<>ColOfPvtB(?o,1))*~ (?y<>ColOfPvtC(?o,1))*(abs(?o_(4,?y))>ThresholdOfZero);~ ColOfPvtD(?o,?y+1),(?y0)))~p0 5 ~d~V?f0 (Min)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})&# b'4" Helvetica~: ;bP6&c55*dim ,]| | 2}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*Functions| | dim2}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*Swap dim| |2}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(((Swap_2)_1)_2(?o)=(0,1;1,0)*?o)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55*Minimum| | ColOf pivots}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(Min_2(?o)=min(ColOfPvtA(?o,1),ColOfPvtB(?o,~ 1)))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})&# b'4" Helvetica~: ;bP6&c55*ClearAdds| | dim2,L }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(((ClearAdd_2)_1)_2(?c,?o)=(1,0;?c,1)*?o)~p0 5 ~d~A(((ClearAdd_2)_2)_1(?c,?o)=(1,?c;0,1)*?o)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*MakeOnes| | dim2}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A((MakeOne_2)_1(?c,?o)=(?c,0;0,1)*?o)~p0 5 ~d~A((MakeOne_2)_2(?c,?o)=(1,0;0,?c)*?o)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*MakePivotOne| | dim2}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(MakePvtA_2(?o)=Conditional((MakeOne_2)_1(1/~ ?o_(1,ColOfPvtA(?o,1)),?o),(Min_2(?o)<100)*(ColOfPvtA(~ ?o,1)=Min_2(?o));(MakeOne_2)_1(1/(((Swap_2)_1)_~ 2(?o))_(1,ColOfPvtA(((Swap_2)_1)_2(?o),1)),((Swap_~ 2)_1)_2(?o)),(Min_2(?o)<100)*(ColOfPvtB(?o,1)=~ Min_2(?o));?o,1))~p0 5 ~d~A(MakePvtB_2(?o)=Conditional((MakeOne_2)_2(~ 1/?o_(2,ColOfPvtB(?o,1)),?o),(ColOfPvtB(?o,1)<>~ 100);?o,1))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*ClearPivotCol| | dim2}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(ClearPvtColA_2(?o)=Conditional(((ClearAdd_2)_~ 1)_2(-?o_(2,ColOfPvtA(?o,1)),?o),(ColOfPvtA(?o,~ 1)<>100);?o,1))~p0 5 ~d~A(ClearPvtColB_2(?o)=Conditional(((ClearAdd_~ 2)_2)_1(-?o_(1,ColOfPvtB(?o,1)),?o),(ColOfPvtB(~ ?o,1)<>100);?o,1))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*AutoRowReduce| | dim2}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(RRMatrix_2(?o)=ClearPvtColB_2(MakePvtB_2(ClearPvtColA_~ 2(MakePvtA_2(?o)))))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*Examples| | dim2}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~A(EM=(5,1,1,0;1,4,0,1))~p0 4 ~A(EM_1=(0,4,6;3,1,4))~p0 255 ~d~A(EM_2=(0,3,0,6;0,4,0,1))~p0 255 ~d~A(RRMatrix_2(EM))~p1 4 ~A(RRMatrix_2(EM)=(1,2.2204460492503132e-17,0.2105263157894737,~ -0.052631578947368418;0,1,-0.052631578947368418,~ 0.26315789473684209))~p0 5 ~A(RRMatrix_2(EM)=(1,0,4/19,-1/19;0,1,-1/19,5/~ 19))~p0 6 ~sb/_!!! } .&!! c#T"!c&T(_c/__c/__} ^ _~A(RRMatrix_~ 2(EM_1))~p1 4 ~A(RRMatrix_2(EM_1)=(0,1,1.5;1,0,0.83333333333333326))~p0 5 ~A(RRMatrix_2(EM_1)=(0,1,3/2;1,0,5/6))~p0 6 ~sb/_!!! } .&!! c#T"!c&T&_c/__c/__} ^ _~A(RRMatrix_~ 2(EM_2))~p1 4 ~A(RRMatrix_2(EM_2)=(0,1,0,0;0,0,0,1))~p0 5 ~A(RRMatrix_2(0,0,0;0,2,3))~p1 4 ~A(RRMatrix_2(0,0,0;0,2,3)=(0,1,1.5;0,0,0))~p0 5 ~A(RRMatrix_2(0,0,0;0,2,3)=(0,1,3/2;0,0,0))~p0 6 ~sb/_!!! } .&!! c#T"!c&T&_c/__c/__} ^ _~A(RRMatrix_~ 2(0,9,10;0,0,0))~p1 4 ~A(RRMatrix_2(0,9,10;0,0,0)=(0,1,1.1111111111111112;~ 0,0,0))~p0 5 ~A(RRMatrix_2(0,9,10;0,0,0)=(0,1,10/9;0,0,0))~p0 6 ~sb/_!! } .&! c#T"!c&T&_c/__c/__} ^ _~A(RRMatrix_~ 2(0,0,0;0,0,0))~p1 4 ~A(RRMatrix_2(0,0,0;0,0,0)=(0,0,0;0,0,0))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55*dim ,] | |3}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*Functions| | dim3}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" Helvetica~: ;bP6&c55*Swap lines| | dim3 }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(((Swap_3)_1)_2(?o)=(0,1,0;1,0,0;0,0,1)*?o)~p0 5 ~d~A(((Swap_3)_1)_3(?o)=(0,0,1;0,1,0;1,0,0)*?o)~p0 5 ~d~A(((Swap_3)_2)_3(?o)=(1,0,0;0,0,1;0,1,0)*?o)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55*Minimum| | ColOf pivots}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(Min_3(?o)=min(ColOfPvtA(?o,1),ColOfPvtB(?o,~ 1),ColOfPvtC(?o,1)))~p0 5 ~d~A(Min_32(?o)=min(ColOfPvtB(?o,1),ColOfPvtC(~ ?o,1)))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*ClearAdds| | dim3}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(((ClearAdd_3)_1)_2(?c,?o)=(1,0,0;?c,1,0;0,0,~ 1)*?o)~p0 5 ~d~A(((ClearAdd_3)_1)_3(?c,?o)=(1,0,0;0,1,0;?c,~ 0,1)*?o)~p0 5 ~d~A(((ClearAdd_3)_2)_3(?c,?o)=(1,0,0;0,1,0;0,~ ?c,1)*?o)~p0 5 ~d~A(((ClearAdd_3)_3)_2(?c,?o)=(1,0,0;0,1,?c;0,~ 0,1)*?o)~p0 5 ~d~A(((ClearAdd_3)_3)_1(?c,?o)=(1,0,?c;0,1,0;0,~ 0,1)*?o)~p0 5 ~d~A(((ClearAdd_3)_2)_1(?c,?o)=(1,?c,0;0,1,0;0,~ 0,1)*?o)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*MakeOnes| | dim3}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A((MakeOne_3)_1(?c,?o)=(?c,0,0;0,1,0;0,0,1)*?o)~p0 5 ~d~A((MakeOne_3)_2(?c,?o)=(1,0,0;0,?c,0;0,0,1)*~ ?o)~p0 5 ~d~A((MakeOne_3)_3(?c,?o)=(1,0,0;0,1,0;0,0,?c)*~ ?o)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*MakePivotsOne| | dim3}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(MakePvtA_3(?o)=Conditional((MakeOne_3)_1(1/~ ?o_(1,ColOfPvtA(?o,1)),?o),(Min_3(?o)<100)*(ColOfPvtA(~ ?o,1)=Min_3(?o));(MakeOne_3)_1(1/(((Swap_3)_1)_~ 2(?o))_(1,ColOfPvtA(((Swap_3)_1)_2(?o),1)),((Swap_~ 3)_1)_2(?o)),(Min_3(?o)<100)*(ColOfPvtB(?o,1)=~ Min_3(?o));(MakeOne_3)_1(1/(((Swap_3)_1)_3(?o))_~ (1,ColOfPvtA(((Swap_3)_1)_3(?o),1)),((Swap_3)_~ 1)_3(?o)),(Min_3(?o)<100)*(ColOfPvtC(?o,1)=Min_~ 3(?o));?o,1))~p0 5 ~d~A(MakePvtB_3(?o)=Conditional((MakeOne_3)_2(~ 1/?o_(2,ColOfPvtB(?o,1)),?o),(Min_32(?o)<100)*~ (ColOfPvtB(?o,1)=Min_32(?o));(MakeOne_3)_2(1/(~ ((Swap_3)_2)_3(?o))_(2,ColOfPvtB(((Swap_3)_2)_~ 3(?o),1)),((Swap_3)_2)_3(?o)),(ColOfPvtC(?o,1)<>~ 100);?o,1))~p0 5 ~d~A(MakePvtC_3(?o)=Conditional((MakeOne_3)_3(~ 1/?o_(3,ColOfPvtC(?o,1)),?o),(ColOfPvtC(?o,1)<>~ 100);?o,1))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*ClearPivotCol| | dim3}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(ClearPvtColA_3(?o)=Conditional(((ClearAdd_3)_~ 1)_3(-?o_(3,ColOfPvtA(?o,1)),((ClearAdd_3)_1)_~ 2(-?o_(2,ColOfPvtA(?o,1)),?o)),(ColOfPvtA(?o,1)<>~ 100);?o,1))~p0 5 ~d~A(ClearPvtColB_3(?o)=Conditional(((ClearAdd_~ 3)_2)_3(-?o_(3,ColOfPvtB(?o,1)),((ClearAdd_3)_~ 2)_1(-?o_(1,ColOfPvtB(?o,1)),?o)),(ColOfPvtB(?o,~ 1)<>100);?o,1))~p0 5 ~d~A(ClearPvtColC_3(?o)=Conditional(((ClearAdd_~ 3)_3)_1(-?o_(1,ColOfPvtC(?o,1)),((ClearAdd_3)_~ 3)_2(-?o_(2,ColOfPvtC(?o,1)),?o)),(ColOfPvtC(?o,~ 1)<>100);?o,1))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*AutoRowReduce| | dim3}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(RRMatrix_3(?o)=ClearPvtColC_3(MakePvtC_3(ClearPvtColB_~ 3(MakePvtB_3(ClearPvtColA_3(MakePvtA_3(?o)))))))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*Examples| | dim3}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~A(CM=(2,1,2,4;4,2,3,8;7,0,-2,4))~p0 4 ~A(CM_1=(0,0,6,1;0,2,-5,0;0,0,-2,4))~p0 255 ~d~A(RRMatrix_3(CM_1))~p1 4 ~A(RRMatrix_3(CM_1)=(0,1,0,0;0,0,1,0;0,0,0,1))~p0 5 ~sb/^!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(RRMatrix_~ 3(CM))~p1 4 ~A(RRMatrix_3(CM)=(1,0,0,0.57142857142857162;0,~ 1,0,2.8571428571428568;0,0,1,0))~p0 5 ~A(RRMatrix_3(CM)=(1,0,0,4/7;0,1,0,20/7;0,0,1,~ 0))~p0 6 ~sb/_!! } .&! c#T"!c&T,_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55*dim ,] | |4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*Functions| | dim4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})&# b'4" Helvetica~: ;bP6&c55*Swap lines| | dim4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(((Swap_4)_1)_2(?o)=(0,1,0,0;1,0,0,0;0,0,1,0;~ 0,0,0,1)*?o)~p0 5 ~d~A(((Swap_4)_1)_3(?o)=(0,0,1,0;0,1,0,0;1,0,0,~ 0;0,0,0,1)*?o)~p0 5 ~d~A(((Swap_4)_1)_4(?o)=(0,0,0,1;0,1,0,0;0,0,1,~ 0;1,0,0,0)*?o)~p0 5 ~d~A(((Swap_4)_2)_3(?o)=(1,0,0,0;0,0,1,0;0,1,0,~ 0;0,0,0,1)*?o)~p0 5 ~d~A(((Swap_4)_2)_4(?o)=(1,0,0,0;0,0,0,1;0,0,1,~ 0;0,1,0,0)*?o)~p0 5 ~d~A(((Swap_4)_3)_4(?o)=(1,0,0,0;0,1,0,0;0,0,0,~ 1;0,0,1,0)*?o)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55*Minimum| | ColOf pivots}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(Min_4(?o)=min(ColOfPvtA(?o,1),ColOfPvtB(?o,~ 1),ColOfPvtC(?o,1),ColOfPvtD(?o,1)))~p0 5 ~d~A(Min_43(?o)=min(ColOfPvtB(?o,1),ColOfPvtC(~ ?o,1),ColOfPvtD(?o,1)))~p0 5 ~d~A(Min_42(?o)=min(ColOfPvtC(?o,1),ColOfPvtD(~ ?o,1)))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*ClearAdds| | dim4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(((ClearAdd_4)_1)_2(?c,?o)=(1,0,0,0;?c,1,0,0;~ 0,0,1,0;0,0,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_1)_3(?c,?o)=(1,0,0,0;0,1,0,~ 0;?c,0,1,0;0,0,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_1)_4(?c,?o)=(1,0,0,0;0,1,0,~ 0;0,0,1,0;?c,0,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_2)_3(?c,?o)=(1,0,0,0;0,1,0,~ 0;0,?c,1,0;0,0,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_2)_4(?c,?o)=(1,0,0,0;0,1,0,~ 0;0,0,1,0;0,?c,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_3)_4(?c,?o)=(1,0,0,0;0,1,0,~ 0;0,0,1,0;0,0,?c,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_4)_3(?c,?o)=(1,0,0,0;0,1,0,~ 0;0,0,1,?c;0,0,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_4)_2(?c,?o)=(1,0,0,0;0,1,0,~ ?c;0,0,1,0;0,0,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_4)_1(?c,?o)=(1,0,0,?c;0,1,0,~ 0;0,0,1,0;0,0,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_3)_2(?c,?o)=(1,0,0,0;0,1,?c,~ 0;0,0,1,0;0,0,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_3)_1(?c,?o)=(1,0,?c,0;0,1,0,~ 0;0,0,1,0;0,0,0,1)*?o)~p0 5 ~d~A(((ClearAdd_4)_2)_1(?c,?o)=(1,?c,0,0;0,1,0,~ 0;0,0,1,0;0,0,0,1)*?o)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*MakeOnes| | dim4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A((MakeOne_4)_1(?c,?o)=(?c,0,0,0;0,1,0,0;0,0,~ 1,0;0,0,0,1)*?o)~p0 5 ~d~A((MakeOne_4)_2(?c,?o)=(1,0,0,0;0,?c,0,0;0,~ 0,1,0;0,0,0,1)*?o)~p0 5 ~d~A((MakeOne_4)_3(?c,?o)=(1,0,0,0;0,1,0,0;0,0,~ ?c,0;0,0,0,1)*?o)~p0 5 ~d~A((MakeOne_4)_4(?c,?o)=(1,0,0,0;0,1,0,0;0,0,~ 1,0;0,0,0,?c)*?o)~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55*MakePivotsOne| | dim4 }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(MakePvtA_4(?o)=Conditional((MakeOne_4)_1(1/~ ?o_(1,ColOfPvtA(?o,1)),?o),(Min_4(?o)<100)*(ColOfPvtA(~ ?o,1)=Min_4(?o));(MakeOne_4)_1(1/(((Swap_4)_1)_~ 2(?o))_(1,ColOfPvtA(((Swap_4)_1)_2(?o),1)),((Swap_~ 4)_1)_2(?o)),(Min_4(?o)<100)*(ColOfPvtB(?o,1)=~ Min_4(?o));(MakeOne_4)_1(1/(((Swap_4)_1)_3(?o))_~ (1,ColOfPvtA(((Swap_4)_1)_3(?o),1)),((Swap_4)_~ 1)_3(?o)),(Min_4(?o)<100)*(ColOfPvtC(?o,1)=Min_~ 4(?o));(MakeOne_4)_1(1/(((Swap_4)_1)_4(?o))_(1,~ ColOfPvtA(((Swap_4)_1)_4(?o),1)),((Swap_4)_1)_~ 4(?o)),(Min_4(?o)<100)*(ColOfPvtD(?o,1)=Min_4(~ ?o));?o,1))~p0 5 ~d~A(MakePvtB_4(?o)=Conditional((MakeOne_4)_2(~ 1/?o_(2,ColOfPvtB(?o,1)),?o),(Min_43(?o)<100)*~ (ColOfPvtB(?o,1)=Min_43(?o));(MakeOne_4)_2(1/(~ ((Swap_4)_2)_3(?o))_(2,ColOfPvtB(((Swap_4)_2)_~ 3(?o),1)),((Swap_4)_2)_3(?o)),(Min_43(?o)<100)*~ (ColOfPvtC(?o,1)=Min_43(?o));(MakeOne_4)_2(1/(~ ((Swap_4)_2)_4(?o))_(2,ColOfPvtB(((Swap_4)_2)_~ 4(?o),1)),((Swap_4)_2)_4(?o)),(Min_43(?o)<100)*~ (ColOfPvtD(?o,1)=Min_43(?o));?o,1))~p0 5 ~d~A(MakePvtC_4(?o)=Conditional((MakeOne_4)_3(~ 1/?o_(3,ColOfPvtC(?o,1)),?o),(Min_42(?o)<100)*~ (ColOfPvtC(?o,1)=Min_42(?o));(MakeOne_4)_3(1/(~ ((Swap_4)_3)_4(?o))_(3,ColOfPvtC(((Swap_4)_3)_~ 4(?o),1)),((Swap_4)_3)_4(?o)),(Min_42(?o)<100)*~ (ColOfPvtD(?o,1)=Min_42(?o));?o,1))~p0 5 ~d~A(MakePvtD_4(?o)=Conditional((MakeOne_4)_4(~ 1/?o_(4,ColOfPvtD(?o,1)),?o),(ColOfPvtD(?o,1)<>~ 100);?o,1))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55*ClearPivotCol| | dim4 }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(ClearPvtColA_4(?o)=Conditional(((ClearAdd_4)_~ 1)_4(-?o_(4,ColOfPvtA(?o,1)),((ClearAdd_4)_1)_~ 3(-?o_(3,ColOfPvtA(?o,1)),((ClearAdd_4)_1)_2(-~ ?o_(2,ColOfPvtA(?o,1)),?o))),(ColOfPvtA(?o,1)<>~ 100);?o,1))~p0 5 ~d~A(ClearPvtColB_4(?o)=Conditional(((ClearAdd_~ 4)_2)_4(-?o_(4,ColOfPvtB(?o,1)),((ClearAdd_4)_~ 2)_3(-?o_(3,ColOfPvtB(?o,1)),((ClearAdd_4)_2)_~ 1(-?o_(1,ColOfPvtB(?o,1)),?o))),(ColOfPvtB(?o,~ 1)<>100);?o,1))~p0 5 ~d~A(ClearPvtColC_4(?o)=Conditional(((ClearAdd_~ 4)_3)_4(-?o_(4,ColOfPvtC(?o,1)),((ClearAdd_4)_~ 3)_1(-?o_(1,ColOfPvtC(?o,1)),((ClearAdd_4)_3)_~ 2(-?o_(2,ColOfPvtC(?o,1)),?o))),(ColOfPvtC(?o,~ 1)<>100);?o,1))~p0 5 ~d~A(ClearPvtColD_4(?o)=Conditional(((ClearAdd_~ 4)_4)_3(-?o_(3,ColOfPvtD(?o,1)),((ClearAdd_4)_~ 4)_2(-?o_(2,ColOfPvtD(?o,1)),((ClearAdd_4)_4)_~ 1(-?o_(1,ColOfPvtD(?o,1)),?o))),(ColOfPvtD(?o,~ 1)<>100);?o,1))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" Helvetica~: ;bP6&c55*AutoRowReduce| | dim4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~A(RRMatrix_4(?o)=ClearPvtColD_4(MakePvtD_4(ClearPvtColC_~ 4(MakePvtC_4(ClearPvtColB_4(MakePvtB_4(ClearPvtColA_~ 4(MakePvtA_4(?o)))))))))~p0 5 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" Helvetica~: ;bP6&c55*Examples| | dim4 }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~A(MM=(2,1,2,4,1;4,2,3,8,3;7,0,-2,4,4;3,2,-1,0,~ 3))~p0 4 ~A(RRMatrix_4(MM))~p0 4 ~A(RRMatrix_4(MM)=(1,0,0,0,0;0,1,0,0,1;0,0,1,0,~ -1;0,0,0,1,0.5))~p0 5 ~A(RRMatrix_4(MM)=(1,0,0,0,0;0,1,0,0,1;0,0,1,0,~ -1;0,0,0,1,1/2))~p0 6 ~sb/_!! } .&! c#T"!c&T4_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP6&c55*Examples| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~A(EM=(5,1,1,0;1,4,0,1))~p0 3 ~d~A(CM=(2,1,2,4;4,2,3,8;7,0,-2,4))~p0 3 ~d~A(MM=(2,1,2,4,1;4,2,3,8,3;7,0,-2,4,4;3,2,-1,~ 0,3))~p0 3 ~d~A(RRMatrix(EM))~p0 3 ~A(RRMatrix(EM)=(1,2.2204460492503132e-17,0.2105263157894737,~ -0.052631578947368418;0,1,-0.052631578947368418,~ 0.26315789473684209))~p0 4 ~sb/^!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(RRMatrix(~ EM)=(1,0,4/19,-1/19;0,1,-1/19,5/19))~p0 5 ~sb/_!! } .&! c#T"!c&T(_c/__c/__} ^ _~A(RRMatrix(~ CM))~p0 3 ~A(RRMatrix(CM)=(1,0,0,0.57142857142857162;0,1,~ 0,2.8571428571428568;0,0,1,0))~p0 4 ~sb/^!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(RRMatrix(~ CM)=(1,0,0,4/7;0,1,0,20/7;0,0,1,0))~p0 5 ~sb/_!! } .&! c#T"!c&T,_c/__c/__} ^ _~A(RRMatrix(~ MM))~p0 3 ~A(RRMatrix(MM)=(1,0,0,0,0;0,1,0,0,1;0,0,1,0,-~ 1;0,0,0,1,0.5))~p0 4 ~sb/^!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(RRMatrix(~ MM)=(1,0,0,0,0;0,1,0,0,1;0,0,1,0,-1;0,0,0,1,1/~ 2))~p0 5 ~sb/_!! } .&! c#T"!c&T4_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}))# b'4" *~: ;bP6&c55*Derivatives of | |Absolute Value Functions}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP6&c55*Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(Diff(?x)*abs(?x)):(Conditional(1,(?x>0);-1,~ (?x<0)))~p0 3 ~Hs(Diff(?x)*abs(?o)):(Conditional(Diff(?x)*?o,~ (?o>0);-Diff(?x)*?o,(?o<0)))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP6&c55*Examples| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~A(Diff(x)*abs(x))~p0 3 ~A(Diff(x)*abs(x)=Conditional(1,(x>0);-1,(x<0)))~p0 4 ~sb/^!! } !&! c#T"!c"H"_c/__c/__} ^ _~A(Diff(~ x)*abs(x^3+1))~p0 3 ~A(Diff(x)*abs(x^3+1)=Conditional(3*x^2,(x^3+1>~ 0);-3*x^2,(x^3+1<0)))~p0 4 ~sb/^!! } !&! c#T"!c"H"_c/__c/__} ^ _~A(Diff(~ x)*sqrt(x))~p0 3 ~A(Diff(x)*sqrt(x)=1/2*1/sqrt(x))~p0 4 ~sb/^!! } !&! c#T"!c"H"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#@})!# b'4`f }[$! `fb#@}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})'# b'4" Helvetica~: ;bP7&c55)Basic| | New Notebook Definitions}& b!( b"0 b#8 b$@ b%H b&P!WW})4# b'4| |;bP6&c55*The below items provided basic functionality of a notebook| |,N }& b!( b"0 b#8 b$@ b%H b&P!WW})6# b'4It is probably not a| | good idea to delete these below,N}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" Helvetica~: ;bP5&c55*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~V?f276 (arccsc)~p0 2 ~V?f278 (arccot)~p0 2 ~V?f256 (sin)~p0 2 ~V?f257 (cos)~p0 2 ~V?f258 (tan)~p0 2 ~V?f261 (sec)~p0 2 ~V?f260 (csc)~p0 2 ~V?f262 (cot)~p0 2 ~V?f272 (arcsin)~p0 2 ~V?f273 (arccos)~p0 2 ~V?f274 (arctan)~p0 2 ~V?f277 (arcsec)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" Helvetica~: ;bP5&c55*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f309 (arcsech)~p0 2 ~V?f304 (arcsinh)~p0 2 ~V?f294 (coth)~p0 2 ~V?f310 (arccoth)~p0 2 ~V?f306 (arctanh)~p0 2 ~V?f293 (sech)~p0 2 ~V?f288 (sinh)~p0 2 ~V?f289 (cosh)~p0 2 ~V?f290 (tanh)~p0 2 ~V?f305 (arccosh)~p0 2 ~V?f308 (arccsch)~p0 2 ~V?f292 (csch)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" Helvetica~: ;bP5&c55*Logarithms| | ,F Powers}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f32 (log)~p0 2 ~V?f307 (ln)~p0 2 ~V?f291 (exp)~p0 2 ~V?c2 (e)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" Helvetica~: ;bP5&c55*Standard| | Rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" Helvetica~: ;bP5&c55*Logarithms| | ,F Powers}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Ht(?x^(-?y)):(1/?x^?y)~p0 3 ~Hs(exp(?z)):(e^?z)~p0 3 ~Hs(e^(ln(?x))):(?x)~p0 3 ~Hs(10^(log(?x))):(?x)~p0 3 ~Hs(?y^(log_?y(?x))):(?x)~p0 3 ~Hs(ln(e^?x)):(?x)~p0 3 ~Hs(log(10^?x)):(?x)~p0 3 ~Hs(log_?y(?y^?x)):(?x)~p0 3 ~He(ln(?u*?v)):(ln(?u)+ln(?v))~p0 3 ~He(log(?u*?v)):(log(?u)+log(?v))~p0 3 ~He(log_?y(?u*?v)):(log_?y(?u)+log_?y(?v))~p0 3 ~He(ln(?u/?v)):(ln(?u)-ln(?v))~p0 3 ~He(log(?u/?v)):(log(?u)-log(?v))~p0 3 ~He(log_?y(?u/?v)):(log_?y(?u)-log_?y(?v))~p0 3 ~He(ln(?u^?v)):(?v*ln(?u))~p0 3 ~He(log(?u^?v)):(?v*log(?u))~p0 3 ~He(log_?y(?u^?v)):(?v*log_?y(?u))~p0 3 ~He(ln(sqrt(?u))):(1/2*ln(?u))~p0 3 ~He(log(sqrt(?u))):(1/2*log(?u))~p0 3 ~He(log_?y(sqrt(?u))):(1/2*log_?y(?u))~p0 3 ~He(?z^(?x+?y)):(?z^?x*?z^?y)~p0 3 ~He(?z^(?x-?y)):(?z^?x*?z^(-?y))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" Helvetica~: ;bP5&c55*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" Helvetica~: ;bP5&c55*Simplify| | ,M negation and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sin(-?x)):(-sin(?x))~p0 4 ~Hs(cos(-?x)):(cos(?x))~p0 4 ~Hs(tan(-?x)):(-tan(?x))~p0 4 ~Hs(sin('p)):(0)~p0 4 ~Hs(sin(?n*'p)):(0)~p0 4 ~Hs(cos(1/2*'p)):(0)~p0 4 ~Hs(cos(?n/2*'p)):(0)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" Helvetica~: ;bP5&c55*Transform| | to basic types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(tan(?x)):((sin(?x))/(cos(?x)))~p0 4 ~Ht(csc(?x)):(1/(sin(?x)))~p0 4 ~Ht(sin(?x)):(1/(csc(?x)))~p0 4 ~Ht(sec(?x)):(1/(cos(?x)))~p0 4 ~Ht(cos(?x)):(1/(sec(?x)))~p0 4 ~Ht(cot(?x)):((cos(?x))/(sin(?x)))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" Helvetica~: ;bP5&c55*Trig Addition| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(cos(?x+?y)):(cos(?x)*cos(?y)-sin(?x)*sin(?y))~p0 4 ~Ht(sin(?x+?y)):(cos(?x)*sin(?y)+sin(?x)*cos(?y))~p0 4 ~Ht(cos(2*?x)):(2*(cos(?x))^2-1)~p0 4 ~Ht(sin(2*?x)):(2*cos(?x)*sin(?x))~p0 4 ~Ht(sin(?n*?x)):(cos((?n-1)*?x)*sin(?x)+cos(?x)*~ sin((?n-1)*?x))~p0 4 ~Ht(cos(?n*?x)):(cos(?x)*cos((?n-1)*?x)-sin(?x)*~ sin((?n-1)*?x))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})/# b$L" Helvetica~: ;bP5&c55*Transform| | ,M into another flavor of trig function| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((sin(?x))^2):(1-(cos(?x))^2)~p0 4 ~Ht((cos(?x))^2):(1-(sin(?x))^2)~p0 4 ~Ht((tan(?x))^2):((sec(?x))^2-1)~p0 4 ~Ht((sec(?x))^2):((tan(?x))^2+1)~p0 4 ~Ht((csc(?x))^2):((cot(?x))^2+1)~p0 4 ~Ht((cot(?x))^2):((csc(?x))^2-1)~p0 4 ~Hs((sin(?x))^2+(cos(?x))^2):(1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})b @# b%4" Helvetica~: ;bP5&c55*substituting| | z,]tan,Hx,O2,I into a rational function in sin,Hx,I and cos,H| |x,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0 4 ~Hs(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" Helvetica~: ;bP5&c55*Other rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cos(?x))^2):(1/2*(cos(2*?x)+1))~p0 4 ~Ht((sin(?x))^2):(1/2*(-cos(2*?x)+1))~p0 4 ~Ht(cos(?x)*sin(?x)):(1/2*sin(2*?x))~p0 4 ~Hs(sin(arccos(?x))):(sqrt(-?x^2+1))~p0 4 ~Hs(cos(arcsin(?x))):(sqrt(-?x^2+1))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b!T" Helvetica~: ;bP5&c55*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" Helvetica~: ;bP5&c55*Simplify| | ,M negation and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sinh(-?x)):(-sinh(?x))~p0 4 ~Hs(cosh(-?x)):(cosh(?x))~p0 4 ~Hs(tanh(-?x)):(-tanh(?x))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" Helvetica~: ;bP5&c55*Transform| | into other types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((sinh(?x))^2):((cosh(?x))^2-1)~p0 4 ~Ht((cosh(?x))^2):(1+(sinh(?x))^2)~p0 4 ~Ht((tanh(?x))^2):(1-(sech(?x))^2)~p0 4 ~Ht(sinh(?x)):((e^?x-e^(-?x))/2)~p0 4 ~Ht(cosh(?x)):((e^?x+e^(-?x))/2)~p0 4 ~Ht(tanh(?x)):((e^?x-e^(-?x))/(e^?x+e^(-?x)))~p0 4 ~Ht(tanh(?x)):((sinh(?x))/(cosh(?x)))~p0 4 ~Hs((cosh(?x))^2-(sinh(?x))^2):(1)~p0 4 ~Hs(-(cosh(?x))^2+(sinh(?x))^2):(-1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" Helvetica~: ;bP5&c55*Other hyperbolic| | rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cosh(?x))^2):(1/2*(cosh(2*?x)+1))~p0 4 ~Ht((sinh(?x))^2):(1/2*(cosh(2*?x)-1))~p0 4 ~Ht(sinh(2*?x)):(2*cosh(?x)*sinh(?x))~p0 4 ~Ht(cosh(2*?x)):(2*(cosh(?x))^2-1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP5&c55*Constants| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?c5 ('o)~p0 2 ~V?c1 ('p)~p0 2 ~V?c0 (c)~p0 2 ~V?c0 (b)~p0 2 ~V?c0 (a)~p0 2 ~V?c4 (i)~p0 2 ~V?c3 ('N)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP5&c55*Variables| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?v0 (n)~p0 2 ~V?m0 (C)~p0 2 ~V?m0 (P)~p0 2 ~V?v0 (y')~p0 2 ~V?v0 (h)~p0 2 ~V?v0 (v)~p0 2 ~V?v0 (u)~p0 2 ~V?v0 (w)~p0 2 ~V?v0 ('f)~p0 2 ~V?v0 ('r)~p0 2 ~V?v0 ('q)~p0 2 ~V?v0 (r)~p0 2 ~V?v0 (t)~p0 2 ~V?v0 (z)~p0 2 ~V?v0 (y)~p0 2 ~V?v0 (x)~p0 2 ~V?v0 (k)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" Helvetica~: ;bP5&c55*Functions| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f132 (FromSpherical)~p0 2 ~V?f130 (FromCylindrical)~p0 2 ~V?f128 (FromPolar)~p0 2 ~V?f144 (RowsOf)~p0 2 ~V?f146 (ColsOf)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" Helvetica~: ;bP5&c55*Names to| | the back}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f0 (dlim)~p0 3 ~V?f0 (SAEQN)~p0 3 ~V?f0 (SA)~p0 3 ~V?f0 (D)~p0 3 ~V?f0 (N)~p0 3 ~V?v0 (xSV)~p0 3 ~V?d16 (d)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})b!9# b'4" *~: ;bP7&c54JData,Z&c55* | |You can highlight and change any one of the following data and| | see the effect on the solution,N `fb#@}Be careful not to delete| | the degree symbol when changing the value of an angle as that| | would cause an error in the solution,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(F_a=500)~p0 1 ~d~A('q_ax=65*'o)~p0 255 ~d~A('q_ay=30*'o)~p0 255 ~d~A(F_b=650)~p0 1 ~d~A('q_by=150*'o)~p0 255 ~d~A('q_bz=65*'o)~p0 255 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}`fb"#})"# b'4" *~: ;bP7&c54JSolution,Z| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}):# b'4" *~: ;bP7&c55*We begin by finding| | the x,Ly,Lz components of the known forces,Z| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#@})<# b'4" *~: ;bP7&c55)Force $^F| |^;bP:a_;bP7,Z `f }&c55*,HDouble click on the ,GQ,G symbol to | |see the content,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})b L# b'4" *~: ;bP7&c55*Since we know| | the direction angles from x and y axes,L we can solve for the| | direction angle from z axis as}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 3 ~A('q_az=arccos(sqrt(1-(cos('q_ax))^2-(cos('q_~ ay))^2)))~p0 4 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#@})/# b'4" *~: ;bP7&c55*Note that| | LiveMath gives $^"!Symbol^:!&c0 q(": ;bP:&c55*az }_;bP7in radians| |,N }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 5 ~A('q_az=1.3003140690106658)~p0 5 ~sb/_! } $& c#T"!c#L"_c/__c/__} ^ _~A(F_ax=~ F_a*cos('q_ax))~p0 3 ~d~A(F_ax=211.30913087034972)~p0 255 ~sb/_! } $& c#T"!c"H"_c/__c/__} ^ _~A(F_ay=~ F_a*cos('q_ay))~p0 3 ~d~A(F_ay=433.01270189221935)~p0 255 ~sb/_! } $& c#T"!c"H"_c/__c/__} ^ _~A(F_az=~ F_a*cos('q_az))~p0 3 ~d~A(F_az=133.59809583529764)~p0 255 ~sb/_! } $& c#T"!c"H"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}`f<})<# b'4" *~: ;bP7&c55)Force $^F^b| |_,Z `f }&c55*,HDouble click on the ,GQ,G symbol to see the content| |,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})b L# b'4" *~: ;bP7&c55*Since we know| | the direction angles from y and z axes,L we can solve for the| | direction angle from z axis as}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 3 ~A('q_bx=arccos(sqrt(1-(cos('q_by))^2-(cos('q_~ bz))^2)))~p0 4 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#@})/# b'4" *~: ;bP7&c55*Note that| | LiveMath gives $^"!Symbol^:!&c0 q(": ;bP:&c55*bx }_;bP7in radians| |,N }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 5 ~A('q_bx=1.3003140690106658)~p0 5 ~sb/_! } $& c#T"!c#L"_c/__c/__} ^ _~A(F_bx=~ F_b*cos('q_bx))~p0 3 ~d~A(F_bx=173.67752458588691)~p0 255 ~sb/_! } $& c#T"!c"H"_c/__c/__} ^ _~A(F_by=~ F_b*cos('q_by))~p0 3 ~d~A(F_by=-562.91651245988521)~p0 255 ~sb/_! } $& c#T"!c"H"_c/__c/__} ^ _~A(F_bz=~ F_b*cos('q_bz))~p0 3 ~d~A(F_bz=274.70187013145465)~p0 255 ~sb/_! } $& c#T"!c"H"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})b V# b'4" *~: ;bP7&c55*Equilibrium of| | forces requires the sum of all the forces to be zero,N This| | means that the individual components must add up to zero as | |well,N}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(F_ax+F_bx+F_cx=0)~p0 2 ~A(F_cx=0-(F_ax+F_bx))~p0 255 ~d~sb/_! } )+ c#T" c"L#"c%\"_c/__c/__! !} ^ _~ ~A(F_cx=-384.98665545623663)~p0 255 ~sb/_! } $& c#T"!c"L"_c/__c/__} ^ _~A(F_ay+~ F_by+F_cy=0)~p0 2 ~A(F_cy=0-(F_ay+F_by))~p0 255 ~d~sb/_! } )+ c#T" c"L#"c%\"_c/__c/__! !} ^ _~ ~A(F_cy=129.90381056766586)~p0 255 ~sb/_! } $& c#T"!c"L"_c/__c/__} ^ _~A(F_az+~ F_bz+F_cz=0)~p0 2 ~A(F_cz=0-(F_az+F_bz))~p0 255 ~d~sb/_! } )) c#T" c"L#_"#! !} ^ _~A(F_cz=~ -408.29996596675232)~p0 255 ~sb/_! } $& c#T"!c"L"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}).# b'4" *~: ;bP7&c55*The magnitude of| | $^F^c_ is found as,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(F_c=sqrt(F_cx^2+F_cy^2+F_cz^2))~p0 2 ~d~A(F_c=576.01960651338095)~p0 255 ~sb/_! } $& c#T"!c"4!_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})-# b'4" *~: ;bP7&c55*The direction angles| | of $^F^c_ are,Z }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#@})b B# b'4" *~: ;bP7&c55*Note that| | the factor ,B <2(!180}^"!Symbol^:!p}: ,B is used here since | |LiveMath gives the angles in radians,N;bP8 | |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 2 ~A('q_cx=arccos(F_cx/F_c)*180/'p)~p0 2 ~A('q_cx=131.94037278949287)~p0 255 ~sb/_! } $& c#T"!c"H"_c/__c/__} ^ _~A('q_~ cy=arccos(F_cy/F_c)*180/'p)~p0 2 ~A('q_cy=76.966555476180048)~p0 255 ~sb/_! } $& c#T"!c"H"_c/__c/__} ^ _~A('q_~ cz=arccos(F_cz/F_c)*180/'p)~p0 2 ~A('q_cz=135.1397988225587)~p0 255 ~sb/_! } $& c#T"!c"H"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})b F# b'4" *~: ;bP7&c55*The graph of | |the 3 forces acting on the particle is shown below,N `fb#L}Force| | $^F^c_ is in orange,N}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Z1 1 432 642 0 -0.68590 0.72770 0.00000 0.32348 0.30491 -0.89575 -0.65184 -0.61440 -0.44452 2 4 4 3 10 0 0 ? ? (~ 600-1200...-600+1200):(600-1200...-600+1200):(~ 600-1200...-600+1200):(?=0...2*'p):('p/5):(10)~ ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b#@" *~: ;bP7&c55*Declarations| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~R5592405 ? (t,y,0):(y=south...north):(t=west...~ east):(50)~p0 1 ~R5592405 ? (t,y,0):(t=west...east):(y=south...~ north):(50)~p0 1 ~X1 0 (0,0,z):(z=bottom...top):(z)~p0 1 ~X1 0 (0,y,0):(y=south...north):(y)~p0 1 ~X1 0 (x,0,0):(x=west...east):(x)~p0 1 ~V?c69 (west)~p0 1 ~V?c68 (east)~p0 1 ~V?c70 (south)~p0 1 ~V?c71 (north)~p0 1 ~V?c66 (bottom)~p0 1 ~V?c67 (top)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" *~: ;bP7&c55*Plot Vector Commands| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~S21 ? 65280 ? ? (k/500*PlotVectorII_n):((n=1...~ RowsOf(PlotVectorI))*(k=1...500)):(3)~p0 1 ~S21 ? 16711680 ? ? (k/500*PlotVectorI_n):((n=~ 1...RowsOf(PlotVectorI))*(k=1...500)):(3)~p0 1 ~S21 ? 16744448 ? ? (k/500*PlotVectorIII_n):((~ n=1...RowsOf(PlotVectorI))*(k=1...500)):(3)~p0 1 ~A(TheFactor=Min((east-west)/25,(north-south)/~ 25,(top-bottom)/25))~p0 1 ~d~A(R=PlotVectorI_n*(cos('p/6),sin('p/6),0;-sin(~ 'p/6),cos('p/6),0;0,0,1))~p0 1 ~d~A(C=PlotVectorI*(cos('p/6),-sin('p/6),0;sin(~ 'p/6),cos('p/6),0;0,0,1))~p0 1 ~d~S4 ? 16711680 ? ? (PlotVectorI_k):(k=1...RowsOf(~ PlotVectorI)):(8)~p0 1 ~S4 ? 65280 ? ? (PlotVectorII_k):(k=1...RowsOf(~ PlotVectorI)):(8)~p0 1 ~S4 ? 16744448 ? ? (PlotVectorIII_k):(k=1...RowsOf(~ PlotVectorI)):(8)~p0 1 ~D1 2 1 8355839 ? ? (x,y,z):(x=west...east):(y=~ south...north):(z=bottom...top)~p0 0 ~D1 2 1 12566527 ? ? (x,y,z):(y=south...north):(~ z=bottom...top):(z=bottom...top)~p0 0 ~D1 2 1 14803967 ? ? (x,y,z):(x=west...east):(~ z=bottom...top):(z=bottom...top)~p0 0 ~t~p0 2 ~c5 1377 -1 1376 -1 1375 -1 1293 -1 1291 -1 1318 -1 ~c1 1378 -1 1377 -1 ~c3 1380 -1 1379 -1 1291 -1 1321 -1 ~c1 1381 -1 1380 -1 ~c3 1383 -1 1382 -1 1291 -1 1319 -1 ~c1 1384 -1 1383 -1 ~c1 1452 -1 1451 -1 ~c1 1455 -1 1454 -1 ~c1 1460 -1 1459 -1 ~c1 1463 -1 1462 -1 ~c41 1500 -1 1499 -1 1498 -1 1388 -1 1396 -1 1395 -1 1407 -1 1406 -1 1409 -1 1408 -1 1411 -1 1410 -1 1473 -1 1425 -1 1469 -1 1418 -1 1483 -1 1403 -1 1487 -1 1414 -1 1476 -1 1402 -1 1477 -1 1491 -1 1419 -1 1474 -1 1484 -1 1488 -1 1415 -1 1481 -1 1478 -1 1492 -1 1420 -1 1485 -1 1489 -1 1416 -1 1479 -1 1480 -1 1493 -1 1421 -1 1495 -1 1423 -1 ~c1 1503 -1 1502 -1 ~c1 1551 -1 1550 -1 ~c28 1557 -1 1556 -1 1553 -1 1389 -1 1396 -1 1395 -1 1407 -1 1406 -1 1409 -1 1408 -1 1431 -1 1425 -1 1436 -1 1403 -1 1439 -1 1414 -1 1433 -1 1402 -1 1442 -1 1419 -1 1437 -1 1440 -1 1415 -1 1434 -1 1443 -1 1420 -1 1445 -1 1423 -1 1424 -1 ~c1 1558 -1 1557 -1 ~c42 1560 -1 1559 -1 1554 -1 1388 -1 1396 -1 1395 -1 1407 -1 1406 -1 1409 -1 1408 -1 1411 -1 1410 -1 1473 -1 1425 -1 1483 -1 1403 -1 1487 -1 1414 -1 1476 -1 1402 -1 1477 -1 1491 -1 1419 -1 1474 -1 1471 -1 1418 -1 1484 -1 1488 -1 1415 -1 1481 -1 1478 -1 1492 -1 1420 -1 1485 -1 1489 -1 1416 -1 1479 -1 1480 -1 1493 -1 1421 -1 1495 -1 1423 -1 1424 -1 ~c1 1561 -1 1560 -1 ~c56 1563 -1 1562 -1 1555 -1 1390 -1 1396 -1 1395 -1 1407 -1 1406 -1 1409 -1 1408 -1 1411 -1 1410 -1 1413 -1 1412 -1 1514 -1 1425 -1 1531 -1 1403 -1 1536 -1 1414 -1 1518 -1 1402 -1 1519 -1 1520 -1 1541 -1 1419 -1 1515 -1 1510 -1 1418 -1 1532 -1 1537 -1 1415 -1 1529 -1 1521 -1 1522 -1 1542 -1 1420 -1 1516 -1 1533 -1 1538 -1 1416 -1 1527 -1 1528 -1 1523 -1 1543 -1 1421 -1 1534 -1 1539 -1 1417 -1 1526 -1 1525 -1 1524 -1 1544 -1 1422 -1 1546 -1 1423 -1 1424 -1 ~c1 1564 -1 1563 -1 ~c2 1571 -1 1570 -1 1567 -1 ~c2 1573 -1 1572 -1 1568 -1 ~c1 1575 -1 1574 -1 ~c4 1745 -1 1743 -1 1734 -1 1711 -1 1735 -1 ~c5 1747 -1 1746 -1 1734 -1 1711 -1 1733 -1 22 -1 ~c5 1749 -1 1748 -1 1735 -1 1711 -1 1733 -1 22 -1 ~c7 1751 -1 1750 -1 1734 -1 1711 -1 1735 -1 1743 -1 1733 -1 22 -1 ~c4 1756 -1 1754 -1 1737 -1 1711 -1 1738 -1 ~c7 1758 -1 1757 -1 1737 -1 1711 -1 1738 -1 1754 -1 1736 -1 22 -1 ~c5 1760 -1 1759 -1 1737 -1 1711 -1 1736 -1 22 -1 ~c5 1762 -1 1761 -1 1738 -1 1711 -1 1736 -1 22 -1 ~c1 1765 -1 1764 -1 ~c11 1766 -1 1765 -1 1734 -1 1711 -1 1733 -1 22 -1 1746 -1 1737 -1 1738 -1 1754 -1 1736 -1 1757 -1 ~c1 1768 -1 1767 -1 ~c9 1769 -1 1768 -1 1735 -1 1711 -1 1733 -1 22 -1 1748 -1 1737 -1 1736 -1 1759 -1 ~c1 1771 -1 1770 -1 ~c11 1772 -1 1771 -1 1734 -1 1711 -1 1735 -1 1743 -1 1733 -1 22 -1 1750 -1 1738 -1 1736 -1 1761 -1 ~c20 1775 -1 1774 -1 1734 -1 1711 -1 1733 -1 22 -1 1746 -1 1737 -1 1738 -1 1754 -1 1736 -1 1757 -1 1765 -1 1735 -1 1748 -1 1759 -1 1768 -1 1743 -1 1750 -1 1761 -1 1771 -1 ~c21 1779 -1 1778 -1 1734 -1 1711 -1 1733 -1 22 -1 1746 -1 1737 -1 1738 -1 1754 -1 1736 -1 1757 -1 1765 -1 1735 -1 1748 -1 1759 -1 1768 -1 1743 -1 1750 -1 1761 -1 1771 -1 1774 -1 ~c21 1781 -1 1780 -1 1735 -1 1711 -1 1733 -1 22 -1 1748 -1 1737 -1 1736 -1 1759 -1 1768 -1 1734 -1 1746 -1 1738 -1 1754 -1 1757 -1 1765 -1 1743 -1 1750 -1 1761 -1 1771 -1 1774 -1 ~c21 1783 -1 1782 -1 1734 -1 1711 -1 1735 -1 1743 -1 1733 -1 22 -1 1750 -1 1738 -1 1736 -1 1761 -1 1771 -1 1746 -1 1737 -1 1754 -1 1757 -1 1765 -1 1748 -1 1759 -1 1768 -1 1774 -1 ~e