1,1,135,83,0.030000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","\frac{b C \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{b B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{C \left(\tan^{2}\left(d x +c \right)\right) a}{2 d}+\frac{a B \tan \left(d x +c \right)}{d}-\frac{b C \tan \left(d x +c \right)}{d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B b}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a C}{2 d}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a}{d}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) b}{d}"," ",0,"1/3*b*C*tan(d*x+c)^3/d+1/2*b*B*tan(d*x+c)^2/d+1/2/d*C*tan(d*x+c)^2*a+1/d*a*B*tan(d*x+c)-b*C*tan(d*x+c)/d-1/2/d*ln(1+tan(d*x+c)^2)*B*b-1/2/d*ln(1+tan(d*x+c)^2)*a*C-1/d*B*arctan(tan(d*x+c))*a+1/d*C*arctan(tan(d*x+c))*b","A"
2,1,105,64,0.024000," ","int((a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","\frac{C b \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b B \tan \left(d x +c \right)}{d}+\frac{C \tan \left(d x +c \right) a}{d}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right) B}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C b}{2 d}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) b}{d}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) a}{d}"," ",0,"1/2/d*C*b*tan(d*x+c)^2+b*B*tan(d*x+c)/d+1/d*C*tan(d*x+c)*a+1/2/d*ln(1+tan(d*x+c)^2)*a*B-1/2/d*ln(1+tan(d*x+c)^2)*C*b-1/d*B*arctan(tan(d*x+c))*b-1/d*C*arctan(tan(d*x+c))*a","A"
3,1,66,42,0.386000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","a B x -b C x -\frac{b B \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{B a c}{d}+\frac{b C \tan \left(d x +c \right)}{d}-\frac{a C \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{C b c}{d}"," ",0,"a*B*x-b*C*x-b*B*ln(cos(d*x+c))/d+1/d*B*a*c+b*C*tan(d*x+c)/d-1/d*a*C*ln(cos(d*x+c))-1/d*C*b*c","A"
4,1,51,37,0.569000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","B x b +a C x +\frac{a B \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{B b c}{d}-\frac{b C \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{C a c}{d}"," ",0,"B*x*b+a*C*x+a*B*ln(sin(d*x+c))/d+1/d*B*b*c-b*C*ln(cos(d*x+c))/d+1/d*C*a*c","A"
5,1,65,43,0.436000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-a B x +b C x -\frac{a B \cot \left(d x +c \right)}{d}+\frac{B b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{B a c}{d}+\frac{a C \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{C b c}{d}"," ",0,"-a*B*x+b*C*x-a*B*cot(d*x+c)/d+1/d*B*b*ln(sin(d*x+c))-1/d*B*a*c+1/d*a*C*ln(sin(d*x+c))+1/d*C*b*c","A"
6,1,96,64,0.523000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-\frac{a B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a B \ln \left(\sin \left(d x +c \right)\right)}{d}-a C x -\frac{C \cot \left(d x +c \right) a}{d}-\frac{C a c}{d}-B x b -\frac{B \cot \left(d x +c \right) b}{d}-\frac{B b c}{d}+\frac{C b \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a*B*cot(d*x+c)^2/d-a*B*ln(sin(d*x+c))/d-a*C*x-1/d*C*cot(d*x+c)*a-1/d*C*a*c-B*x*b-1/d*B*cot(d*x+c)*b-1/d*B*b*c+1/d*C*b*ln(sin(d*x+c))","A"
7,1,124,83,0.513000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-\frac{a B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a B \cot \left(d x +c \right)}{d}+a B x +\frac{B a c}{d}-\frac{a C \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a C \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{B b \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{B b \ln \left(\sin \left(d x +c \right)\right)}{d}-b C x -\frac{C \cot \left(d x +c \right) b}{d}-\frac{C b c}{d}"," ",0,"-1/3*a*B*cot(d*x+c)^3/d+a*B*cot(d*x+c)/d+a*B*x+1/d*B*a*c-1/2/d*a*C*cot(d*x+c)^2-1/d*a*C*ln(sin(d*x+c))-1/2/d*B*b*cot(d*x+c)^2-1/d*B*b*ln(sin(d*x+c))-b*C*x-1/d*C*cot(d*x+c)*b-1/d*C*b*c","A"
8,1,150,102,0.532000," ","int(cot(d*x+c)^6*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-\frac{a B \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a C \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{C \cot \left(d x +c \right) a}{d}+a C x +\frac{C a c}{d}-\frac{B b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{B \cot \left(d x +c \right) b}{d}+B x b +\frac{B b c}{d}-\frac{C b \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{C b \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a*B*cot(d*x+c)^4/d+1/2*a*B*cot(d*x+c)^2/d+a*B*ln(sin(d*x+c))/d-1/3/d*a*C*cot(d*x+c)^3+1/d*C*cot(d*x+c)*a+a*C*x+1/d*C*a*c-1/3/d*B*b*cot(d*x+c)^3+1/d*B*cot(d*x+c)*b+B*x*b+1/d*B*b*c-1/2/d*C*b*cot(d*x+c)^2-1/d*C*b*ln(sin(d*x+c))","A"
9,1,249,142,0.025000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","\frac{b^{2} C \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{B \left(\tan^{3}\left(d x +c \right)\right) b^{2}}{3 d}+\frac{2 C \left(\tan^{3}\left(d x +c \right)\right) a b}{3 d}+\frac{B \left(\tan^{2}\left(d x +c \right)\right) a b}{d}+\frac{C \left(\tan^{2}\left(d x +c \right)\right) a^{2}}{2 d}-\frac{b^{2} C \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} B \tan \left(d x +c \right)}{d}-\frac{b^{2} B \tan \left(d x +c \right)}{d}-\frac{2 C a b \tan \left(d x +c \right)}{d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B a b}{d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} C}{2 d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} C}{2 d}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}+\frac{2 C \arctan \left(\tan \left(d x +c \right)\right) a b}{d}"," ",0,"1/4/d*b^2*C*tan(d*x+c)^4+1/3/d*B*tan(d*x+c)^3*b^2+2/3/d*C*tan(d*x+c)^3*a*b+1/d*B*tan(d*x+c)^2*a*b+1/2/d*C*tan(d*x+c)^2*a^2-1/2/d*b^2*C*tan(d*x+c)^2+a^2*B*tan(d*x+c)/d-b^2*B*tan(d*x+c)/d-2/d*C*a*b*tan(d*x+c)-1/d*ln(1+tan(d*x+c)^2)*B*a*b-1/2/d*ln(1+tan(d*x+c)^2)*a^2*C+1/2/d*ln(1+tan(d*x+c)^2)*b^2*C-1/d*B*arctan(tan(d*x+c))*a^2+1/d*B*arctan(tan(d*x+c))*b^2+2/d*C*arctan(tan(d*x+c))*a*b","A"
10,1,199,108,0.028000," ","int((a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","\frac{b^{2} C \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{B \left(\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d}+\frac{C \left(\tan^{2}\left(d x +c \right)\right) a b}{d}+\frac{2 B \tan \left(d x +c \right) a b}{d}+\frac{C \tan \left(d x +c \right) a^{2}}{d}-\frac{b^{2} C \tan \left(d x +c \right)}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} B}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} B}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C a b}{d}-\frac{2 B \arctan \left(\tan \left(d x +c \right)\right) a b}{d}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}"," ",0,"1/3/d*b^2*C*tan(d*x+c)^3+1/2/d*B*tan(d*x+c)^2*b^2+1/d*C*tan(d*x+c)^2*a*b+2/d*B*tan(d*x+c)*a*b+1/d*C*tan(d*x+c)*a^2-b^2*C*tan(d*x+c)/d+1/2/d*ln(1+tan(d*x+c)^2)*a^2*B-1/2/d*ln(1+tan(d*x+c)^2)*b^2*B-1/d*ln(1+tan(d*x+c)^2)*C*a*b-2/d*B*arctan(tan(d*x+c))*a*b-1/d*C*arctan(tan(d*x+c))*a^2+1/d*C*arctan(tan(d*x+c))*b^2","A"
11,1,140,85,0.496000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","a^{2} B x +\frac{B \,a^{2} c}{d}-\frac{a^{2} C \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{2 B a b \ln \left(\cos \left(d x +c \right)\right)}{d}-2 a b C x +\frac{2 C a b \tan \left(d x +c \right)}{d}-\frac{2 C a b c}{d}-B x \,b^{2}+\frac{b^{2} B \tan \left(d x +c \right)}{d}-\frac{B \,b^{2} c}{d}+\frac{b^{2} C \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{2} C \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"a^2*B*x+1/d*B*a^2*c-1/d*a^2*C*ln(cos(d*x+c))-2/d*B*a*b*ln(cos(d*x+c))-2*a*b*C*x+2/d*C*a*b*tan(d*x+c)-2/d*C*a*b*c-B*x*b^2+b^2*B*tan(d*x+c)/d-1/d*B*b^2*c+1/2/d*b^2*C*tan(d*x+c)^2+b^2*C*ln(cos(d*x+c))/d","A"
12,1,109,70,0.481000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","2 B x a b +a^{2} C x -b^{2} C x +\frac{a^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{2} B \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 B a b c}{d}+\frac{b^{2} C \tan \left(d x +c \right)}{d}-\frac{2 C a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{C \,a^{2} c}{d}-\frac{C \,b^{2} c}{d}"," ",0,"2*B*x*a*b+a^2*C*x-b^2*C*x+a^2*B*ln(sin(d*x+c))/d-b^2*B*ln(cos(d*x+c))/d+2/d*B*a*b*c+b^2*C*tan(d*x+c)/d-2/d*C*a*b*ln(cos(d*x+c))+1/d*C*a^2*c-1/d*C*b^2*c","A"
13,1,110,72,0.515000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-a^{2} B x +B x \,b^{2}+2 a b C x -\frac{a^{2} B \cot \left(d x +c \right)}{d}+\frac{2 B a b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{B \,a^{2} c}{d}+\frac{B \,b^{2} c}{d}+\frac{a^{2} C \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{2} C \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 C a b c}{d}"," ",0,"-a^2*B*x+B*x*b^2+2*a*b*C*x-a^2*B*cot(d*x+c)/d+2/d*B*a*b*ln(sin(d*x+c))-1/d*B*a^2*c+1/d*B*b^2*c+1/d*a^2*C*ln(sin(d*x+c))-b^2*C*ln(cos(d*x+c))/d+2/d*C*a*b*c","A"
14,1,141,86,0.624000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-\frac{a^{2} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}-a^{2} C x -\frac{C \cot \left(d x +c \right) a^{2}}{d}-\frac{C \,a^{2} c}{d}-2 B x a b -\frac{2 B \cot \left(d x +c \right) a b}{d}-\frac{2 B a b c}{d}+\frac{2 C a b \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{b^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}+b^{2} C x +\frac{C \,b^{2} c}{d}"," ",0,"-1/2*a^2*B*cot(d*x+c)^2/d-a^2*B*ln(sin(d*x+c))/d-a^2*C*x-1/d*C*cot(d*x+c)*a^2-1/d*C*a^2*c-2*B*x*a*b-2/d*B*cot(d*x+c)*a*b-2/d*B*a*b*c+2/d*C*a*b*ln(sin(d*x+c))+1/d*b^2*B*ln(sin(d*x+c))+b^2*C*x+1/d*C*b^2*c","A"
15,1,188,114,0.460000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-\frac{a^{2} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} B \cot \left(d x +c \right)}{d}+a^{2} B x +\frac{B \,a^{2} c}{d}-\frac{a^{2} C \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} C \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{B a b \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{2 B a b \ln \left(\sin \left(d x +c \right)\right)}{d}-2 a b C x -\frac{2 C \cot \left(d x +c \right) a b}{d}-\frac{2 C a b c}{d}-B x \,b^{2}-\frac{B \cot \left(d x +c \right) b^{2}}{d}-\frac{B \,b^{2} c}{d}+\frac{b^{2} C \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/3*a^2*B*cot(d*x+c)^3/d+a^2*B*cot(d*x+c)/d+a^2*B*x+1/d*B*a^2*c-1/2/d*a^2*C*cot(d*x+c)^2-1/d*a^2*C*ln(sin(d*x+c))-1/d*B*a*b*cot(d*x+c)^2-2/d*B*a*b*ln(sin(d*x+c))-2*a*b*C*x-2/d*C*cot(d*x+c)*a*b-2/d*C*a*b*c-B*x*b^2-1/d*B*cot(d*x+c)*b^2-1/d*B*b^2*c+1/d*b^2*C*ln(sin(d*x+c))","A"
16,1,238,145,0.562000," ","int(cot(d*x+c)^6*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-\frac{a^{2} B \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} C \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{C \cot \left(d x +c \right) a^{2}}{d}+a^{2} C x +\frac{C \,a^{2} c}{d}-\frac{2 B a b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 B \cot \left(d x +c \right) a b}{d}+2 B x a b +\frac{2 B a b c}{d}-\frac{C a b \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{2 C a b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{2} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}-b^{2} C x -\frac{C \cot \left(d x +c \right) b^{2}}{d}-\frac{C \,b^{2} c}{d}"," ",0,"-1/4*a^2*B*cot(d*x+c)^4/d+1/2*a^2*B*cot(d*x+c)^2/d+a^2*B*ln(sin(d*x+c))/d-1/3/d*a^2*C*cot(d*x+c)^3+1/d*C*cot(d*x+c)*a^2+a^2*C*x+1/d*C*a^2*c-2/3/d*B*a*b*cot(d*x+c)^3+2/d*B*cot(d*x+c)*a*b+2*B*x*a*b+2/d*B*a*b*c-1/d*C*a*b*cot(d*x+c)^2-2/d*C*a*b*ln(sin(d*x+c))-1/2/d*b^2*B*cot(d*x+c)^2-1/d*b^2*B*ln(sin(d*x+c))-b^2*C*x-1/d*C*cot(d*x+c)*b^2-1/d*C*b^2*c","A"
17,1,314,159,0.030000," ","int((a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","\frac{b^{3} C \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{B \left(\tan^{3}\left(d x +c \right)\right) b^{3}}{3 d}+\frac{C \left(\tan^{3}\left(d x +c \right)\right) a \,b^{2}}{d}+\frac{3 B \left(\tan^{2}\left(d x +c \right)\right) a \,b^{2}}{2 d}+\frac{3 C \left(\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d}-\frac{b^{3} C \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 B \tan \left(d x +c \right) a^{2} b}{d}-\frac{B \tan \left(d x +c \right) b^{3}}{d}+\frac{C \tan \left(d x +c \right) a^{3}}{d}-\frac{3 C a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{a^{3} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B a \,b^{2}}{2 d}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) C \,a^{2} b}{2 d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3} C}{2 d}-\frac{3 B \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d}+\frac{3 C \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d}"," ",0,"1/4/d*b^3*C*tan(d*x+c)^4+1/3/d*B*tan(d*x+c)^3*b^3+1/d*C*tan(d*x+c)^3*a*b^2+3/2/d*B*tan(d*x+c)^2*a*b^2+3/2/d*C*tan(d*x+c)^2*a^2*b-1/2/d*b^3*C*tan(d*x+c)^2+3/d*B*tan(d*x+c)*a^2*b-1/d*B*tan(d*x+c)*b^3+1/d*C*tan(d*x+c)*a^3-3/d*C*a*b^2*tan(d*x+c)+1/2/d*ln(1+tan(d*x+c)^2)*a^3*B-3/2/d*ln(1+tan(d*x+c)^2)*B*a*b^2-3/2/d*ln(1+tan(d*x+c)^2)*C*a^2*b+1/2/d*ln(1+tan(d*x+c)^2)*b^3*C-3/d*B*arctan(tan(d*x+c))*a^2*b+1/d*B*arctan(tan(d*x+c))*b^3-1/d*C*arctan(tan(d*x+c))*a^3+3/d*C*arctan(tan(d*x+c))*a*b^2","A"
18,1,234,136,0.473000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","a^{3} B x +\frac{a^{3} B c}{d}-\frac{C \,a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{3 a^{2} b B \ln \left(\cos \left(d x +c \right)\right)}{d}-3 C x \,a^{2} b +\frac{3 C \tan \left(d x +c \right) a^{2} b}{d}-\frac{3 C \,a^{2} b c}{d}-3 B x a \,b^{2}+\frac{3 B \tan \left(d x +c \right) a \,b^{2}}{d}-\frac{3 B a \,b^{2} c}{d}+\frac{3 C a \,b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 C a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{3} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{3} B \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{3} C \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{3} C \tan \left(d x +c \right)}{d}+b^{3} C x +\frac{b^{3} C c}{d}"," ",0,"a^3*B*x+1/d*a^3*B*c-1/d*C*a^3*ln(cos(d*x+c))-3/d*a^2*b*B*ln(cos(d*x+c))-3*C*x*a^2*b+3/d*C*tan(d*x+c)*a^2*b-3/d*C*a^2*b*c-3*B*x*a*b^2+3/d*B*tan(d*x+c)*a*b^2-3/d*B*a*b^2*c+3/2/d*C*a*b^2*tan(d*x+c)^2+3/d*C*a*b^2*ln(cos(d*x+c))+1/2/d*b^3*B*tan(d*x+c)^2+b^3*B*ln(cos(d*x+c))/d+1/3/d*b^3*C*tan(d*x+c)^3-1/d*b^3*C*tan(d*x+c)+b^3*C*x+1/d*b^3*C*c","A"
19,1,183,115,0.566000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","\frac{a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}+a^{3} C x +\frac{C \,a^{3} c}{d}+3 B x \,a^{2} b +\frac{3 B \,a^{2} b c}{d}-\frac{3 C \,a^{2} b \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{3 B a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}-3 a \,b^{2} C x +\frac{3 C a \,b^{2} \tan \left(d x +c \right)}{d}-\frac{3 C a \,b^{2} c}{d}-B x \,b^{3}+\frac{B \tan \left(d x +c \right) b^{3}}{d}-\frac{B \,b^{3} c}{d}+\frac{b^{3} C \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{3} C \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"a^3*B*ln(sin(d*x+c))/d+a^3*C*x+1/d*C*a^3*c+3*B*x*a^2*b+3/d*B*a^2*b*c-3/d*C*a^2*b*ln(cos(d*x+c))-3/d*B*a*b^2*ln(cos(d*x+c))-3*a*b^2*C*x+3/d*C*a*b^2*tan(d*x+c)-3/d*C*a*b^2*c-B*x*b^3+1/d*B*tan(d*x+c)*b^3-1/d*B*b^3*c+1/2/d*b^3*C*tan(d*x+c)^2+b^3*C*ln(cos(d*x+c))/d","A"
20,1,168,119,0.452000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-a^{3} B x +3 B x a \,b^{2}+3 C x \,a^{2} b -b^{3} C x -\frac{B \cot \left(d x +c \right) a^{3}}{d}+\frac{3 a^{2} b B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{3} B \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{a^{3} B c}{d}+\frac{3 B a \,b^{2} c}{d}+\frac{b^{3} C \tan \left(d x +c \right)}{d}+\frac{C \,a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 C a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 C \,a^{2} b c}{d}-\frac{b^{3} C c}{d}"," ",0,"-a^3*B*x+3*B*x*a*b^2+3*C*x*a^2*b-b^3*C*x-1/d*B*cot(d*x+c)*a^3+3/d*a^2*b*B*ln(sin(d*x+c))-b^3*B*ln(cos(d*x+c))/d-1/d*a^3*B*c+3/d*B*a*b^2*c+1/d*b^3*C*tan(d*x+c)+1/d*C*a^3*ln(sin(d*x+c))-3/d*C*a*b^2*ln(cos(d*x+c))+3/d*C*a^2*b*c-1/d*b^3*C*c","A"
21,1,186,125,0.570000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-\frac{a^{3} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}-a^{3} C x -\frac{C \cot \left(d x +c \right) a^{3}}{d}-\frac{C \,a^{3} c}{d}-3 B x \,a^{2} b -\frac{3 B \cot \left(d x +c \right) a^{2} b}{d}-\frac{3 B \,a^{2} b c}{d}+\frac{3 C \,a^{2} b \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{3 B a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+3 a \,b^{2} C x +\frac{3 C a \,b^{2} c}{d}+B x \,b^{3}+\frac{B \,b^{3} c}{d}-\frac{b^{3} C \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^3*B*cot(d*x+c)^2-a^3*B*ln(sin(d*x+c))/d-a^3*C*x-1/d*C*cot(d*x+c)*a^3-1/d*C*a^3*c-3*B*x*a^2*b-3/d*B*cot(d*x+c)*a^2*b-3/d*B*a^2*b*c+3/d*C*a^2*b*ln(sin(d*x+c))+3/d*B*a*b^2*ln(sin(d*x+c))+3*a*b^2*C*x+3/d*C*a*b^2*c+B*x*b^3+1/d*B*b^3*c-b^3*C*ln(cos(d*x+c))/d","A"
22,1,233,148,0.521000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-\frac{a^{3} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{B \cot \left(d x +c \right) a^{3}}{d}+a^{3} B x +\frac{a^{3} B c}{d}-\frac{C \,a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{C \,a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 a^{2} b B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b B \ln \left(\sin \left(d x +c \right)\right)}{d}-3 C x \,a^{2} b -\frac{3 C \cot \left(d x +c \right) a^{2} b}{d}-\frac{3 C \,a^{2} b c}{d}-3 B x a \,b^{2}-\frac{3 B \cot \left(d x +c \right) a \,b^{2}}{d}-\frac{3 B a \,b^{2} c}{d}+\frac{3 C a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{b^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}+b^{3} C x +\frac{b^{3} C c}{d}"," ",0,"-1/3/d*a^3*B*cot(d*x+c)^3+1/d*B*cot(d*x+c)*a^3+a^3*B*x+1/d*a^3*B*c-1/2/d*C*a^3*cot(d*x+c)^2-1/d*C*a^3*ln(sin(d*x+c))-3/2/d*a^2*b*B*cot(d*x+c)^2-3/d*a^2*b*B*ln(sin(d*x+c))-3*C*x*a^2*b-3/d*C*cot(d*x+c)*a^2*b-3/d*C*a^2*b*c-3*B*x*a*b^2-3/d*B*cot(d*x+c)*a*b^2-3/d*B*a*b^2*c+3/d*C*a*b^2*ln(sin(d*x+c))+1/d*b^3*B*ln(sin(d*x+c))+b^3*C*x+1/d*b^3*C*c","A"
23,1,302,185,0.551000," ","int(cot(d*x+c)^6*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-\frac{a^{3} B \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{C \,a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{C \cot \left(d x +c \right) a^{3}}{d}+a^{3} C x +\frac{C \,a^{3} c}{d}-\frac{a^{2} b B \left(\cot^{3}\left(d x +c \right)\right)}{d}+3 B x \,a^{2} b +\frac{3 B \cot \left(d x +c \right) a^{2} b}{d}+\frac{3 B \,a^{2} b c}{d}-\frac{3 C \,a^{2} b \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 C \,a^{2} b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 B a \,b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 B a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-3 a \,b^{2} C x -\frac{3 C \cot \left(d x +c \right) a \,b^{2}}{d}-\frac{3 C a \,b^{2} c}{d}-B x \,b^{3}-\frac{B \cot \left(d x +c \right) b^{3}}{d}-\frac{B \,b^{3} c}{d}+\frac{b^{3} C \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/4/d*a^3*B*cot(d*x+c)^4+1/2/d*a^3*B*cot(d*x+c)^2+a^3*B*ln(sin(d*x+c))/d-1/3/d*C*a^3*cot(d*x+c)^3+1/d*C*cot(d*x+c)*a^3+a^3*C*x+1/d*C*a^3*c-1/d*a^2*b*B*cot(d*x+c)^3+3*B*x*a^2*b+3/d*B*cot(d*x+c)*a^2*b+3/d*B*a^2*b*c-3/2/d*C*a^2*b*cot(d*x+c)^2-3/d*C*a^2*b*ln(sin(d*x+c))-3/2/d*B*a*b^2*cot(d*x+c)^2-3/d*B*a*b^2*ln(sin(d*x+c))-3*a*b^2*C*x-3/d*C*cot(d*x+c)*a*b^2-3/d*C*a*b^2*c-B*x*b^3-1/d*B*cot(d*x+c)*b^3-1/d*B*b^3*c+1/d*b^3*C*ln(sin(d*x+c))","A"
24,1,376,225,0.536000," ","int(cot(d*x+c)^7*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x)","-a^{3} B x -\frac{3 C a \,b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{C \,a^{2} b \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{2} b B \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{B a \,b^{2} \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{a^{3} B c}{d}+\frac{C \,a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{C \,a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{3} C c}{d}+3 C x \,a^{2} b +3 B x a \,b^{2}-\frac{B \cot \left(d x +c \right) a^{3}}{d}+\frac{3 a^{2} b B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{a^{3} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{C \,a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} B \left(\cot^{5}\left(d x +c \right)\right)}{5 d}-\frac{b^{3} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{C \cot \left(d x +c \right) b^{3}}{d}+\frac{3 C \cot \left(d x +c \right) a^{2} b}{d}+\frac{3 B \cot \left(d x +c \right) a \,b^{2}}{d}-\frac{3 C a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{3 C \,a^{2} b c}{d}+\frac{3 B a \,b^{2} c}{d}-b^{3} C x +\frac{3 a^{2} b B \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-a^3*B*x+3/2/d*a^2*b*B*cot(d*x+c)^2-1/d*a^3*B*c+1/d*C*a^3*ln(sin(d*x+c))-1/d*b^3*C*c+3*C*x*a^2*b+3*B*x*a*b^2-1/d*B*cot(d*x+c)*a^3+1/3/d*a^3*B*cot(d*x+c)^3+1/2/d*C*a^3*cot(d*x+c)^2-1/d*b^3*B*ln(sin(d*x+c))-1/4/d*C*a^3*cot(d*x+c)^4-1/5/d*a^3*B*cot(d*x+c)^5-1/2/d*b^3*B*cot(d*x+c)^2-1/d*C*cot(d*x+c)*b^3+3/d*C*cot(d*x+c)*a^2*b+3/d*B*cot(d*x+c)*a*b^2-3/d*C*a*b^2*ln(sin(d*x+c))+3/d*C*a^2*b*c+3/d*B*a*b^2*c-b^3*C*x-3/2/d*C*a*b^2*cot(d*x+c)^2-1/d*C*a^2*b*cot(d*x+c)^3-3/4/d*a^2*b*B*cot(d*x+c)^4-1/d*B*a*b^2*cot(d*x+c)^3+3/d*a^2*b*B*ln(sin(d*x+c))","A"
25,1,211,125,0.255000," ","int(tan(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x)","\frac{C \left(\tan^{2}\left(d x +c \right)\right)}{2 b d}+\frac{B \tan \left(d x +c \right)}{b d}-\frac{C \tan \left(d x +c \right) a}{d \,b^{2}}-\frac{a^{3} B \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{2} \left(a^{2}+b^{2}\right) d}+\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \,b^{3} \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a B}{2 d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) a}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/2*C*tan(d*x+c)^2/b/d+B*tan(d*x+c)/b/d-1/d/b^2*C*tan(d*x+c)*a-a^3*B*ln(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d+1/d/b^3*a^4/(a^2+b^2)*ln(a+b*tan(d*x+c))*C-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*B-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*C*b-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b+1/d/(a^2+b^2)*C*arctan(tan(d*x+c))*a","A"
26,1,179,101,0.255000," ","int(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x)","\frac{C \tan \left(d x +c \right)}{b d}+\frac{a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d b \left(a^{2}+b^{2}\right)}-\frac{a^{3} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \,b^{2} \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B b}{2 d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a C}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a}{d \left(a^{2}+b^{2}\right)}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}"," ",0,"C*tan(d*x+c)/b/d+1/d/b*a^2/(a^2+b^2)*ln(a+b*tan(d*x+c))*B-1/d/b^2*a^3/(a^2+b^2)*ln(a+b*tan(d*x+c))*C+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*C-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a-1/d/(a^2+b^2)*C*arctan(tan(d*x+c))*b","A"
27,1,159,85,0.276000," ","int((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x)","-\frac{a \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)}+\frac{a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right) b}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a B}{2 d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C b}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) a}{d \left(a^{2}+b^{2}\right)}"," ",0,"-1/d*a/(a^2+b^2)*ln(a+b*tan(d*x+c))*B+1/d*a^2/(a^2+b^2)/b*ln(a+b*tan(d*x+c))*C+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*B+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*C*b+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b-1/d/(a^2+b^2)*C*arctan(tan(d*x+c))*a","A"
28,1,153,58,0.732000," ","int(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x)","\frac{\ln \left(a +b \tan \left(d x +c \right)\right) B b}{d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(a +b \tan \left(d x +c \right)\right) a C}{d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B b}{2 d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a C}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) a}{d \left(a^{2}+b^{2}\right)}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/d/(a^2+b^2)*ln(a+b*tan(d*x+c))*B*b-1/d/(a^2+b^2)*ln(a+b*tan(d*x+c))*a*C-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*C+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a+1/d/(a^2+b^2)*C*arctan(tan(d*x+c))*b","B"
29,1,174,80,0.936000," ","int(cot(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x)","-\frac{b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d a \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)}+\frac{B \ln \left(\tan \left(d x +c \right)\right)}{d a}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a B}{2 d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) a}{d \left(a^{2}+b^{2}\right)}"," ",0,"-1/d*b^2/a/(a^2+b^2)*ln(a+b*tan(d*x+c))*B+1/d*b/(a^2+b^2)*ln(a+b*tan(d*x+c))*C+1/d*B/a*ln(tan(d*x+c))-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*B-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*C*b-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b+1/d/(a^2+b^2)*C*arctan(tan(d*x+c))*a","B"
30,1,214,103,0.756000," ","int(cot(d*x+c)^3*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x)","\frac{b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{2} \left(a^{2}+b^{2}\right)}-\frac{b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d a \left(a^{2}+b^{2}\right)}-\frac{B}{d a \tan \left(d x +c \right)}-\frac{\ln \left(\tan \left(d x +c \right)\right) B b}{d \,a^{2}}+\frac{\ln \left(\tan \left(d x +c \right)\right) C}{d a}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B b}{2 d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a C}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a}{d \left(a^{2}+b^{2}\right)}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/d*b^3/a^2/(a^2+b^2)*ln(a+b*tan(d*x+c))*B-1/d*b^2/a/(a^2+b^2)*ln(a+b*tan(d*x+c))*C-1/d*B/a/tan(d*x+c)-1/d/a^2*ln(tan(d*x+c))*B*b+1/d/a*ln(tan(d*x+c))*C+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*C-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a-1/d/(a^2+b^2)*C*arctan(tan(d*x+c))*b","B"
31,1,266,135,0.981000," ","int(cot(d*x+c)^4*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x)","-\frac{b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{3} \left(a^{2}+b^{2}\right)}+\frac{b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \,a^{2} \left(a^{2}+b^{2}\right)}-\frac{B}{2 d a \tan \left(d x +c \right)^{2}}+\frac{B b}{d \,a^{2} \tan \left(d x +c \right)}-\frac{C}{d a \tan \left(d x +c \right)}-\frac{B \ln \left(\tan \left(d x +c \right)\right)}{d a}+\frac{\ln \left(\tan \left(d x +c \right)\right) b^{2} B}{d \,a^{3}}-\frac{\ln \left(\tan \left(d x +c \right)\right) C b}{d \,a^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a B}{2 d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C b}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) a}{d \left(a^{2}+b^{2}\right)}"," ",0,"-1/d*b^4/a^3/(a^2+b^2)*ln(a+b*tan(d*x+c))*B+1/d*b^3/a^2/(a^2+b^2)*ln(a+b*tan(d*x+c))*C-1/2/d*B/a/tan(d*x+c)^2+1/d/a^2/tan(d*x+c)*B*b-1/d/a/tan(d*x+c)*C-1/d*B/a*ln(tan(d*x+c))+1/d/a^3*ln(tan(d*x+c))*b^2*B-1/d/a^2*ln(tan(d*x+c))*C*b+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*B+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*C*b+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b-1/d/(a^2+b^2)*C*arctan(tan(d*x+c))*a","A"
32,1,364,208,0.252000," ","int(tan(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x)","\frac{C \tan \left(d x +c \right)}{d \,b^{2}}+\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{3 a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 a^{5} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2}}-\frac{4 a^{3} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d b \left(a^{2}+b^{2}\right)^{2}}+\frac{a^{3} B}{d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{4} C}{d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 B \arctan \left(\tan \left(d x +c \right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d*C/b^2*tan(d*x+c)+1/d/b^2*a^4/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B+3/d*a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B-2/d/b^3*a^5/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*C-4/d/b*a^3/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*C+1/d/b^2*a^3/(a^2+b^2)/(a+b*tan(d*x+c))*B-1/d/b^3*a^4/(a^2+b^2)/(a+b*tan(d*x+c))*C-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*B+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2*B-1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*C*a*b-2/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*a*b+1/d/(a^2+b^2)^2*C*arctan(tan(d*x+c))*a^2-1/d/(a^2+b^2)^2*C*arctan(tan(d*x+c))*b^2","A"
33,1,313,157,0.316000," ","int(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} B}{d b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{3} C}{d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 a b \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{2} b^{2}}+\frac{3 a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} C}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} C}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 C \arctan \left(\tan \left(d x +c \right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-1/d*a^2/b/(a^2+b^2)/(a+b*tan(d*x+c))*B+1/d*a^3/b^2/(a^2+b^2)/(a+b*tan(d*x+c))*C-2/d*a/(a^2+b^2)^2*b*ln(a+b*tan(d*x+c))*B+1/d*a^4/(a^2+b^2)^2/b^2*ln(a+b*tan(d*x+c))*C+3/d*a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*C+1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*B*a*b-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*C+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2*C-1/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*a^2+1/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*b^2-2/d/(a^2+b^2)^2*C*arctan(tan(d*x+c))*a*b","A"
34,1,305,115,0.307000," ","int((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x)","\frac{a B}{d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{2} C}{d \left(a^{2}+b^{2}\right) b \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) b^{2} B}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 \ln \left(a +b \tan \left(d x +c \right)\right) C a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(d x +c \right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d*a/(a^2+b^2)/(a+b*tan(d*x+c))*B-1/d*a^2/(a^2+b^2)/b/(a+b*tan(d*x+c))*C-1/d*a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B+1/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*b^2*B-2/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*C*a*b+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*B-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2*B+1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*C*a*b+2/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*a*b-1/d/(a^2+b^2)^2*C*arctan(tan(d*x+c))*a^2+1/d/(a^2+b^2)^2*C*arctan(tan(d*x+c))*b^2","B"
35,1,301,110,0.765000," ","int(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x)","-\frac{B b}{d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}+\frac{a C}{d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 a b \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) b^{2} C}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} C}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} C}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{2 C \arctan \left(\tan \left(d x +c \right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-1/d/(a^2+b^2)/(a+b*tan(d*x+c))*B*b+1/d/(a^2+b^2)/(a+b*tan(d*x+c))*a*C+2/d*a/(a^2+b^2)^2*b*ln(a+b*tan(d*x+c))*B-1/d*a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*C+1/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*b^2*C-1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*B*a*b+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*C-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2*C+1/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*a^2-1/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*b^2+2/d/(a^2+b^2)^2*C*arctan(tan(d*x+c))*a*b","B"
36,1,325,137,0.837000," ","int(cot(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x)","-\frac{3 \ln \left(a +b \tan \left(d x +c \right)\right) b^{2} B}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \ln \left(a +b \tan \left(d x +c \right)\right) C a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{b^{2} B}{d a \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{b C}{d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}+\frac{B \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 B \arctan \left(\tan \left(d x +c \right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-3/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*b^2*B-1/d*b^4/a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B+2/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*C*a*b+1/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))*B-1/d*b/(a^2+b^2)/(a+b*tan(d*x+c))*C+1/d*B/a^2*ln(tan(d*x+c))-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*B+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2*B-1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*C*a*b-2/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*a*b+1/d/(a^2+b^2)^2*C*arctan(tan(d*x+c))*a^2-1/d/(a^2+b^2)^2*C*arctan(tan(d*x+c))*b^2","B"
37,1,399,192,0.856000," ","int(cot(d*x+c)^3*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x)","\frac{4 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d a \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{3} \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \ln \left(a +b \tan \left(d x +c \right)\right) b^{2} C}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{3} B}{d \,a^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{2} C}{d a \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{B}{d \,a^{2} \tan \left(d x +c \right)}-\frac{2 \ln \left(\tan \left(d x +c \right)\right) B b}{d \,a^{3}}+\frac{\ln \left(\tan \left(d x +c \right)\right) C}{d \,a^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} C}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} C}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 C \arctan \left(\tan \left(d x +c \right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"4/d*b^3/a/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B+2/d*b^5/a^3/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B-3/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*b^2*C-1/d*b^4/a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*C-1/d*b^3/a^2/(a^2+b^2)/(a+b*tan(d*x+c))*B+1/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))*C-1/d*B/a^2/tan(d*x+c)-2/d/a^3*ln(tan(d*x+c))*B*b+1/d/a^2*ln(tan(d*x+c))*C+1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*B*a*b-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*C+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2*C-1/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*a^2+1/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*b^2-2/d/(a^2+b^2)^2*C*arctan(tan(d*x+c))*a*b","B"
38,1,619,327,0.283000," ","int(tan(d*x+c)^3*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x)","\frac{C \tan \left(d x +c \right)}{d \,b^{3}}+\frac{a^{6} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,b^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{3 a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d b \left(a^{2}+b^{2}\right)^{3}}+\frac{6 b \,a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a^{7} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \,b^{4} \left(a^{2}+b^{2}\right)^{3}}-\frac{9 a^{5} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \,b^{2} \left(a^{2}+b^{2}\right)^{3}}-\frac{10 a^{3} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{a^{4} B}{2 d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{5} C}{2 d \,b^{4} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{2 a^{5} B}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 a^{3} B}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{6} C}{d \,b^{4} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{5 a^{4} C}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b B}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3} B}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C \,a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) C a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 C \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/d*C/b^3*tan(d*x+c)+1/d/b^3*a^6/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B+3/d/b*a^4/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B+6/d*b*a^2/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-3/d/b^4*a^7/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C-9/d/b^2*a^5/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C-10/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C-1/2/d/b^3*a^4/(a^2+b^2)/(a+b*tan(d*x+c))^2*B+1/2/d/b^4*a^5/(a^2+b^2)/(a+b*tan(d*x+c))^2*C+2/d/b^3*a^5/(a^2+b^2)^2/(a+b*tan(d*x+c))*B+4/d/b*a^3/(a^2+b^2)^2/(a+b*tan(d*x+c))*B-3/d/b^4*a^6/(a^2+b^2)^2/(a+b*tan(d*x+c))*C-5/d/b^2*a^4/(a^2+b^2)^2/(a+b*tan(d*x+c))*C-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b*B+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3*B+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a^3-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a*b^2+1/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a^3-3/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a*b^2+3/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a^2*b-1/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*b^3","A"
39,1,566,248,0.283000," ","int(tan(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a \,b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{a^{6} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{3} b^{3}}+\frac{3 a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{3} b}+\frac{6 a^{2} b \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{a^{4} B}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{2} B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 a^{5} C}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 a^{3} C}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{3} B}{2 d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{4} C}{2 d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3} B}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) C \,a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3} C}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 C \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-3/d*a/(a^2+b^2)^3*b^2*ln(a+b*tan(d*x+c))*B+1/d*a^6/(a^2+b^2)^3/b^3*ln(a+b*tan(d*x+c))*C+3/d*a^4/(a^2+b^2)^3/b*ln(a+b*tan(d*x+c))*C+6/d*a^2/(a^2+b^2)^3*b*ln(a+b*tan(d*x+c))*C-1/d*a^4/b^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*B-3/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*B+2/d*a^5/b^3/(a^2+b^2)^2/(a+b*tan(d*x+c))*C+4/d*a^3/b/(a^2+b^2)^2/(a+b*tan(d*x+c))*C+1/2/d*a^3/b^2/(a^2+b^2)/(a+b*tan(d*x+c))^2*B-1/2/d*a^4/b^3/(a^2+b^2)/(a+b*tan(d*x+c))^2*C-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^3*B+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*B*a*b^2-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a^2*b+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3*C-3/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a^2*b+1/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*b^3+1/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a^3-3/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a*b^2","B"
40,1,495,187,0.342000," ","int(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x)","-\frac{a^{2} B}{2 d b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{3} C}{2 d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 b \,a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) b^{3} B}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{a^{3} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \tan \left(d x +c \right)\right) C a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{2 a b B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{4} C}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{2} C}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b B}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3} B}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C \,a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) C a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 C \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/2/d*a^2/b/(a^2+b^2)/(a+b*tan(d*x+c))^2*B+1/2/d*a^3/b^2/(a^2+b^2)/(a+b*tan(d*x+c))^2*C-3/d*b*a^2/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B+1/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*b^3*B+1/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C-3/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C*a*b^2+2/d*a/(a^2+b^2)^2*b/(a+b*tan(d*x+c))*B-1/d/b^2*a^4/(a^2+b^2)^2/(a+b*tan(d*x+c))*C-3/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*C+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b*B-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3*B-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a^3+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a*b^2-1/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a^3+3/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a*b^2-3/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a^2*b+1/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*b^3","B"
41,1,488,177,0.287000," ","int((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x)","\frac{a B}{2 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{2} C}{2 d \left(a^{2}+b^{2}\right) b \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{2} B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{2} B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 C a b}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{3} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 a \,b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a^{2} b \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) b^{3} C}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3} B}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) C \,a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3} C}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 C \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/2/d*a/(a^2+b^2)/(a+b*tan(d*x+c))^2*B-1/2/d*a^2/(a^2+b^2)/b/(a+b*tan(d*x+c))^2*C+1/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*B-1/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*b^2*B+2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*C*a*b-1/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B+3/d*a/(a^2+b^2)^3*b^2*ln(a+b*tan(d*x+c))*B-3/d*a^2/(a^2+b^2)^3*b*ln(a+b*tan(d*x+c))*C+1/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*b^3*C+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^3*B-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*B*a*b^2+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a^2*b-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3*C+3/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a^2*b-1/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*b^3-1/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a^3+3/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a*b^2","B"
42,1,483,172,0.740000," ","int(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x)","\frac{3 b \,a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(d x +c \right)\right) b^{3} B}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{a^{3} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(a +b \tan \left(d x +c \right)\right) C a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{B b}{2 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a C}{2 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{2 a b B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{2} C}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{2} C}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b B}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3} B}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C \,a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) C a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 C \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{C \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"3/d*b*a^2/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-1/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*b^3*B-1/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C+3/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C*a*b^2-1/2/d/(a^2+b^2)/(a+b*tan(d*x+c))^2*B*b+1/2/d/(a^2+b^2)/(a+b*tan(d*x+c))^2*a*C-2/d*a/(a^2+b^2)^2*b/(a+b*tan(d*x+c))*B+1/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*C-1/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*b^2*C-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b*B+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3*B+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a^3-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a*b^2+1/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a^3-3/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a*b^2+3/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a^2*b-1/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*b^3","B"
43,1,540,213,1.059000," ","int(cot(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x)","\frac{3 b^{2} B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{4} B}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 C a b}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{6 a \,b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d a \left(a^{2}+b^{2}\right)^{3}}-\frac{b^{6} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{3 a^{2} b \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(d x +c \right)\right) b^{3} C}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{b^{2} B}{2 d a \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b C}{2 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{B \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3} B}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) C \,a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3} C}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 C \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"3/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*b^2*B+1/d*b^4/a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*B-2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*C*a*b-6/d*a/(a^2+b^2)^3*b^2*ln(a+b*tan(d*x+c))*B-3/d*b^4/a/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-1/d*b^6/a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B+3/d*a^2/(a^2+b^2)^3*b*ln(a+b*tan(d*x+c))*C-1/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*b^3*C+1/2/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))^2*B-1/2/d*b/(a^2+b^2)/(a+b*tan(d*x+c))^2*C+1/d*B/a^3*ln(tan(d*x+c))-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^3*B+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*B*a*b^2-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a^2*b+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3*C-3/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a^2*b+1/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*b^3+1/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a^3-3/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a*b^2","B"
44,1,651,285,0.930000," ","int(cot(d*x+c)^3*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x)","-\frac{4 b^{3} B}{d a \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 b^{5} B}{d \,a^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 b^{2} C}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{4} C}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{10 \ln \left(a +b \tan \left(d x +c \right)\right) b^{3} B}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{9 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{2} \left(a^{2}+b^{2}\right)^{3}}+\frac{3 b^{7} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{4} \left(a^{2}+b^{2}\right)^{3}}-\frac{6 \ln \left(a +b \tan \left(d x +c \right)\right) C a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d a \left(a^{2}+b^{2}\right)^{3}}-\frac{b^{6} \ln \left(a +b \tan \left(d x +c \right)\right) C}{d \,a^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{b^{3} B}{2 d \,a^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{b^{2} C}{2 d a \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{B}{d \,a^{3} \tan \left(d x +c \right)}-\frac{3 \ln \left(\tan \left(d x +c \right)\right) B b}{d \,a^{4}}+\frac{\ln \left(\tan \left(d x +c \right)\right) C}{d \,a^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b B}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3} B}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) C \,a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) C a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 C \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{C \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-4/d*b^3/a/(a^2+b^2)^2/(a+b*tan(d*x+c))*B-2/d*b^5/a^3/(a^2+b^2)^2/(a+b*tan(d*x+c))*B+3/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*b^2*C+1/d*b^4/a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*C+10/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*b^3*B+9/d*b^5/a^2/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B+3/d*b^7/a^4/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-6/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C*a*b^2-3/d*b^4/a/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C-1/d*b^6/a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*C-1/2/d*b^3/a^2/(a^2+b^2)/(a+b*tan(d*x+c))^2*B+1/2/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))^2*C-1/d*B/a^3/tan(d*x+c)-3/d/a^4*ln(tan(d*x+c))*B*b+1/d/a^3*ln(tan(d*x+c))*C+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b*B-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3*B-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a^3+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*C*a*b^2-1/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a^3+3/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a*b^2-3/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*a^2*b+1/d/(a^2+b^2)^3*C*arctan(tan(d*x+c))*b^3","B"
45,0,0,128,1.112000," ","int(tan(d*x+c)^2*(b*tan(d*x+c))^n*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x)","\int \left(\tan^{2}\left(d x +c \right)\right) \left(b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)+C \left(\tan^{2}\left(d x +c \right)\right)\right)\, dx"," ",0,"int(tan(d*x+c)^2*(b*tan(d*x+c))^n*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x)","F"
46,-1,0,158,180.000000," ","int(tan(d*x+c)^m*(b*tan(d*x+c))^n*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)+C \left(\tan^{2}\left(d x +c \right)\right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(b*tan(d*x+c))^n*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x)","F"
47,0,0,152,1.706000," ","int(tan(d*x+c)^m*(b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \sqrt{b \tan \left(d x +c \right)}\, \left(A +B \tan \left(d x +c \right)+C \left(\tan^{2}\left(d x +c \right)\right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x)","F"
48,0,0,152,1.761000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c)+C*tan(d*x+c)^2)/(b*tan(d*x+c))^(1/2),x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)+C \left(\tan^{2}\left(d x +c \right)\right)\right)}{\sqrt{b \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c)+C*tan(d*x+c)^2)/(b*tan(d*x+c))^(1/2),x)","F"
49,0,0,300,2.042000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^(1/2),x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)+C \left(\tan^{2}\left(d x +c \right)\right)\right)}{\sqrt{a +b \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^(1/2),x)","F"
50,1,994,345,0.032000," ","int((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{3} c}{2 f}+\frac{C \,b^{3} d \left(\tan^{5}\left(f x +e \right)\right)}{5 f}-\frac{B \left(\tan^{2}\left(f x +e \right)\right) b^{3} d}{2 f}+\frac{A \left(\tan^{3}\left(f x +e \right)\right) b^{3} d}{3 f}+\frac{B \left(\tan^{4}\left(f x +e \right)\right) b^{3} d}{4 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,b^{2} d}{2 f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) a \,b^{2} d}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} b c}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{3} d}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} b d}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,b^{2} c}{2 f}+\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} c}{2 f}+\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) a^{2} b d}{2 f}-\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} d}{2 f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,b^{2} d}{2 f}+\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) a^{2} b c}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{3} c}{2 f}+\frac{B \,a^{3} d \tan \left(f x +e \right)}{f}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f}+\frac{C \,b^{3} d \tan \left(f x +e \right)}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) b^{3} c}{3 f}-\frac{C \left(\tan^{2}\left(f x +e \right)\right) b^{3} c}{2 f}+\frac{A \left(\tan^{2}\left(f x +e \right)\right) b^{3} c}{2 f}+\frac{C \left(\tan^{4}\left(f x +e \right)\right) b^{3} c}{4 f}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{3} d}{f}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{3} c}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f}-\frac{B \,b^{3} c \tan \left(f x +e \right)}{f}+\frac{C \,a^{3} c \tan \left(f x +e \right)}{f}-\frac{A \,b^{3} d \tan \left(f x +e \right)}{f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} C d}{2 f}-\frac{C \left(\tan^{3}\left(f x +e \right)\right) b^{3} d}{3 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{3} c}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{3} d}{2 f}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c}{f}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d}{f}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f}-\frac{3 C \,a^{2} b d \tan \left(f x +e \right)}{f}+\frac{3 B \,a^{2} b c \tan \left(f x +e \right)}{f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) a^{3} d}{2 f}-\frac{3 C a \,b^{2} c \tan \left(f x +e \right)}{f}+\frac{3 A \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} d}{2 f}+\frac{3 A \,a^{2} b d \tan \left(f x +e \right)}{f}+\frac{3 A a \,b^{2} c \tan \left(f x +e \right)}{f}-\frac{3 B a \,b^{2} d \tan \left(f x +e \right)}{f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) a^{2} b d}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} b c}{2 f}+\frac{3 C \left(\tan^{4}\left(f x +e \right)\right) a \,b^{2} d}{4 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) a \,b^{2} c}{f}"," ",0,"1/2/f*ln(1+tan(f*x+e)^2)*A*a^3*d-1/2/f*ln(1+tan(f*x+e)^2)*A*b^3*c+1/4/f*B*tan(f*x+e)^4*b^3*d-1/2/f*B*tan(f*x+e)^2*b^3*d+1/2/f*C*tan(f*x+e)^2*a^3*d-1/3/f*C*tan(f*x+e)^3*b^3*d+1/2/f*ln(1+tan(f*x+e)^2)*B*a^3*c+1/2/f*ln(1+tan(f*x+e)^2)*B*b^3*d-1/2/f*ln(1+tan(f*x+e)^2)*a^3*C*d+1/3/f*A*tan(f*x+e)^3*b^3*d+1/3/f*B*tan(f*x+e)^3*b^3*c-3/2/f*ln(1+tan(f*x+e)^2)*A*a*b^2*d+1/f*B*a^3*d*tan(f*x+e)+1/f*B*tan(f*x+e)^3*a*b^2*d-3/2/f*ln(1+tan(f*x+e)^2)*C*a^2*b*c+3/f*C*arctan(tan(f*x+e))*a*b^2*c-3/2/f*ln(1+tan(f*x+e)^2)*B*a^2*b*d-3/2/f*ln(1+tan(f*x+e)^2)*B*a*b^2*c-3/f*A*arctan(tan(f*x+e))*a^2*b*d+1/f*C*b^3*d*tan(f*x+e)-1/2/f*C*tan(f*x+e)^2*b^3*c+1/2/f*A*tan(f*x+e)^2*b^3*c+1/4/f*C*tan(f*x+e)^4*b^3*c-1/f*C*arctan(tan(f*x+e))*b^3*d-1/f*B*arctan(tan(f*x+e))*a^3*d+1/f*B*arctan(tan(f*x+e))*b^3*c-1/f*C*arctan(tan(f*x+e))*a^3*c-1/f*B*b^3*c*tan(f*x+e)+1/f*C*a^3*c*tan(f*x+e)-1/f*A*b^3*d*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*C*b^3*c+1/f*A*arctan(tan(f*x+e))*a^3*c+1/f*A*arctan(tan(f*x+e))*b^3*d+1/5/f*C*b^3*d*tan(f*x+e)^5-3/f*A*arctan(tan(f*x+e))*a*b^2*c-3/f*B*arctan(tan(f*x+e))*a^2*b*c+3/2/f*A*tan(f*x+e)^2*a*b^2*d+3/f*B*arctan(tan(f*x+e))*a*b^2*d+1/f*C*tan(f*x+e)^3*a^2*b*d+3/f*C*arctan(tan(f*x+e))*a^2*b*d-3/f*C*a^2*b*d*tan(f*x+e)+1/f*C*tan(f*x+e)^3*a*b^2*c+3/2/f*B*tan(f*x+e)^2*a*b^2*c+3/f*B*a^2*b*c*tan(f*x+e)+3/2/f*B*tan(f*x+e)^2*a^2*b*d+3/2/f*ln(1+tan(f*x+e)^2)*A*a^2*b*c-3/f*C*a*b^2*c*tan(f*x+e)+3/f*A*a^2*b*d*tan(f*x+e)+3/4/f*C*tan(f*x+e)^4*a*b^2*d+3/f*A*a*b^2*c*tan(f*x+e)-3/f*B*a*b^2*d*tan(f*x+e)-3/2/f*C*tan(f*x+e)^2*a*b^2*d+3/2/f*ln(1+tan(f*x+e)^2)*C*a*b^2*d+3/2/f*C*tan(f*x+e)^2*a^2*b*c","B"
51,1,631,242,0.028000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f}+\frac{2 A a b d \tan \left(f x +e \right)}{f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) b^{2} d}{3 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) b^{2} c}{3 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} d}{2 f}-\frac{B \,b^{2} d \tan \left(f x +e \right)}{f}+\frac{B \,a^{2} d \tan \left(f x +e \right)}{f}+\frac{A \,b^{2} c \tan \left(f x +e \right)}{f}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{2} d}{f}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{2} d}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c}{2 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) a^{2} d}{2 f}-\frac{C \,b^{2} c \tan \left(f x +e \right)}{f}+\frac{C \,a^{2} c \tan \left(f x +e \right)}{f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f}+\frac{A \left(\tan^{2}\left(f x +e \right)\right) b^{2} d}{2 f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) b^{2} c}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} d}{2 f}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f}+\frac{C \,b^{2} d \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} d}{2 f}-\frac{C \left(\tan^{2}\left(f x +e \right)\right) b^{2} d}{2 f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) a b d}{f}-\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) a b d}{f}-\frac{2 C a b d \tan \left(f x +e \right)}{f}+\frac{2 C \left(\tan^{3}\left(f x +e \right)\right) a b d}{3 f}+\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) a b d}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b c}{f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) a b c}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b d}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b c}{f}+\frac{2 B a b c \tan \left(f x +e \right)}{f}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b c}{f}"," ",0,"-1/f*C*arctan(tan(f*x+e))*a^2*c+1/f*C*arctan(tan(f*x+e))*b^2*c-1/2/f*ln(1+tan(f*x+e)^2)*B*b^2*c+1/3/f*B*tan(f*x+e)^3*b^2*d+1/3/f*C*tan(f*x+e)^3*b^2*c+2/f*A*a*b*d*tan(f*x+e)-1/f*B*b^2*d*tan(f*x+e)+1/f*B*a^2*d*tan(f*x+e)+1/f*A*b^2*c*tan(f*x+e)-1/f*B*arctan(tan(f*x+e))*a^2*d+1/f*B*arctan(tan(f*x+e))*b^2*d-1/2/f*ln(1+tan(f*x+e)^2)*C*a^2*d+1/2/f*A*tan(f*x+e)^2*b^2*d+1/2/f*B*tan(f*x+e)^2*b^2*c-1/2/f*ln(1+tan(f*x+e)^2)*A*b^2*d+1/2/f*ln(1+tan(f*x+e)^2)*B*a^2*c+1/2/f*C*tan(f*x+e)^2*a^2*d+1/4/f*C*b^2*d*tan(f*x+e)^4-1/f*C*b^2*c*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*A*a^2*d+1/f*C*a^2*c*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*C*b^2*d+1/f*A*arctan(tan(f*x+e))*a^2*c-1/2/f*C*tan(f*x+e)^2*b^2*d-1/f*A*arctan(tan(f*x+e))*b^2*c-1/f*ln(1+tan(f*x+e)^2)*C*a*b*c-2/f*A*arctan(tan(f*x+e))*a*b*d-2/f*C*a*b*d*tan(f*x+e)+1/f*C*tan(f*x+e)^2*a*b*c+2/f*C*arctan(tan(f*x+e))*a*b*d-1/f*ln(1+tan(f*x+e)^2)*B*a*b*d+1/f*ln(1+tan(f*x+e)^2)*A*a*b*c+1/f*B*tan(f*x+e)^2*a*b*d+2/f*B*a*b*c*tan(f*x+e)-2/f*B*arctan(tan(f*x+e))*a*b*c+2/3/f*C*tan(f*x+e)^3*a*b*d","B"
52,1,334,157,0.025000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\frac{C b d \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) b d}{2 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) a d}{2 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) b c}{2 f}+\frac{A b d \tan \left(f x +e \right)}{f}+\frac{B a d \tan \left(f x +e \right)}{f}+\frac{B b c \tan \left(f x +e \right)}{f}+\frac{C a c \tan \left(f x +e \right)}{f}-\frac{C b d \tan \left(f x +e \right)}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b c}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a c}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b d}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a C d}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b c}{2 f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a c}{f}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b d}{f}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) a d}{f}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b c}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a c}{f}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b d}{f}"," ",0,"1/3/f*C*b*d*tan(f*x+e)^3+1/2/f*B*tan(f*x+e)^2*b*d+1/2/f*C*tan(f*x+e)^2*a*d+1/2/f*C*tan(f*x+e)^2*b*c+1/f*A*b*d*tan(f*x+e)+1/f*B*a*d*tan(f*x+e)+1/f*B*b*c*tan(f*x+e)+1/f*C*a*c*tan(f*x+e)-1/f*C*b*d*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*A*a*d+1/2/f*ln(1+tan(f*x+e)^2)*A*b*c+1/2/f*ln(1+tan(f*x+e)^2)*B*a*c-1/2/f*ln(1+tan(f*x+e)^2)*B*b*d-1/2/f*ln(1+tan(f*x+e)^2)*a*C*d-1/2/f*ln(1+tan(f*x+e)^2)*C*b*c+1/f*A*arctan(tan(f*x+e))*a*c-1/f*A*arctan(tan(f*x+e))*b*d-1/f*B*arctan(tan(f*x+e))*a*d-1/f*B*arctan(tan(f*x+e))*b*c-1/f*C*arctan(tan(f*x+e))*a*c+1/f*C*arctan(tan(f*x+e))*b*d","B"
53,1,136,71,0.025000," ","int((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\frac{C d \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{B d \tan \left(f x +e \right)}{f}+\frac{c C \tan \left(f x +e \right)}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B c}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C d}{2 f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) c}{f}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) d}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) c}{f}"," ",0,"1/2/f*C*d*tan(f*x+e)^2+B*d*tan(f*x+e)/f+1/f*c*C*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*A*d+1/2/f*ln(1+tan(f*x+e)^2)*B*c-1/2/f*ln(1+tan(f*x+e)^2)*C*d+1/f*A*arctan(tan(f*x+e))*c-1/f*B*arctan(tan(f*x+e))*d-1/f*C*arctan(tan(f*x+e))*c","A"
54,1,506,156,0.244000," ","int((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x)","\frac{C d \tan \left(f x +e \right)}{b f}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A a d}{f \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(a +b \tan \left(f x +e \right)\right) A c}{f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} d}{f b \left(a^{2}+b^{2}\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B a c}{f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{3} C d}{f \,b^{2} \left(a^{2}+b^{2}\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{2} c}{f b \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a d}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b c}{2 f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a c}{2 f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b d}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a C d}{2 f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b c}{2 f \left(a^{2}+b^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a c}{f \left(a^{2}+b^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b d}{f \left(a^{2}+b^{2}\right)}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) a d}{f \left(a^{2}+b^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b c}{f \left(a^{2}+b^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a c}{f \left(a^{2}+b^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b d}{f \left(a^{2}+b^{2}\right)}"," ",0,"C*d*tan(f*x+e)/b/f-1/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*A*a*d+1/f*b/(a^2+b^2)*ln(a+b*tan(f*x+e))*A*c+1/f/b/(a^2+b^2)*ln(a+b*tan(f*x+e))*B*a^2*d-1/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*B*a*c-1/f/b^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^3*C*d+1/f/b/(a^2+b^2)*ln(a+b*tan(f*x+e))*C*a^2*c+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*a*d-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*b*c+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*a*c+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*b*d-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*a*C*d+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*C*b*c+1/f/(a^2+b^2)*A*arctan(tan(f*x+e))*a*c+1/f/(a^2+b^2)*A*arctan(tan(f*x+e))*b*d-1/f/(a^2+b^2)*B*arctan(tan(f*x+e))*a*d+1/f/(a^2+b^2)*B*arctan(tan(f*x+e))*b*c-1/f/(a^2+b^2)*C*arctan(tan(f*x+e))*a*c-1/f/(a^2+b^2)*C*arctan(tan(f*x+e))*b*d","B"
55,1,948,265,0.296000," ","int((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x)","\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) B a d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{4} C d}{f \left(a^{2}+b^{2}\right)^{2} b^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b c}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b c}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{A a d}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) a b d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b c}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) a b d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{B \,a^{2} d}{f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{a^{3} C d}{f \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{C \,a^{2} c}{f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) A a c}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) C a c}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) B c}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} c}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) A d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{b A c}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{B a c}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}"," ",0,"1/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*a^2*c-1/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*b^2*c-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*b^2*d+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*d-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*d-1/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a^2*d-2/f/(a^2+b^2)^2*b*ln(a+b*tan(f*x+e))*B*a*d+1/f/(a^2+b^2)^2/b^2*ln(a+b*tan(f*x+e))*a^4*C*d-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*a*b*c+1/f/(a^2+b^2)/(a+b*tan(f*x+e))*A*a*d+3/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^2*d+1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*a*b*c+2/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*a*b*d+2/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*a*b*c-2/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*a*b*d-1/f/b/(a^2+b^2)/(a+b*tan(f*x+e))*B*a^2*d+1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*a*b*d+1/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))*a^3*C*d-1/f/b/(a^2+b^2)/(a+b*tan(f*x+e))*C*a^2*c+2/f/(a^2+b^2)^2*b*ln(a+b*tan(f*x+e))*A*a*c-2/f/(a^2+b^2)^2*b*ln(a+b*tan(f*x+e))*C*a*c-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*b^2*c+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*c-1/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*a^2*d+1/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*b^2*d+1/f/(a^2+b^2)^2*b^2*ln(a+b*tan(f*x+e))*B*c+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*b^2*d-1/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*a^2*c+1/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*b^2*c-1/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^2*c+1/f/(a^2+b^2)^2*b^2*ln(a+b*tan(f*x+e))*A*d-1/f*b/(a^2+b^2)/(a+b*tan(f*x+e))*A*c+1/f/(a^2+b^2)/(a+b*tan(f*x+e))*B*a*c","B"
56,1,1513,318,0.332000," ","int((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x)","\frac{\ln \left(a +b \tan \left(f x +e \right)\right) C \,b^{3} c}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{A a d}{2 f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}-\frac{a^{4} C d}{f \left(a^{2}+b^{2}\right)^{2} b^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{2 b C a c}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{2 b A a c}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,b^{2} c}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} b c}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} b c}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{B \,a^{2} c}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{B a c}{2 f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,b^{3} d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{3} C d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{2} b c}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{B \,a^{2} d}{2 f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{a^{3} C d}{2 f \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}-\frac{C \,a^{2} c}{2 f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) A a \,b^{2} d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{2 b B a d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} b d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) B a \,b^{2} c}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} b c}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) C a \,b^{2} d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} b d}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{3} d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{b A c}{2 f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}-\frac{b^{2} A d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{b^{2} B c}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A \,b^{3} c}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{3} c}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{A \,a^{2} d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{3} c}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{3} c}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{3} d}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{3} c}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{3} d}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} C d}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 C \,a^{2} d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{3} d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{3} c}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*b^3*c+1/2/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*a*d-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a*b^2*d+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*b*d-1/f/(a^2+b^2)^2/b^2/(a+b*tan(f*x+e))*a^4*C*d+2/f/(a^2+b^2)^2*b/(a+b*tan(f*x+e))*C*a*c+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a*b^2*d-2/f/(a^2+b^2)^2*b/(a+b*tan(f*x+e))*A*a*c+3/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a*b^2*d-3/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a^2*b*d+3/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a*b^2*c+1/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^2*c+1/2/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a*c+1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*b^3*d+1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^3*C*d-3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^2*b*c-1/2/f/b/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a^2*d+1/2/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*a^3*C*d-1/2/f/b/(a^2+b^2)/(a+b*tan(f*x+e))^2*C*a^2*c+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a*b^2*d+2/f/(a^2+b^2)^2*b/(a+b*tan(f*x+e))*B*a*d-3/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a*b^2*c-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a*b^2*c-3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^2*b*d+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a*b^2*c+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^2*b*c-3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a*b^2*d+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*b*c+3/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a^2*b*c+3/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a^2*b*d-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*b*c-1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^3*d+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a^3*c-1/2/f*b/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*c-1/f/(a^2+b^2)^2*b^2/(a+b*tan(f*x+e))*A*d-1/f/(a^2+b^2)^2*b^2/(a+b*tan(f*x+e))*B*c+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a^3*d-1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*b^3*c-1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^3*c+1/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a^2*d+1/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*b^3*d+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*b^3*c-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*b^3*d-3/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^2*d-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^3*C*d-1/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a^3*c-1/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a^3*d-1/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*b^3*c-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*b^3*c+1/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a^3*c-1/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*b^3*d","B"
57,1,1807,651,0.034000," ","int((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{3} c d}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{3} c d}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} b \,d^{2}}{2 f}+\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} c^{2}}{2 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) a \,b^{2} c^{2}}{f}+\frac{B \left(\tan^{4}\left(f x +e \right)\right) b^{3} c d}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,b^{2} c^{2}}{2 f}+\frac{3 B \left(\tan^{4}\left(f x +e \right)\right) a \,b^{2} d^{2}}{4 f}+\frac{3 C \left(\tan^{5}\left(f x +e \right)\right) a \,b^{2} d^{2}}{5 f}-\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) a^{2} b \,d^{2}}{2 f}+\frac{2 C \left(\tan^{5}\left(f x +e \right)\right) b^{3} c d}{5 f}-\frac{B \left(\tan^{2}\left(f x +e \right)\right) b^{3} c d}{f}-\frac{A \left(\tan^{2}\left(f x +e \right)\right) b^{3} d^{2}}{2 f}+\frac{A \left(\tan^{4}\left(f x +e \right)\right) b^{3} d^{2}}{4 f}+\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) a^{2} b c d}{f}-\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} c d}{f}+\frac{2 B \left(\tan^{3}\left(f x +e \right)\right) a \,b^{2} c d}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,b^{2} c d}{f}+\frac{C \,b^{3} d^{2} \left(\tan^{6}\left(f x +e \right)\right)}{6 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{3} d^{2}}{2 f}-\frac{C \left(\tan^{4}\left(f x +e \right)\right) b^{3} d^{2}}{4 f}+\frac{6 A \,a^{2} b c d \tan \left(f x +e \right)}{f}-\frac{6 B a \,b^{2} c d \tan \left(f x +e \right)}{f}-\frac{6 C \,a^{2} b c d \tan \left(f x +e \right)}{f}-\frac{6 A \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c d}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} b c d}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,b^{2} c d}{f}+\frac{6 B \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c d}{f}+\frac{6 C \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c d}{f}+\frac{2 C \left(\tan^{3}\left(f x +e \right)\right) a^{2} b c d}{f}+\frac{3 A \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} c d}{f}+\frac{3 C \left(\tan^{4}\left(f x +e \right)\right) a \,b^{2} c d}{2 f}+\frac{A \left(\tan^{3}\left(f x +e \right)\right) a \,b^{2} d^{2}}{f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) a^{2} b \,d^{2}}{f}+\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) a^{2} b \,c^{2}}{2 f}-\frac{C \left(\tan^{3}\left(f x +e \right)\right) a \,b^{2} d^{2}}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,b^{2} d^{2}}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} b \,c^{2}}{2 f}+\frac{B \,b^{3} d^{2} \tan \left(f x +e \right)}{f}+\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) b^{3} c d}{f}+\frac{3 A a \,b^{2} c^{2} \tan \left(f x +e \right)}{f}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a^{3} c d}{f}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{2}}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{3} c^{2}}{2 f}-\frac{C \left(\tan^{2}\left(f x +e \right)\right) b^{3} c^{2}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{3} d^{2}}{2 f}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{3} d^{2}}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{2}}{f}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{3} c^{2}}{f}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{3} d^{2}}{f}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{3} d^{2}}{f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) a^{3} d^{2}}{2 f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) b^{3} c^{2}}{3 f}+\frac{A \left(\tan^{2}\left(f x +e \right)\right) b^{3} c^{2}}{2 f}-\frac{B \,b^{3} c^{2} \tan \left(f x +e \right)}{f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{2}}{f}+\frac{C \,a^{3} c^{2} \tan \left(f x +e \right)}{f}-\frac{C \,a^{3} d^{2} \tan \left(f x +e \right)}{f}+\frac{B \left(\tan^{5}\left(f x +e \right)\right) b^{3} d^{2}}{5 f}-\frac{B \left(\tan^{3}\left(f x +e \right)\right) b^{3} d^{2}}{3 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) a^{3} d^{2}}{3 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{3} d^{2}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{3} c^{2}}{2 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) b^{3} d^{2}}{2 f}+\frac{C \left(\tan^{4}\left(f x +e \right)\right) b^{3} c^{2}}{4 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{3} c^{2}}{2 f}+\frac{A \,a^{3} d^{2} \tan \left(f x +e \right)}{f}+\frac{3 C a \,b^{2} d^{2} \tan \left(f x +e \right)}{f}-\frac{3 C a \,b^{2} c^{2} \tan \left(f x +e \right)}{f}+\frac{2 B \,a^{3} c d \tan \left(f x +e \right)}{f}-\frac{3 A a \,b^{2} d^{2} \tan \left(f x +e \right)}{f}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,d^{2}}{f}+\frac{3 B \,a^{2} b \,c^{2} \tan \left(f x +e \right)}{f}+\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d^{2}}{f}+\frac{2 C \,b^{3} c d \tan \left(f x +e \right)}{f}+\frac{3 A \left(\tan^{2}\left(f x +e \right)\right) a^{2} b \,d^{2}}{2 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) a^{3} c d}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{3} c d}{f}+\frac{2 A \left(\tan^{3}\left(f x +e \right)\right) b^{3} c d}{3 f}+\frac{3 C \left(\tan^{4}\left(f x +e \right)\right) a^{2} b \,d^{2}}{4 f}-\frac{2 C \left(\tan^{3}\left(f x +e \right)\right) b^{3} c d}{3 f}-\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} d^{2}}{2 f}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,c^{2}}{f}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{2}}{f}-\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d^{2}}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} b \,d^{2}}{2 f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} b \,c^{2}}{2 f}-\frac{3 B \,a^{2} b \,d^{2} \tan \left(f x +e \right)}{f}-\frac{2 A \,b^{3} c d \tan \left(f x +e \right)}{f}-\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) b^{3} c d}{f}"," ",0,"-1/f*B*tan(f*x+e)^2*b^3*c*d-3/f*ln(1+tan(f*x+e)^2)*B*a^2*b*c*d+3/f*ln(1+tan(f*x+e)^2)*C*a*b^2*c*d+2/f*C*tan(f*x+e)^3*a^2*b*c*d+3/f*A*tan(f*x+e)^2*a*b^2*c*d+3/2/f*C*tan(f*x+e)^4*a*b^2*c*d+6/f*A*a^2*b*c*d*tan(f*x+e)+3/f*B*tan(f*x+e)^2*a^2*b*c*d-6/f*B*a*b^2*c*d*tan(f*x+e)-6/f*C*a^2*b*c*d*tan(f*x+e)-3/f*C*tan(f*x+e)^2*a*b^2*c*d+2/f*B*tan(f*x+e)^3*a*b^2*c*d-6/f*A*arctan(tan(f*x+e))*a^2*b*c*d-3/f*ln(1+tan(f*x+e)^2)*A*a*b^2*c*d+6/f*B*arctan(tan(f*x+e))*a*b^2*c*d+6/f*C*arctan(tan(f*x+e))*a^2*b*c*d+3/2/f*ln(1+tan(f*x+e)^2)*B*a*b^2*d^2+1/f*B*b^3*d^2*tan(f*x+e)-3/2/f*ln(1+tan(f*x+e)^2)*C*a^2*b*c^2+3/2/f*ln(1+tan(f*x+e)^2)*A*a^2*b*c^2-3/2/f*ln(1+tan(f*x+e)^2)*A*a^2*b*d^2+2/f*A*arctan(tan(f*x+e))*b^3*c*d+3/4/f*C*tan(f*x+e)^4*a^2*b*d^2+1/f*A*tan(f*x+e)^3*a*b^2*d^2+1/f*B*tan(f*x+e)^3*a^2*b*d^2+3/f*A*a*b^2*c^2*tan(f*x+e)+3/2/f*C*tan(f*x+e)^2*a^2*b*c^2-1/f*C*tan(f*x+e)^3*a*b^2*d^2-2/3/f*C*tan(f*x+e)^3*b^3*c*d-2/f*B*arctan(tan(f*x+e))*a^3*c*d-3/2/f*B*tan(f*x+e)^2*a*b^2*d^2-3/f*A*arctan(tan(f*x+e))*a*b^2*c^2+1/f*C*arctan(tan(f*x+e))*a^3*d^2+1/2/f*B*tan(f*x+e)^2*a^3*d^2-1/f*C*arctan(tan(f*x+e))*a^3*c^2+1/f*B*arctan(tan(f*x+e))*b^3*c^2-1/f*B*arctan(tan(f*x+e))*b^3*d^2+1/3/f*B*tan(f*x+e)^3*b^3*c^2+1/2/f*A*tan(f*x+e)^2*b^3*c^2-1/2/f*A*tan(f*x+e)^2*b^3*d^2+1/4/f*A*tan(f*x+e)^4*b^3*d^2+1/5/f*B*tan(f*x+e)^5*b^3*d^2-1/f*A*arctan(tan(f*x+e))*a^3*d^2-1/3/f*B*tan(f*x+e)^3*b^3*d^2+1/3/f*C*tan(f*x+e)^3*a^3*d^2-1/f*B*b^3*c^2*tan(f*x+e)-1/2/f*ln(1+tan(f*x+e)^2)*C*b^3*d^2+1/f*A*arctan(tan(f*x+e))*a^3*c^2+1/2/f*ln(1+tan(f*x+e)^2)*B*a^3*c^2+1/2/f*C*tan(f*x+e)^2*b^3*d^2+1/4/f*C*tan(f*x+e)^4*b^3*c^2+1/2/f*ln(1+tan(f*x+e)^2)*C*b^3*c^2-1/2/f*ln(1+tan(f*x+e)^2)*A*b^3*c^2+1/f*C*a^3*c^2*tan(f*x+e)-1/f*C*a^3*d^2*tan(f*x+e)-1/2/f*C*tan(f*x+e)^2*b^3*c^2+1/2/f*ln(1+tan(f*x+e)^2)*A*b^3*d^2+1/6/f*C*b^3*d^2*tan(f*x+e)^6+1/f*A*a^3*d^2*tan(f*x+e)-1/2/f*ln(1+tan(f*x+e)^2)*B*a^3*d^2-1/4/f*C*tan(f*x+e)^4*b^3*d^2+3/2/f*A*tan(f*x+e)^2*a^2*b*d^2+3/f*C*a*b^2*d^2*tan(f*x+e)-3/f*C*a*b^2*c^2*tan(f*x+e)+2/f*B*a^3*c*d*tan(f*x+e)+1/f*C*tan(f*x+e)^2*a^3*c*d+1/f*ln(1+tan(f*x+e)^2)*B*b^3*c*d-3/f*A*a*b^2*d^2*tan(f*x+e)+2/3/f*A*tan(f*x+e)^3*b^3*c*d+3/f*B*arctan(tan(f*x+e))*a^2*b*d^2+3/f*B*a^2*b*c^2*tan(f*x+e)-1/f*ln(1+tan(f*x+e)^2)*C*a^3*c*d+1/f*ln(1+tan(f*x+e)^2)*A*a^3*c*d+3/2/f*ln(1+tan(f*x+e)^2)*C*a^2*b*d^2+3/2/f*B*tan(f*x+e)^2*a*b^2*c^2+3/f*A*arctan(tan(f*x+e))*a*b^2*d^2+1/f*C*tan(f*x+e)^3*a*b^2*c^2+1/2/f*B*tan(f*x+e)^4*b^3*c*d+2/f*C*b^3*c*d*tan(f*x+e)-3/f*B*arctan(tan(f*x+e))*a^2*b*c^2-3/2/f*ln(1+tan(f*x+e)^2)*B*a*b^2*c^2+3/f*C*arctan(tan(f*x+e))*a*b^2*c^2-3/f*C*arctan(tan(f*x+e))*a*b^2*d^2+3/4/f*B*tan(f*x+e)^4*a*b^2*d^2-3/f*B*a^2*b*d^2*tan(f*x+e)-2/f*A*b^3*c*d*tan(f*x+e)-2/f*C*arctan(tan(f*x+e))*b^3*c*d+3/5/f*C*tan(f*x+e)^5*a*b^2*d^2-3/2/f*C*tan(f*x+e)^2*a^2*b*d^2+2/5/f*C*tan(f*x+e)^5*b^3*c*d","B"
58,1,1165,435,0.031000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\frac{4 A a b c d \tan \left(f x +e \right)}{f}+\frac{4 C \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f}-\frac{4 C a b c d \tan \left(f x +e \right)}{f}-\frac{4 A \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f}+\frac{B \left(\tan^{4}\left(f x +e \right)\right) b^{2} d^{2}}{4 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} d^{2}}{2 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) b^{2} c^{2}}{3 f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) b^{2} c^{2}}{2 f}+\frac{2 B \left(\tan^{2}\left(f x +e \right)\right) a b c d}{f}-\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b c d}{f}+\frac{4 C \left(\tan^{3}\left(f x +e \right)\right) a b c d}{3 f}+\frac{C \,b^{2} d^{2} \tan \left(f x +e \right)}{f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f}+\frac{A \,b^{2} c^{2} \tan \left(f x +e \right)}{f}+\frac{A \,a^{2} d^{2} \tan \left(f x +e \right)}{f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f}-\frac{A \,b^{2} d^{2} \tan \left(f x +e \right)}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,c^{2}}{f}+\frac{C \,a^{2} c^{2} \tan \left(f x +e \right)}{f}-\frac{C \,b^{2} c^{2} \tan \left(f x +e \right)}{f}-\frac{a^{2} C \,d^{2} \tan \left(f x +e \right)}{f}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,d^{2}}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} c d}{f}+\frac{C \left(\tan^{4}\left(f x +e \right)\right) b^{2} c d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} c d}{f}-\frac{C \left(\tan^{3}\left(f x +e \right)\right) b^{2} d^{2}}{3 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} d^{2}}{2 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) a^{2} d^{2}}{3 f}+\frac{C \,b^{2} d^{2} \left(\tan^{5}\left(f x +e \right)\right)}{5 f}-\frac{B \left(\tan^{2}\left(f x +e \right)\right) b^{2} d^{2}}{2 f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) a^{2} d^{2}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c^{2}}{2 f}+\frac{A \left(\tan^{3}\left(f x +e \right)\right) b^{2} d^{2}}{3 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c^{2}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} c d}{f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) a b \,c^{2}}{f}+\frac{A \left(\tan^{2}\left(f x +e \right)\right) b^{2} c d}{f}-\frac{2 B \,b^{2} c d \tan \left(f x +e \right)}{f}+\frac{2 B \,a^{2} c d \tan \left(f x +e \right)}{f}+\frac{2 B a b \,c^{2} \tan \left(f x +e \right)}{f}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} c d}{f}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2}}{f}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) b^{2} c d}{f}-\frac{C \left(\tan^{2}\left(f x +e \right)\right) b^{2} c d}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,d^{2}}{f}+\frac{A \left(\tan^{2}\left(f x +e \right)\right) a b \,d^{2}}{f}+\frac{C \left(\tan^{4}\left(f x +e \right)\right) a b \,d^{2}}{2 f}+\frac{2 B \left(\tan^{3}\left(f x +e \right)\right) a b \,d^{2}}{3 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) a^{2} c d}{f}-\frac{C \left(\tan^{2}\left(f x +e \right)\right) a b \,d^{2}}{f}+\frac{2 B \left(\tan^{3}\left(f x +e \right)\right) b^{2} c d}{3 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} c d}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,c^{2}}{f}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{2}}{f}-\frac{2 B a b \,d^{2} \tan \left(f x +e \right)}{f}"," ",0,"4/3/f*C*tan(f*x+e)^3*a*b*c*d+2/f*B*tan(f*x+e)^2*a*b*c*d+4/f*A*a*b*c*d*tan(f*x+e)+4/f*C*arctan(tan(f*x+e))*a*b*c*d-4/f*C*a*b*c*d*tan(f*x+e)-2/f*ln(1+tan(f*x+e)^2)*B*a*b*c*d-4/f*A*arctan(tan(f*x+e))*a*b*c*d+2/3/f*B*tan(f*x+e)^3*b^2*c*d+1/f*C*b^2*d^2*tan(f*x+e)+1/f*A*arctan(tan(f*x+e))*b^2*d^2+1/f*A*b^2*c^2*tan(f*x+e)-1/2/f*B*tan(f*x+e)^2*b^2*d^2+1/2/f*B*tan(f*x+e)^2*a^2*d^2+1/f*A*a^2*d^2*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*B*a^2*c^2+1/f*A*arctan(tan(f*x+e))*a^2*c^2-1/f*A*b^2*d^2*tan(f*x+e)-1/f*C*arctan(tan(f*x+e))*a^2*c^2+1/4/f*B*tan(f*x+e)^4*b^2*d^2-1/2/f*ln(1+tan(f*x+e)^2)*B*a^2*d^2+1/f*C*arctan(tan(f*x+e))*a^2*d^2+1/f*C*arctan(tan(f*x+e))*b^2*c^2+1/3/f*C*tan(f*x+e)^3*b^2*c^2+1/2/f*B*tan(f*x+e)^2*b^2*c^2+1/3/f*A*tan(f*x+e)^3*b^2*d^2-1/2/f*ln(1+tan(f*x+e)^2)*B*b^2*c^2+1/f*C*a^2*c^2*tan(f*x+e)-1/f*C*b^2*c^2*tan(f*x+e)-1/f*a^2*C*d^2*tan(f*x+e)+1/5/f*C*b^2*d^2*tan(f*x+e)^5-1/3/f*C*tan(f*x+e)^3*b^2*d^2-1/f*A*arctan(tan(f*x+e))*a^2*d^2+1/2/f*ln(1+tan(f*x+e)^2)*B*b^2*d^2+1/3/f*C*tan(f*x+e)^3*a^2*d^2-1/f*A*arctan(tan(f*x+e))*b^2*c^2-1/f*C*arctan(tan(f*x+e))*b^2*d^2-2/f*B*b^2*c*d*tan(f*x+e)+2/3/f*B*tan(f*x+e)^3*a*b*d^2+2/f*B*a^2*c*d*tan(f*x+e)+1/f*C*tan(f*x+e)^2*a^2*c*d+2/f*B*a*b*c^2*tan(f*x+e)-1/f*C*tan(f*x+e)^2*a*b*d^2-1/f*C*tan(f*x+e)^2*b^2*c*d+1/f*ln(1+tan(f*x+e)^2)*C*a*b*d^2+1/f*A*tan(f*x+e)^2*a*b*d^2-2/f*B*arctan(tan(f*x+e))*a^2*c*d-2/f*B*arctan(tan(f*x+e))*a*b*c^2+1/2/f*C*tan(f*x+e)^4*a*b*d^2+2/f*B*arctan(tan(f*x+e))*b^2*c*d+1/f*ln(1+tan(f*x+e)^2)*A*a^2*c*d+1/f*ln(1+tan(f*x+e)^2)*A*a*b*c^2-1/f*ln(1+tan(f*x+e)^2)*A*a*b*d^2-1/f*ln(1+tan(f*x+e)^2)*A*b^2*c*d+1/2/f*C*tan(f*x+e)^4*b^2*c*d+2/f*B*arctan(tan(f*x+e))*a*b*d^2-2/f*B*a*b*d^2*tan(f*x+e)+1/f*ln(1+tan(f*x+e)^2)*C*b^2*c*d+1/f*C*tan(f*x+e)^2*a*b*c^2+1/f*A*tan(f*x+e)^2*b^2*c*d-1/f*ln(1+tan(f*x+e)^2)*C*a^2*c*d-1/f*ln(1+tan(f*x+e)^2)*C*a*b*c^2","B"
59,1,631,260,0.030000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","-\frac{C a \,d^{2} \tan \left(f x +e \right)}{f}+\frac{C b \,d^{2} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) a c d}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a c d}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a c d}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b c d}{f}+\frac{2 C \left(\tan^{3}\left(f x +e \right)\right) b c d}{3 f}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2}}{f}+\frac{A a \,d^{2} \tan \left(f x +e \right)}{f}-\frac{C \left(\tan^{2}\left(f x +e \right)\right) b \,d^{2}}{2 f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2}}{2 f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f}+\frac{C a \,c^{2} \tan \left(f x +e \right)}{f}+\frac{B b \,c^{2} \tan \left(f x +e \right)}{f}-\frac{B b \,d^{2} \tan \left(f x +e \right)}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,d^{2}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,c^{2}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,d^{2}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,c^{2}}{2 f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) b \,d^{2}}{3 f}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,d^{2}}{f}+\frac{A \left(\tan^{2}\left(f x +e \right)\right) b \,d^{2}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,d^{2}}{2 f}+\frac{2 A b c d \tan \left(f x +e \right)}{f}-\frac{2 C b c d \tan \left(f x +e \right)}{f}+\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) b c d}{f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) a \,d^{2}}{3 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) b \,c^{2}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,c^{2}}{2 f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) b c d}{f}+\frac{2 B a c d \tan \left(f x +e \right)}{f}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a c d}{f}-\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) b c d}{f}"," ",0,"1/4/f*C*b*d^2*tan(f*x+e)^4-1/f*C*a*d^2*tan(f*x+e)+1/2/f*B*tan(f*x+e)^2*a*d^2-1/f*B*arctan(tan(f*x+e))*b*c^2+1/f*A*a*d^2*tan(f*x+e)-1/2/f*C*tan(f*x+e)^2*b*d^2-1/f*C*arctan(tan(f*x+e))*a*c^2-1/f*A*arctan(tan(f*x+e))*a*d^2-1/2/f*ln(1+tan(f*x+e)^2)*A*b*d^2+1/2/f*ln(1+tan(f*x+e)^2)*B*a*c^2-1/2/f*ln(1+tan(f*x+e)^2)*B*a*d^2+1/2/f*A*tan(f*x+e)^2*b*d^2+1/f*C*a*c^2*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*A*b*c^2+1/f*B*b*c^2*tan(f*x+e)-1/f*B*b*d^2*tan(f*x+e)+1/3/f*C*tan(f*x+e)^3*a*d^2+1/f*C*tan(f*x+e)^2*a*c*d+1/f*C*arctan(tan(f*x+e))*a*d^2+1/2/f*C*tan(f*x+e)^2*b*c^2+1/f*B*arctan(tan(f*x+e))*b*d^2+1/2/f*ln(1+tan(f*x+e)^2)*C*b*d^2+2/f*A*b*c*d*tan(f*x+e)-1/f*ln(1+tan(f*x+e)^2)*C*a*c*d-2/f*C*b*c*d*tan(f*x+e)+1/f*ln(1+tan(f*x+e)^2)*A*a*c*d+2/f*C*arctan(tan(f*x+e))*b*c*d+1/f*A*arctan(tan(f*x+e))*a*c^2-1/2/f*ln(1+tan(f*x+e)^2)*C*b*c^2+1/3/f*B*tan(f*x+e)^3*b*d^2-1/f*ln(1+tan(f*x+e)^2)*B*b*c*d+2/3/f*C*tan(f*x+e)^3*b*c*d+2/f*B*a*c*d*tan(f*x+e)-2/f*B*arctan(tan(f*x+e))*a*c*d-2/f*A*arctan(tan(f*x+e))*b*c*d+1/f*B*tan(f*x+e)^2*b*c*d","B"
60,1,262,127,0.026000," ","int((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\frac{C \,d^{2} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) d^{2}}{2 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) c d}{f}+\frac{A \,d^{2} \tan \left(f x +e \right)}{f}+\frac{2 B c d \tan \left(f x +e \right)}{f}+\frac{c^{2} C \tan \left(f x +e \right)}{f}-\frac{C \,d^{2} \tan \left(f x +e \right)}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A c d}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,c^{2}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,d^{2}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c C d}{f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) c d}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f}"," ",0,"1/3/f*C*d^2*tan(f*x+e)^3+1/2/f*B*tan(f*x+e)^2*d^2+1/f*C*tan(f*x+e)^2*c*d+1/f*A*d^2*tan(f*x+e)+2/f*B*c*d*tan(f*x+e)+1/f*c^2*C*tan(f*x+e)-1/f*C*d^2*tan(f*x+e)+1/f*ln(1+tan(f*x+e)^2)*A*c*d+1/2/f*ln(1+tan(f*x+e)^2)*B*c^2-1/2/f*ln(1+tan(f*x+e)^2)*B*d^2-1/f*ln(1+tan(f*x+e)^2)*c*C*d+1/f*A*arctan(tan(f*x+e))*c^2-1/f*A*arctan(tan(f*x+e))*d^2-2/f*B*arctan(tan(f*x+e))*c*d-1/f*C*arctan(tan(f*x+e))*c^2+1/f*C*arctan(tan(f*x+e))*d^2","B"
61,1,861,252,0.239000," ","int((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x)","\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f \left(a^{2}+b^{2}\right)}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) A a c d}{f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{4} d^{2}}{f \,b^{3} \left(a^{2}+b^{2}\right)}+\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) b c d}{f \left(a^{2}+b^{2}\right)}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a c d}{f \left(a^{2}+b^{2}\right)}-\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) b c d}{f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{2} A \,d^{2}}{f b \left(a^{2}+b^{2}\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{2} C \,c^{2}}{f b \left(a^{2}+b^{2}\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{3} d^{2}}{f \,b^{2} \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b c d}{f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a c d}{f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a c d}{f \left(a^{2}+b^{2}\right)}+\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} B c d}{f b \left(a^{2}+b^{2}\right)}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{3} c d}{f \,b^{2} \left(a^{2}+b^{2}\right)}+\frac{d^{2} C \left(\tan^{2}\left(f x +e \right)\right)}{2 f b}+\frac{d^{2} B \tan \left(f x +e \right)}{f b}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,c^{2}}{2 f \left(a^{2}+b^{2}\right)}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f \left(a^{2}+b^{2}\right)}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,d^{2}}{f \left(a^{2}+b^{2}\right)}-\frac{d^{2} C \tan \left(f x +e \right) a}{f \,b^{2}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B a \,c^{2}}{f \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(a +b \tan \left(f x +e \right)\right) A \,c^{2}}{f \left(a^{2}+b^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2}}{f \left(a^{2}+b^{2}\right)}+\frac{2 d C c \tan \left(f x +e \right)}{f b}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,d^{2}}{2 f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,c^{2}}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,d^{2}}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,c^{2}}{2 f \left(a^{2}+b^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f \left(a^{2}+b^{2}\right)}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,d^{2}}{2 f \left(a^{2}+b^{2}\right)}"," ",0,"1/f/(a^2+b^2)*A*arctan(tan(f*x+e))*a*c^2-2/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*A*a*c*d+1/f/b^3/(a^2+b^2)*ln(a+b*tan(f*x+e))*C*a^4*d^2+2/f/(a^2+b^2)*A*arctan(tan(f*x+e))*b*c*d-2/f/(a^2+b^2)*B*arctan(tan(f*x+e))*a*c*d-2/f/(a^2+b^2)*C*arctan(tan(f*x+e))*b*c*d+1/f/b/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^2*A*d^2+1/f/b/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^2*C*c^2-1/f/b^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*B*a^3*d^2+1/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*b*c*d-1/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*C*a*c*d+1/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*a*c*d+2/f/b/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^2*B*c*d-2/f/b^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*C*a^3*c*d+1/2/f*d^2/b*C*tan(f*x+e)^2+1/f*d^2/b*B*tan(f*x+e)+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*b*d^2+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*a*c^2-1/f/(a^2+b^2)*A*arctan(tan(f*x+e))*a*d^2-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*C*b*d^2-1/f/(a^2+b^2)*B*arctan(tan(f*x+e))*b*d^2-1/f*d^2/b^2*C*tan(f*x+e)*a-1/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*B*a*c^2-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*b*c^2+1/f*b/(a^2+b^2)*ln(a+b*tan(f*x+e))*A*c^2+1/f/(a^2+b^2)*B*arctan(tan(f*x+e))*b*c^2+2/f*d/b*C*c*tan(f*x+e)+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*C*b*c^2-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*a*d^2-1/f/(a^2+b^2)*C*arctan(tan(f*x+e))*a*c^2+1/f/(a^2+b^2)*C*arctan(tan(f*x+e))*a*d^2","B"
62,1,1554,415,0.292000," ","int((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x)","\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b c d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 C \,a^{3} c d}{f \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{4 C \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 B \,a^{2} c d}{f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{4 b \ln \left(a +b \tan \left(f x +e \right)\right) B a c d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{4 A \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{4} c d}{f \,b^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{5} d^{2}}{f \,b^{3} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) A c d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{4} d^{2}}{f \,b^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) A a \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 A a c d}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{6 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{C \,a^{2} c^{2}}{f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{B \,a^{3} d^{2}}{f \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{C \,a^{4} d^{2}}{f \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{4 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{3} d^{2}}{f b \left(a^{2}+b^{2}\right)^{2}}-\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) C a \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) A a \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{A \,a^{2} d^{2}}{f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{C \,d^{2} \tan \left(f x +e \right)}{f \,b^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c^{2}}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} d^{2}}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c^{2}}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} d^{2}}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{B a \,c^{2}}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) B \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{b A \,c^{2}}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}"," ",0,"2/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))*C*a^3*c*d-4/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*a*b*c*d-2/f/b/(a^2+b^2)/(a+b*tan(f*x+e))*B*a^2*c*d-4/f*b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a*c*d+4/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*a*b*c*d+2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*a*b*c*d+2/f/b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^4*c*d-2/f/b^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^5*d^2+2/f*b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*c*d+1/f/b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^4*d^2-2/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*a^2*c*d+2/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*a*b*c^2-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*a*b*c^2+1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*a*b*d^2+2/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*b^2*c*d-2/f*b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a*d^2+2/f/(a^2+b^2)/(a+b*tan(f*x+e))*A*a*c*d+1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*b^2*c*d-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*a*b*d^2+6/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^2*c*d-2/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a^2*c*d-1/f/b/(a^2+b^2)/(a+b*tan(f*x+e))*C*a^2*c^2+1/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))*B*a^3*d^2-1/f/b^3/(a^2+b^2)/(a+b*tan(f*x+e))*C*a^4*d^2-4/f/b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^3*d^2-2/f*b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a*c^2+2/f*b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a*c^2+1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*c*d-1/f/b/(a^2+b^2)/(a+b*tan(f*x+e))*A*a^2*d^2-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*c*d+1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*a*b*c^2-2/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*a*b*d^2-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*b^2*c*d+1/f*C*d^2/b^2*tan(f*x+e)-1/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*b^2*d^2-1/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*b^2*c^2+1/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*b^2*d^2-1/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*a^2*c^2+1/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*a^2*d^2+1/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*b^2*c^2+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*c^2-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*d^2-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*b^2*c^2-1/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^2*c^2+3/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^2*d^2+1/f/(a^2+b^2)/(a+b*tan(f*x+e))*B*a*c^2+1/f*b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*c^2-1/f*b/(a^2+b^2)/(a+b*tan(f*x+e))*A*c^2+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*b^2*d^2+1/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*a^2*c^2-1/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*a^2*d^2","B"
63,1,2465,595,0.334000," ","int((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"-3/f/(a^2+b^2)^3*b*ln(a+b*tan(f*x+e))*A*a^2*d^2+3/f/(a^2+b^2)^3*b^2*ln(a+b*tan(f*x+e))*a*B*c^2-3/f/(a^2+b^2)^3*b^2*ln(a+b*tan(f*x+e))*B*a*d^2+2/f/(a^2+b^2)^3*b^3*ln(a+b*tan(f*x+e))*B*c*d+1/f/(a^2+b^2)^3/b^3*ln(a+b*tan(f*x+e))*a^6*C*d^2+3/f/(a^2+b^2)^3/b*ln(a+b*tan(f*x+e))*a^4*C*d^2-3/f/(a^2+b^2)^3*b*ln(a+b*tan(f*x+e))*C*a^2*c^2+6/f/(a^2+b^2)^3*b*ln(a+b*tan(f*x+e))*C*a^2*d^2-6/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^2*c*d-2/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^3*c*d+2/f*b/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a*d^2+2/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*b^3*c*d+2/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a^2*c*d+1/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*a*c*d-1/2/f/b/(a^2+b^2)/(a+b*tan(f*x+e))^2*C*a^2*c^2-2/f*b/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a*c^2+2/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^3*c*d-1/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a^3*c*d+1/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a^3*c*d-3/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a*b^2*c^2+3/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a*b^2*d^2-2/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*b^3*c*d-2/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a^3*c*d+3/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a^2*b*c^2-3/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a^2*b*d^2+3/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a*b^2*c^2-3/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a*b^2*d^2+3/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a*b^2*c*d+6/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a*b^2*c*d-6/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a^2*b*c*d+1/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*C*a^3*c*d+4/f*b/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a*c*d+6/f/(a^2+b^2)^3*b^2*ln(a+b*tan(f*x+e))*A*a*c*d-6/f/(a^2+b^2)^3*b*ln(a+b*tan(f*x+e))*B*a^2*c*d-3/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a*b^2*c*d+3/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*b*c*d-2/f/b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^4*c*d+6/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a^2*b*c*d-1/f/b/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a^2*c*d-6/f/(a^2+b^2)^3*b^2*ln(a+b*tan(f*x+e))*C*a*c*d-2/f*b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*c*d-1/f/b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^4*d^2-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a*b^2*c^2+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a*b^2*d^2-1/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*b^3*c*d+1/2/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a^3*d^2-1/2/f/b^3/(a^2+b^2)/(a+b*tan(f*x+e))^2*C*a^4*d^2+2/f/b^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^5*d^2+4/f/b/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^3*d^2+2/f*b/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a*c^2+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*b*c^2-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*b*d^2-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*b*c^2+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*b*d^2-1/2/f/b/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*a^2*d^2+3/f/(a^2+b^2)^3*b*ln(a+b*tan(f*x+e))*A*a^2*c^2-1/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*b^3*c^2+1/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*b^3*d^2-1/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a^3*c^2+1/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a^3*d^2+1/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^2*c^2+1/2/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a*c^2-3/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^2*d^2-1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^3*c^2+1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^3*d^2-1/2/f*b/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*c^2+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*b^3*c^2-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*b^3*d^2+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a^3*c^2-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a^3*d^2-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*b^3*c^2+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*b^3*d^2+1/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a^3*c^2-1/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a^3*d^2-1/f*b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*c^2-1/f/(a^2+b^2)^3*b^3*ln(a+b*tan(f*x+e))*A*c^2+1/f/(a^2+b^2)^3*b^3*ln(a+b*tan(f*x+e))*A*d^2+1/f/(a^2+b^2)^3*b^3*ln(a+b*tan(f*x+e))*C*c^2","B"
64,1,1807,593,0.033000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\frac{A \,b^{2} c^{3} \tan \left(f x +e \right)}{f}-\frac{B \,a^{2} d^{3} \tan \left(f x +e \right)}{f}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{3}}{f}-\frac{C \,b^{2} c^{3} \tan \left(f x +e \right)}{f}-\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) b^{2} c \,d^{2}}{2 f}+\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) a^{2} c^{2} d}{2 f}-\frac{6 A \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2} d}{f}+\frac{6 B \arctan \left(\tan \left(f x +e \right)\right) a b c \,d^{2}}{f}+\frac{6 C \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2} d}{f}+\frac{6 A a b \,c^{2} d \tan \left(f x +e \right)}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{3}}{f}-\frac{2 C \left(\tan^{3}\left(f x +e \right)\right) a b \,d^{3}}{3 f}-\frac{C \left(\tan^{3}\left(f x +e \right)\right) b^{2} c \,d^{2}}{f}-\frac{6 B a b c \,d^{2} \tan \left(f x +e \right)}{f}-\frac{6 C a b \,c^{2} d \tan \left(f x +e \right)}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} d^{3}}{2 f}+\frac{3 C \left(\tan^{5}\left(f x +e \right)\right) b^{2} c \,d^{2}}{5 f}+\frac{2 A \left(\tan^{3}\left(f x +e \right)\right) a b \,d^{3}}{3 f}-\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) b^{2} c^{2} d}{2 f}+\frac{C \,b^{2} d^{3} \left(\tan^{6}\left(f x +e \right)\right)}{6 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} d^{3}}{2 f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{3}}{f}+\frac{B \,b^{2} d^{3} \tan \left(f x +e \right)}{f}+\frac{C \,a^{2} c^{3} \tan \left(f x +e \right)}{f}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{3}}{f}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{3}}{f}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c \,d^{2}}{f}+\frac{3 C \left(\tan^{4}\left(f x +e \right)\right) a b c \,d^{2}}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b c \,d^{2}}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b \,c^{2} d}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b c \,d^{2}}{f}+\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) a b \,c^{2} d}{f}+\frac{2 B \left(\tan^{3}\left(f x +e \right)\right) a b c \,d^{2}}{f}+\frac{2 C \left(\tan^{3}\left(f x +e \right)\right) a b \,c^{2} d}{f}+\frac{3 A \left(\tan^{2}\left(f x +e \right)\right) a b c \,d^{2}}{f}-\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) a b c \,d^{2}}{f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) a^{2} d^{3}}{3 f}-\frac{A \left(\tan^{2}\left(f x +e \right)\right) b^{2} d^{3}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} d^{3}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c^{3}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c^{3}}{2 f}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{3}}{f}+\frac{3 A \left(\tan^{2}\left(f x +e \right)\right) b^{2} c^{2} d}{2 f}+\frac{2 C \left(\tan^{5}\left(f x +e \right)\right) a b \,d^{3}}{5 f}+\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) a^{2} c \,d^{2}}{2 f}+\frac{B \left(\tan^{2}\left(f x +e \right)\right) b^{2} c^{3}}{2 f}-\frac{B \left(\tan^{3}\left(f x +e \right)\right) b^{2} d^{3}}{3 f}+\frac{C \left(\tan^{4}\left(f x +e \right)\right) a^{2} d^{3}}{4 f}+\frac{A \left(\tan^{2}\left(f x +e \right)\right) a^{2} d^{3}}{2 f}-\frac{C \left(\tan^{2}\left(f x +e \right)\right) a^{2} d^{3}}{2 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) b^{2} d^{3}}{2 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) b^{2} c^{3}}{3 f}-\frac{C \left(\tan^{4}\left(f x +e \right)\right) b^{2} d^{3}}{4 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} d^{3}}{2 f}+\frac{B \left(\tan^{5}\left(f x +e \right)\right) b^{2} d^{3}}{5 f}+\frac{A \left(\tan^{4}\left(f x +e \right)\right) b^{2} d^{3}}{4 f}+\frac{3 C \left(\tan^{4}\left(f x +e \right)\right) b^{2} c^{2} d}{4 f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} c^{2} d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b \,d^{3}}{f}+\frac{A \left(\tan^{3}\left(f x +e \right)\right) b^{2} c \,d^{2}}{f}-\frac{3 A \,b^{2} c \,d^{2} \tan \left(f x +e \right)}{f}-\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c \,d^{2}}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c \,d^{2}}{2 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) a^{2} c \,d^{2}}{f}-\frac{B \left(\tan^{2}\left(f x +e \right)\right) a b \,d^{3}}{f}+\frac{2 B a b \,c^{3} \tan \left(f x +e \right)}{f}+\frac{3 A \,a^{2} c \,d^{2} \tan \left(f x +e \right)}{f}+\frac{3 B \left(\tan^{4}\left(f x +e \right)\right) b^{2} c \,d^{2}}{4 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,c^{3}}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} c^{2} d}{2 f}+\frac{B \left(\tan^{4}\left(f x +e \right)\right) a b \,d^{3}}{2 f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) a b \,c^{3}}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c \,d^{2}}{2 f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) b^{2} c^{2} d}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} c^{2} d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,c^{3}}{f}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{3}}{f}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2} d}{f}-\frac{2 A a b \,d^{3} \tan \left(f x +e \right)}{f}-\frac{3 C \,a^{2} c \,d^{2} \tan \left(f x +e \right)}{f}+\frac{2 C a b \,d^{3} \tan \left(f x +e \right)}{f}+\frac{3 C \,b^{2} c \,d^{2} \tan \left(f x +e \right)}{f}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2} d}{f}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c \,d^{2}}{f}-\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{3}}{f}-\frac{3 B \,b^{2} c^{2} d \tan \left(f x +e \right)}{f}+\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c \,d^{2}}{f}+\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{3}}{f}+\frac{3 B \,a^{2} c^{2} d \tan \left(f x +e \right)}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} c^{2} d}{2 f}"," ",0,"-1/4/f*C*tan(f*x+e)^4*b^2*d^3+1/f*A*b^2*c^3*tan(f*x+e)-1/f*B*a^2*d^3*tan(f*x+e)-1/f*B*arctan(tan(f*x+e))*b^2*d^3+1/5/f*B*tan(f*x+e)^5*b^2*d^3+1/4/f*A*tan(f*x+e)^4*b^2*d^3-1/2/f*C*tan(f*x+e)^2*a^2*d^3+1/2/f*C*tan(f*x+e)^2*b^2*d^3+1/3/f*B*tan(f*x+e)^3*a^2*d^3-1/f*C*b^2*c^3*tan(f*x+e)-3/2/f*ln(1+tan(f*x+e)^2)*C*a^2*c^2*d-3/f*C*tan(f*x+e)^2*a*b*c*d^2+3/2/f*C*tan(f*x+e)^4*a*b*c*d^2-3/f*ln(1+tan(f*x+e)^2)*A*a*b*c*d^2-3/f*ln(1+tan(f*x+e)^2)*B*a*b*c^2*d+3/f*ln(1+tan(f*x+e)^2)*C*a*b*c*d^2-6/f*A*arctan(tan(f*x+e))*a*b*c^2*d+6/f*B*arctan(tan(f*x+e))*a*b*c*d^2+6/f*C*arctan(tan(f*x+e))*a*b*c^2*d+6/f*A*a*b*c^2*d*tan(f*x+e)+1/3/f*C*tan(f*x+e)^3*b^2*c^3-1/f*C*arctan(tan(f*x+e))*a^2*c^3+3/f*B*tan(f*x+e)^2*a*b*c^2*d+2/f*B*tan(f*x+e)^3*a*b*c*d^2+2/f*C*tan(f*x+e)^3*a*b*c^2*d+3/f*A*tan(f*x+e)^2*a*b*c*d^2-6/f*B*a*b*c*d^2*tan(f*x+e)-6/f*C*a*b*c^2*d*tan(f*x+e)+1/f*A*arctan(tan(f*x+e))*a^2*c^3+1/2/f*B*tan(f*x+e)^2*b^2*c^3-1/3/f*B*tan(f*x+e)^3*b^2*d^3+1/f*B*b^2*d^3*tan(f*x+e)+1/f*C*a^2*c^3*tan(f*x+e)-1/f*A*arctan(tan(f*x+e))*b^2*c^3+1/f*B*arctan(tan(f*x+e))*a^2*d^3+1/4/f*C*tan(f*x+e)^4*a^2*d^3-3/f*A*arctan(tan(f*x+e))*a^2*c*d^2+1/2/f*A*tan(f*x+e)^2*a^2*d^3-1/2/f*A*tan(f*x+e)^2*b^2*d^3-1/2/f*ln(1+tan(f*x+e)^2)*A*a^2*d^3+1/2/f*ln(1+tan(f*x+e)^2)*A*b^2*d^3+1/2/f*ln(1+tan(f*x+e)^2)*B*a^2*c^3-1/2/f*ln(1+tan(f*x+e)^2)*B*b^2*c^3+1/6/f*C*b^2*d^3*tan(f*x+e)^6+1/f*C*arctan(tan(f*x+e))*b^2*c^3+1/2/f*ln(1+tan(f*x+e)^2)*C*a^2*d^3-1/2/f*ln(1+tan(f*x+e)^2)*C*b^2*d^3+3/2/f*A*tan(f*x+e)^2*b^2*c^2*d-3/f*A*b^2*c*d^2*tan(f*x+e)+2/5/f*C*tan(f*x+e)^5*a*b*d^3+3/2/f*B*tan(f*x+e)^2*a^2*c*d^2-2/3/f*C*tan(f*x+e)^3*a*b*d^3-1/f*C*tan(f*x+e)^3*b^2*c*d^2+3/2/f*ln(1+tan(f*x+e)^2)*C*b^2*c^2*d+1/f*ln(1+tan(f*x+e)^2)*B*a*b*d^3+1/f*A*tan(f*x+e)^3*b^2*c*d^2-3/f*C*arctan(tan(f*x+e))*b^2*c*d^2+3/2/f*ln(1+tan(f*x+e)^2)*B*b^2*c*d^2+1/f*C*tan(f*x+e)^3*a^2*c*d^2+2/f*B*a*b*c^3*tan(f*x+e)+3/f*A*a^2*c*d^2*tan(f*x+e)-1/f*B*tan(f*x+e)^2*a*b*d^3+3/4/f*B*tan(f*x+e)^4*b^2*c*d^2-1/f*ln(1+tan(f*x+e)^2)*C*a*b*c^3-2/f*B*arctan(tan(f*x+e))*a*b*c^3+3/f*B*arctan(tan(f*x+e))*b^2*c^2*d+3/2/f*ln(1+tan(f*x+e)^2)*A*a^2*c^2*d+1/2/f*B*tan(f*x+e)^4*a*b*d^3-2/f*A*a*b*d^3*tan(f*x+e)-3/f*C*a^2*c*d^2*tan(f*x+e)+2/f*C*a*b*d^3*tan(f*x+e)+1/f*C*tan(f*x+e)^2*a*b*c^3-3/2/f*ln(1+tan(f*x+e)^2)*B*a^2*c*d^2+3/f*C*b^2*c*d^2*tan(f*x+e)+1/f*B*tan(f*x+e)^3*b^2*c^2*d-3/2/f*ln(1+tan(f*x+e)^2)*A*b^2*c^2*d+1/f*ln(1+tan(f*x+e)^2)*A*a*b*c^3-3/f*B*arctan(tan(f*x+e))*a^2*c^2*d+3/f*C*arctan(tan(f*x+e))*a^2*c*d^2-2/f*C*arctan(tan(f*x+e))*a*b*d^3+3/5/f*C*tan(f*x+e)^5*b^2*c*d^2+2/3/f*A*tan(f*x+e)^3*a*b*d^3-3/2/f*C*tan(f*x+e)^2*b^2*c^2*d-3/f*B*b^2*c^2*d*tan(f*x+e)+3/f*A*arctan(tan(f*x+e))*b^2*c*d^2+2/f*A*arctan(tan(f*x+e))*a*b*d^3-3/2/f*B*tan(f*x+e)^2*b^2*c*d^2+3/2/f*C*tan(f*x+e)^2*a^2*c^2*d+3/f*B*a^2*c^2*d*tan(f*x+e)+3/4/f*C*tan(f*x+e)^4*b^2*c^2*d","B"
65,1,994,381,0.036000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f}+\frac{C \left(\tan^{2}\left(f x +e \right)\right) b \,c^{3}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,c^{3}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,d^{3}}{2 f}+\frac{A \left(\tan^{3}\left(f x +e \right)\right) b \,d^{3}}{3 f}+\frac{A \left(\tan^{2}\left(f x +e \right)\right) a \,d^{3}}{2 f}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a \,d^{3}}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f}-\frac{C \left(\tan^{2}\left(f x +e \right)\right) a \,d^{3}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,d^{3}}{2 f}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,c^{3}}{f}-\frac{A b \,d^{3} \tan \left(f x +e \right)}{f}+\frac{C a \,c^{3} \tan \left(f x +e \right)}{f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) a \,d^{3}}{3 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,c^{3}}{2 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) a c \,d^{2}}{f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) b c \,d^{2}}{f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) b \,c^{2} d}{f}+\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) a \,c^{2} d}{2 f}+\frac{3 C \left(\tan^{4}\left(f x +e \right)\right) b c \,d^{2}}{4 f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,c^{2} d}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A b c \,d^{2}}{2 f}+\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) b \,c^{2} d}{2 f}+\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) a c \,d^{2}}{2 f}+\frac{C b \,d^{3} \tan \left(f x +e \right)}{f}-\frac{B \left(\tan^{2}\left(f x +e \right)\right) b \,d^{3}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,c^{3}}{2 f}+\frac{C \left(\tan^{4}\left(f x +e \right)\right) a \,d^{3}}{4 f}+\frac{C b \,d^{3} \left(\tan^{5}\left(f x +e \right)\right)}{5 f}-\frac{C \left(\tan^{3}\left(f x +e \right)\right) b \,d^{3}}{3 f}+\frac{B \left(\tan^{4}\left(f x +e \right)\right) b \,d^{3}}{4 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b \,d^{3}}{2 f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f}-\frac{B a \,d^{3} \tan \left(f x +e \right)}{f}+\frac{B b \,c^{3} \tan \left(f x +e \right)}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f}-\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) b c \,d^{2}}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a c \,d^{2}}{2 f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C b c \,d^{2}}{2 f}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f}-\frac{3 C a c \,d^{2} \tan \left(f x +e \right)}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B b \,c^{2} d}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,c^{2} d}{2 f}+\frac{3 A \left(\tan^{2}\left(f x +e \right)\right) b c \,d^{2}}{2 f}+\frac{3 B a \,c^{2} d \tan \left(f x +e \right)}{f}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2} d}{f}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) b c \,d^{2}}{f}+\frac{3 A a c \,d^{2} \tan \left(f x +e \right)}{f}-\frac{3 B b c \,d^{2} \tan \left(f x +e \right)}{f}-\frac{3 C b \,c^{2} d \tan \left(f x +e \right)}{f}+\frac{3 A b \,c^{2} d \tan \left(f x +e \right)}{f}"," ",0,"-3/f*A*arctan(tan(f*x+e))*a*c*d^2-1/2/f*C*tan(f*x+e)^2*a*d^3+1/f*B*arctan(tan(f*x+e))*a*d^3-1/2/f*ln(1+tan(f*x+e)^2)*A*a*d^3-1/f*C*arctan(tan(f*x+e))*a*c^3-3/2/f*ln(1+tan(f*x+e)^2)*B*b*c^2*d-3/2/f*ln(1+tan(f*x+e)^2)*C*a*c^2*d+3/2/f*A*tan(f*x+e)^2*b*c*d^2-1/f*B*arctan(tan(f*x+e))*b*c^3-1/f*A*b*d^3*tan(f*x+e)+1/3/f*B*tan(f*x+e)^3*a*d^3+1/2/f*ln(1+tan(f*x+e)^2)*A*b*c^3+1/2/f*C*tan(f*x+e)^2*b*c^3+1/2/f*ln(1+tan(f*x+e)^2)*B*a*c^3+1/f*C*a*c^3*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*C*a*d^3+1/3/f*A*tan(f*x+e)^3*b*d^3+1/2/f*A*tan(f*x+e)^2*a*d^3+1/5/f*C*b*d^3*tan(f*x+e)^5+1/4/f*C*tan(f*x+e)^4*a*d^3+1/f*C*b*d^3*tan(f*x+e)-1/3/f*C*tan(f*x+e)^3*b*d^3+1/4/f*B*tan(f*x+e)^4*b*d^3+1/f*A*arctan(tan(f*x+e))*a*c^3+1/f*A*arctan(tan(f*x+e))*b*d^3-1/f*B*a*d^3*tan(f*x+e)+1/f*B*b*c^3*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*B*b*d^3-1/f*C*arctan(tan(f*x+e))*b*d^3-1/2/f*B*tan(f*x+e)^2*b*d^3-1/2/f*ln(1+tan(f*x+e)^2)*C*b*c^3-3/f*A*arctan(tan(f*x+e))*b*c^2*d+3/f*C*arctan(tan(f*x+e))*a*c*d^2+3/f*C*arctan(tan(f*x+e))*b*c^2*d+3/2/f*ln(1+tan(f*x+e)^2)*A*a*c^2*d-3/2/f*ln(1+tan(f*x+e)^2)*A*b*c*d^2+3/2/f*B*tan(f*x+e)^2*b*c^2*d+3/2/f*B*tan(f*x+e)^2*a*c*d^2-3/2/f*ln(1+tan(f*x+e)^2)*B*a*c*d^2-3/f*C*a*c*d^2*tan(f*x+e)+3/2/f*ln(1+tan(f*x+e)^2)*C*b*c*d^2+3/f*B*a*c^2*d*tan(f*x+e)-3/f*B*arctan(tan(f*x+e))*a*c^2*d+3/f*B*arctan(tan(f*x+e))*b*c*d^2-3/2/f*C*tan(f*x+e)^2*b*c*d^2+3/f*A*a*c*d^2*tan(f*x+e)-3/f*B*b*c*d^2*tan(f*x+e)-3/f*C*b*c^2*d*tan(f*x+e)+1/f*C*tan(f*x+e)^3*a*c*d^2+1/f*B*tan(f*x+e)^3*b*c*d^2+1/f*C*tan(f*x+e)^3*b*c^2*d+3/2/f*C*tan(f*x+e)^2*a*c^2*d+3/4/f*C*tan(f*x+e)^4*b*c*d^2+3/f*A*b*c^2*d*tan(f*x+e)","B"
66,1,420,185,0.031000," ","int((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\frac{C \,d^{3} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{B \left(\tan^{3}\left(f x +e \right)\right) d^{3}}{3 f}+\frac{C \left(\tan^{3}\left(f x +e \right)\right) c \,d^{2}}{f}+\frac{A \left(\tan^{2}\left(f x +e \right)\right) d^{3}}{2 f}+\frac{3 B \left(\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{2 f}+\frac{3 C \left(\tan^{2}\left(f x +e \right)\right) c^{2} d}{2 f}-\frac{C \left(\tan^{2}\left(f x +e \right)\right) d^{3}}{2 f}+\frac{3 A c \,d^{2} \tan \left(f x +e \right)}{f}+\frac{3 B \,c^{2} d \tan \left(f x +e \right)}{f}-\frac{B \,d^{3} \tan \left(f x +e \right)}{f}+\frac{c^{3} C \tan \left(f x +e \right)}{f}-\frac{3 c C \,d^{2} \tan \left(f x +e \right)}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,c^{2} d}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,d^{3}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,c^{3}}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B c \,d^{2}}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,c^{2} d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,d^{3}}{2 f}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) c^{2} d}{f}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) d^{3}}{f}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f}"," ",0,"1/4/f*C*d^3*tan(f*x+e)^4+1/3/f*B*tan(f*x+e)^3*d^3+1/f*C*tan(f*x+e)^3*c*d^2+1/2/f*A*tan(f*x+e)^2*d^3+3/2/f*B*tan(f*x+e)^2*c*d^2+3/2/f*C*tan(f*x+e)^2*c^2*d-1/2/f*C*tan(f*x+e)^2*d^3+3/f*A*c*d^2*tan(f*x+e)+3/f*B*c^2*d*tan(f*x+e)-1/f*B*d^3*tan(f*x+e)+1/f*c^3*C*tan(f*x+e)-3/f*c*C*d^2*tan(f*x+e)+3/2/f*ln(1+tan(f*x+e)^2)*A*c^2*d-1/2/f*ln(1+tan(f*x+e)^2)*A*d^3+1/2/f*ln(1+tan(f*x+e)^2)*B*c^3-3/2/f*ln(1+tan(f*x+e)^2)*B*c*d^2-3/2/f*ln(1+tan(f*x+e)^2)*C*c^2*d+1/2/f*ln(1+tan(f*x+e)^2)*C*d^3+1/f*A*arctan(tan(f*x+e))*c^3-3/f*A*arctan(tan(f*x+e))*c*d^2-3/f*B*arctan(tan(f*x+e))*c^2*d+1/f*B*arctan(tan(f*x+e))*d^3-1/f*C*arctan(tan(f*x+e))*c^3+3/f*C*arctan(tan(f*x+e))*c*d^2","B"
67,1,1304,359,0.253000," ","int((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x)","\frac{d^{3} C \left(\tan^{3}\left(f x +e \right)\right)}{3 f b}+\frac{d^{3} B \left(\tan^{2}\left(f x +e \right)\right)}{2 f b}-\frac{d^{3} B a \tan \left(f x +e \right)}{f \,b^{2}}+\frac{3 d^{2} B c \tan \left(f x +e \right)}{f b}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a \,d^{3}}{f \left(a^{2}+b^{2}\right)}+\frac{d^{3} a^{2} C \tan \left(f x +e \right)}{f \,b^{3}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{4} d^{3}}{f \,b^{3} \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} B \,c^{2} d}{f b \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{4} c \,d^{2}}{f \,b^{3} \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} c \,d^{2}}{f b \left(a^{2}+b^{2}\right)}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{3} c^{2} d}{f \,b^{2} \left(a^{2}+b^{2}\right)}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{3} B c \,d^{2}}{f \,b^{2} \left(a^{2}+b^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,c^{2} d}{2 f \left(a^{2}+b^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a c \,d^{2}}{2 f \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B b \,c^{2} d}{2 f \left(a^{2}+b^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C b c \,d^{2}}{2 f \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,c^{2} d}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{3} d^{3}}{f \,b^{2} \left(a^{2}+b^{2}\right)}+\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f \left(a^{2}+b^{2}\right)}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) b c \,d^{2}}{f \left(a^{2}+b^{2}\right)}-\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A b c \,d^{2}}{2 f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{2} c^{3}}{f b \left(a^{2}+b^{2}\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{5} d^{3}}{f \,b^{4} \left(a^{2}+b^{2}\right)}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(a^{2}+b^{2}\right)}-\frac{3 d^{2} C a c \tan \left(f x +e \right)}{f \,b^{2}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) A a \,c^{2} d}{f \left(a^{2}+b^{2}\right)}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2} d}{f \left(a^{2}+b^{2}\right)}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(a^{2}+b^{2}\right)}+\frac{3 d C \,c^{2} \tan \left(f x +e \right)}{f b}+\frac{b \ln \left(a +b \tan \left(f x +e \right)\right) A \,c^{3}}{f \left(a^{2}+b^{2}\right)}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f \left(a^{2}+b^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,c^{3}}{f \left(a^{2}+b^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B a \,c^{3}}{f \left(a^{2}+b^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f \left(a^{2}+b^{2}\right)}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,c^{3}}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b \,d^{3}}{2 f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,c^{3}}{2 f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,d^{3}}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,d^{3}}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,c^{3}}{2 f \left(a^{2}+b^{2}\right)}-\frac{d^{3} C \left(\tan^{2}\left(f x +e \right)\right) a}{2 f \,b^{2}}+\frac{3 d^{2} C \left(\tan^{2}\left(f x +e \right)\right) c}{2 f b}+\frac{d^{3} A \tan \left(f x +e \right)}{f b}-\frac{d^{3} C \tan \left(f x +e \right)}{f b}"," ",0,"-1/f*d^3/b^2*B*a*tan(f*x+e)+3/f*d^2/b*B*c*tan(f*x+e)+1/f/(a^2+b^2)*B*arctan(tan(f*x+e))*a*d^3+1/f*d^3/b^3*a^2*C*tan(f*x+e)+1/f/b^3/(a^2+b^2)*ln(a+b*tan(f*x+e))*B*a^4*d^3+3/f/b/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^2*B*c^2*d+3/f/b^3/(a^2+b^2)*ln(a+b*tan(f*x+e))*C*a^4*c*d^2+3/f/b/(a^2+b^2)*ln(a+b*tan(f*x+e))*A*a^2*c*d^2-3/f/b^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*C*a^3*c^2*d-3/f/b^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^3*B*c*d^2-1/f/b^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*A*a^3*d^3+3/f/(a^2+b^2)*A*arctan(tan(f*x+e))*b*c^2*d+3/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*b*c*d^2-3/f/(a^2+b^2)*B*arctan(tan(f*x+e))*b*c*d^2-3/f/(a^2+b^2)*C*arctan(tan(f*x+e))*b*c^2*d-3/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*C*a*c^2*d-3/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*a*c*d^2+3/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*b*c^2*d-3/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*C*b*c*d^2+1/f/b/(a^2+b^2)*ln(a+b*tan(f*x+e))*C*a^2*c^3-1/f/b^4/(a^2+b^2)*ln(a+b*tan(f*x+e))*C*a^5*d^3-3/f/(a^2+b^2)*A*arctan(tan(f*x+e))*a*c*d^2-3/f*d^2/b^2*C*a*c*tan(f*x+e)+3/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*a*c^2*d-3/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*A*a*c^2*d-3/f/(a^2+b^2)*B*arctan(tan(f*x+e))*a*c^2*d+3/f/(a^2+b^2)*C*arctan(tan(f*x+e))*a*c*d^2+3/f*d/b*C*c^2*tan(f*x+e)+1/f*b/(a^2+b^2)*ln(a+b*tan(f*x+e))*A*c^3+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*a*c^3-1/f/(a^2+b^2)*A*arctan(tan(f*x+e))*b*d^3+1/f/(a^2+b^2)*B*arctan(tan(f*x+e))*b*c^3-1/f/(a^2+b^2)*C*arctan(tan(f*x+e))*a*c^3+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*C*a*d^3-1/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*B*a*c^3+1/f/(a^2+b^2)*A*arctan(tan(f*x+e))*a*c^3-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*a*d^3-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*b*c^3-1/2/f*d^3/b^2*C*tan(f*x+e)^2*a+3/2/f*d^2/b*C*tan(f*x+e)^2*c+1/f/(a^2+b^2)*C*arctan(tan(f*x+e))*b*d^3+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*C*b*c^3-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*b*d^3+1/3/f*d^3/b*C*tan(f*x+e)^3+1/2/f*d^3/b*B*tan(f*x+e)^2+1/f*d^3/b*A*tan(f*x+e)-1/f*d^3/b*C*tan(f*x+e)","B"
68,1,2250,572,0.296000," ","int((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x)","\frac{B a \,c^{3}}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{b A \,c^{3}}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) B \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 d^{3} C \tan \left(f x +e \right) a}{f \,b^{3}}+\frac{3 d^{2} C c \tan \left(f x +e \right)}{f \,b^{2}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} d^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{5 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{4} d^{3}}{f \,b^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) C a \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{B \,a^{4} d^{3}}{f \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{C \,a^{2} c^{3}}{f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{C \,a^{5} d^{3}}{f \,b^{4} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{9 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{2} c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{4} d^{3}}{f \,b^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) A a \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) A \,c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{5} d^{3}}{f \,b^{3} \left(a^{2}+b^{2}\right)^{2}}-\frac{4 \ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{3} d^{3}}{f b \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{6} d^{3}}{f \,b^{4} \left(a^{2}+b^{2}\right)^{2}}+\frac{9 \ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 A a \,c^{2} d}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{12 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{3} c \,d^{2}}{f b \left(a^{2}+b^{2}\right)^{2}}-\frac{6 C \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 a^{2} B \,c^{2} d}{f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{4} c \,d^{2}}{f \,b^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{3 a^{3} B c \,d^{2}}{f \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 A \,a^{2} c \,d^{2}}{f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{6 B \arctan \left(\tan \left(f x +e \right)\right) a b c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{6 A \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{6 b \ln \left(a +b \tan \left(f x +e \right)\right) B a \,c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 C \,a^{3} c^{2} d}{f \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{6 b \ln \left(a +b \tan \left(f x +e \right)\right) A a c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 C \,a^{4} c \,d^{2}}{f \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{6 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{5} c \,d^{2}}{f \,b^{3} \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{4} c^{2} d}{f \,b^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{d^{3} B \tan \left(f x +e \right)}{f \,b^{2}}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b \,c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b \,d^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c \,d^{2}}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c \,d^{2}}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{A \,a^{3} d^{3}}{f \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{d^{3} C \left(\tan^{2}\left(f x +e \right)\right)}{2 f \,b^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c^{3}}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c^{3}}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/f/(a^2+b^2)/(a+b*tan(f*x+e))*B*a*c^3-1/f*b/(a^2+b^2)/(a+b*tan(f*x+e))*A*c^3+1/f*b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*c^3+1/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*a^2*c^3-1/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*b^2*c^3-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*b^2*d^3-2/f*d^3/b^3*C*tan(f*x+e)*a+3/f*d^2/b^2*C*c*tan(f*x+e)+3/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a^2*d^3-1/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^2*c^3+1/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*a^2*d^3+5/f/b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^4*d^3-2/f*b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a*c^3-1/f/b^3/(a^2+b^2)/(a+b*tan(f*x+e))*B*a^4*d^3-1/f/b/(a^2+b^2)/(a+b*tan(f*x+e))*C*a^2*c^3+1/f/b^4/(a^2+b^2)/(a+b*tan(f*x+e))*C*a^5*d^3+9/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^2*c^2*d+1/f/b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a^4*d^3+2/f*b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a*c^3+3/f*b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*c^2*d-2/f/b^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^5*d^3-4/f/b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^3*d^3+3/f/b^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^6*d^3+9/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^2*c*d^2-3/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a^2*c^2*d+3/f/(a^2+b^2)/(a+b*tan(f*x+e))*A*a*c^2*d-3/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*c^2*d+1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*a*b*c^3+3/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*b^2*c^2*d-3/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*a^2*c*d^2-2/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*a*b*d^3+3/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*b^2*c*d^2-3/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*a^2*c^2*d-12/f/b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^3*c*d^2-6/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*a*b*c^2*d-3/f/b/(a^2+b^2)/(a+b*tan(f*x+e))*a^2*B*c^2*d+2/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*a*b*d^3+3/f/b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^4*c*d^2+3/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*a*b*c^2*d-3/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*a*b*c*d^2+3/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))*a^3*B*c*d^2-3/f/b/(a^2+b^2)/(a+b*tan(f*x+e))*A*a^2*c*d^2-6/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*a*b*c*d^2+6/f/(a^2+b^2)^2*A*arctan(tan(f*x+e))*a*b*c^2*d-6/f*b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a*c^2*d+3/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))*C*a^3*c^2*d-6/f*b/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a*c*d^2+3/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*a*b*c*d^2-3/f/b^3/(a^2+b^2)/(a+b*tan(f*x+e))*C*a^4*c*d^2-6/f/b^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^5*c*d^2+3/f/b^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^4*c^2*d+1/f*d^3/b^2*B*tan(f*x+e)+3/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*b^2*c^2*d+3/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*a^2*c*d^2+2/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*a*b*c^3-3/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*b^2*c*d^2+1/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))*A*a^3*d^3+3/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*c^2*d-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*a*b*c^3-3/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*b^2*c^2*d-3/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*c*d^2-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*a*b*d^3+3/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*b^2*c*d^2+1/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*b^2*c^3+1/2/f*d^3/b^2*C*tan(f*x+e)^2+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*d^3-1/f/(a^2+b^2)^2*B*arctan(tan(f*x+e))*b^2*d^3-1/f/(a^2+b^2)^2*C*arctan(tan(f*x+e))*a^2*c^3-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*d^3+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*A*b^2*d^3+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*c^3-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*B*b^2*c^3","B"
69,1,3522,794,0.316000," ","int((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"3/2/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*a*c^2*d+3/f*b/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^2*c^3-3/f*b^2/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a*d^3+3/f*b^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*c*d^2+1/f/b^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^6*d^3-3/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a*b^2*d^3+1/2/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*a^3*d^3+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^3*c*d^2+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^3*c^2*d-9/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^2*c*d^2-9/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^2*c^2*d-3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^3*c^2*d+3/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a^3*c*d^2-3/2/f/b^3/(a^2+b^2)/(a+b*tan(f*x+e))^2*C*a^4*c*d^2+6/f/b^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^5*c*d^2-3/f/b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^4*c^2*d+12/f/b/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^3*c*d^2+9/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a*b^2*c^2*d-3/f/b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^4*c*d^2+18/f*b/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^2*c*d^2-9/f*b^2/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a*c^2*d-9/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a^2*b*c*d^2+6/f*b/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a*c^2*d+3/2/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*C*a^3*c^2*d-3/2/f/b/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a^2*c^2*d-3/2/f/b/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*a^2*c*d^2+3/2/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a^3*c*d^2+9/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a*b^2*c^2*d+9/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a^2*b*c^2*d+9/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a*b^2*c*d^2-9/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a*b^2*c*d^2+9/f*b^2/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a*c^2*d-9/f*b/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^2*c*d^2+6/f*b/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a*c*d^2-9/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a^2*b*c^2*d+9/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*b*c*d^2-9/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a*b^2*c^2*d+9/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*b*c^2*d+9/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a*b^2*c*d^2-9/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*b*c*d^2-9/f*b/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^2*c^2*d-9/f*b^2/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a*c*d^2+3/f/b^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^6*c*d^2+9/f/b/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^4*c*d^2+3/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a^2*b*d^3+3/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a*b^2*c^3+3/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*b^3*c^2*d+1/2/f/b^4/(a^2+b^2)/(a+b*tan(f*x+e))^2*C*a^5*d^3-1/2/f/b/(a^2+b^2)/(a+b*tan(f*x+e))^2*C*a^2*c^3-1/f/b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a^4*d^3-2/f*b/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a*c^3-3/f*b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*c^2*d+2/f/b^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^5*d^3+4/f/b/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^3*d^3-3/f/b^4/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^6*d^3-5/f/b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^4*d^3+2/f*b/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a*c^3-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a*b^2*d^3-1/2/f/b^3/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a^4*d^3+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*b^3*c*d^2-3/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a^3*c*d^2-3/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a^2*b*d^3+1/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a^3*c^3+1/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*b^3*d^3+1/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a^3*d^3-1/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*b^3*c^3-1/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*a^3*c^3-1/f/(a^2+b^2)^3*C*arctan(tan(f*x+e))*b^3*d^3-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a^3*d^3+1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^3*d^3-1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^3*c^3-10/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^3*d^3+1/2/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a*c^3-3/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a^2*d^3+1/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^2*c^3-1/2/f*b/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*c^3-1/f*b^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*c^3-1/f*b^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*c^3+1/f*b^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*c^3+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*b^3*c^3+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a^3*c^3+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*b^3*d^3+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^3*C*d^3-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*b^3*c^3+3/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*b^3*c*d^2+3/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a^2*c^2*d+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a^3*c^2*d-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*b*c^3+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*a*b^2*d^3-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*A*b^3*c*d^2-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a^3*c*d^2-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*b*d^3-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*a*b^2*c^3-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*B*b^3*c^2*d-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a^3*c^2*d+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*b*c^3-3/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*a*b^2*c^3-3/f/(a^2+b^2)^3*A*arctan(tan(f*x+e))*b^3*c^2*d-3/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a^3*c^2*d+3/f/(a^2+b^2)^3*B*arctan(tan(f*x+e))*a^2*b*c^3+3/f/b/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^4*d^3+6/f*b/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^2*d^3+3/f*b^2/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a*c^3+3/f*b^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*c^2*d-3/f/b^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^7*d^3-9/f/b^2/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^5*d^3-3/f*b/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^2*c^3+1/f*C*d^3/b^3*tan(f*x+e)","B"
70,1,1304,333,0.266000," ","int((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x)","\frac{b^{3} A \tan \left(f x +e \right)}{f d}-\frac{b^{3} C \tan \left(f x +e \right)}{f d}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B a \,b^{2} c^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{2} b \,c^{2}}{f d \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C \,a^{2} b \,c^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C \,c^{4} a \,b^{2}}{f \,d^{3} \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A a \,b^{2} c^{2}}{f d \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{3} c}{2 f \left(c^{2}+d^{2}\right)}-\frac{b^{3} C \left(\tan^{2}\left(f x +e \right)\right) c}{2 f \,d^{2}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A \,a^{2} b c}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{3} d}{2 f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{3} c}{2 f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{3} d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} C d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{3} c}{2 f \left(c^{2}+d^{2}\right)}+\frac{3 b^{2} C \left(\tan^{2}\left(f x +e \right)\right) a}{2 f d}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d}{f \left(c^{2}+d^{2}\right)}-\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} b c}{2 f \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,b^{2} d}{2 f \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,b^{2} c}{2 f \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} b c}{2 f \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,b^{2} d}{2 f \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} b d}{2 f \left(c^{2}+d^{2}\right)}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(c^{2}+d^{2}\right)}-\frac{3 b^{2} C a c \tan \left(f x +e \right)}{f \,d^{2}}+\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,c^{4} b^{3}}{f \,d^{3} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C \,a^{3} c^{2}}{f d \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C \,c^{5} b^{3}}{f \,d^{4} \left(c^{2}+d^{2}\right)}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A \,b^{3} c^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right)}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c}{f \left(c^{2}+d^{2}\right)}+\frac{d \ln \left(c +d \tan \left(f x +e \right)\right) A \,a^{3}}{f \left(c^{2}+d^{2}\right)}+\frac{3 b^{2} B a \tan \left(f x +e \right)}{f d}-\frac{b^{3} B c \tan \left(f x +e \right)}{f \,d^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f \left(c^{2}+d^{2}\right)}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{3} c}{f \left(c^{2}+d^{2}\right)}+\frac{3 b \,a^{2} C \tan \left(f x +e \right)}{f d}+\frac{b^{3} C \,c^{2} \tan \left(f x +e \right)}{f \,d^{3}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f \left(c^{2}+d^{2}\right)}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f \left(c^{2}+d^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{3} d}{f \left(c^{2}+d^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{3} c}{f \left(c^{2}+d^{2}\right)}+\frac{b^{3} C \left(\tan^{3}\left(f x +e \right)\right)}{3 f d}+\frac{b^{3} B \left(\tan^{2}\left(f x +e \right)\right)}{2 f d}"," ",0,"1/2/f*b^3/d*B*tan(f*x+e)^2+1/f*b^3/d*A*tan(f*x+e)-1/f*b^3/d*C*tan(f*x+e)-3/f/d^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*a*b^2*c^3+3/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*a^2*b*c^2-3/f/d^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*C*a^2*b*c^3+3/f/d^3/(c^2+d^2)*ln(c+d*tan(f*x+e))*C*c^4*a*b^2+3/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*a*b^2*c^2+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a^3*c-3/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*a^2*b*c-3/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*a*b^2*d-3/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*a^2*b*c-3/f/(c^2+d^2)*B*arctan(tan(f*x+e))*a*b^2*d-3/f/(c^2+d^2)*C*arctan(tan(f*x+e))*a^2*b*d-3/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a*b^2*c+3/f/(c^2+d^2)*C*arctan(tan(f*x+e))*a*b^2*c-3/f*b^2/d^2*C*a*c*tan(f*x+e)+3/f/(c^2+d^2)*A*arctan(tan(f*x+e))*a^2*b*d+1/f/d^3/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*c^4*b^3+1/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*C*a^3*c^2-1/f/d^4/(c^2+d^2)*ln(c+d*tan(f*x+e))*C*c^5*b^3+3/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a^2*b*c+3/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a*b^2*d-3/f/(c^2+d^2)*A*arctan(tan(f*x+e))*a*b^2*c+3/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a^2*b*d-1/f/d^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*b^3*c^3-3/f/(c^2+d^2)*B*arctan(tan(f*x+e))*a^2*b*c-1/2/f*b^3/d^2*C*tan(f*x+e)^2*c+1/f*d/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*a^3+3/f*b^2/d*B*a*tan(f*x+e)-1/f*b^3/d^2*B*c*tan(f*x+e)-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a^3*d-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*b^3*c-1/f/(c^2+d^2)*C*arctan(tan(f*x+e))*a^3*c+1/f/(c^2+d^2)*C*arctan(tan(f*x+e))*b^3*d-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*b^3*d+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^3*C*d+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*b^3*c-1/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*a^3*c+3/f*b/d*a^2*C*tan(f*x+e)+1/f*b^3/d^3*C*c^2*tan(f*x+e)+3/2/f*b^2/d*C*tan(f*x+e)^2*a+1/f/(c^2+d^2)*A*arctan(tan(f*x+e))*a^3*c-1/f/(c^2+d^2)*A*arctan(tan(f*x+e))*b^3*d+1/f/(c^2+d^2)*B*arctan(tan(f*x+e))*a^3*d+1/f/(c^2+d^2)*B*arctan(tan(f*x+e))*b^3*c+1/3/f*b^3/d*C*tan(f*x+e)^3","B"
71,1,861,234,0.291000," ","int((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x)","-\frac{b^{2} C c \tan \left(f x +e \right)}{f \,d^{2}}-\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) a b d}{f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A \,c^{2} b^{2}}{f d \left(c^{2}+d^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f \left(c^{2}+d^{2}\right)}+\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) a b d}{f \left(c^{2}+d^{2}\right)}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b c}{f \left(c^{2}+d^{2}\right)}+\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) B \,c^{2} a b}{f d \left(c^{2}+d^{2}\right)}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) C \,c^{3} a b}{f \,d^{2} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b d}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b c}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,c^{3} b^{2}}{f \,d^{2} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C \,c^{2} a^{2}}{f d \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C \,c^{4} b^{2}}{f \,d^{3} \left(c^{2}+d^{2}\right)}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) A a c b}{f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b c}{f \left(c^{2}+d^{2}\right)}+\frac{b^{2} C \left(\tan^{2}\left(f x +e \right)\right)}{2 f d}+\frac{b^{2} B \tan \left(f x +e \right)}{f d}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{2} c}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} d}{2 f \left(c^{2}+d^{2}\right)}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{2} d}{f \left(c^{2}+d^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f \left(c^{2}+d^{2}\right)}+\frac{2 b C \tan \left(f x +e \right) a}{f d}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f \left(c^{2}+d^{2}\right)}+\frac{d \ln \left(c +d \tan \left(f x +e \right)\right) A \,a^{2}}{f \left(c^{2}+d^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{2} d}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} d}{2 f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c}{2 f \left(c^{2}+d^{2}\right)}"," ",0,"-1/f*b^2/d^2*C*c*tan(f*x+e)-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*b^2*d-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a^2*d-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*b^2*c+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*a^2*d-2/f/(c^2+d^2)*C*arctan(tan(f*x+e))*a*b*d+1/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*c^2*b^2+1/f/(c^2+d^2)*A*arctan(tan(f*x+e))*a^2*c+1/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a*b*c+1/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a*b*d+2/f/(c^2+d^2)*A*arctan(tan(f*x+e))*a*b*d-2/f/(c^2+d^2)*B*arctan(tan(f*x+e))*a*b*c+2/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*c^2*a*b-2/f/d^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*C*c^3*a*b-1/f/d^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*c^3*b^2+1/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*C*c^2*a^2+1/f/d^3/(c^2+d^2)*ln(c+d*tan(f*x+e))*C*c^4*b^2-1/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*a*b*c-2/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*a*c*b+1/f*b^2/d*B*tan(f*x+e)+1/f/(c^2+d^2)*C*arctan(tan(f*x+e))*b^2*c-1/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*a^2*c-1/f/(c^2+d^2)*B*arctan(tan(f*x+e))*b^2*d-1/f/(c^2+d^2)*C*arctan(tan(f*x+e))*a^2*c+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*b^2*d+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a^2*c+1/2/f*b^2/d*C*tan(f*x+e)^2+2/f*b/d*C*tan(f*x+e)*a-1/f/(c^2+d^2)*A*arctan(tan(f*x+e))*b^2*c+1/f*d/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*a^2+1/f/(c^2+d^2)*B*arctan(tan(f*x+e))*a^2*d","B"
72,1,506,156,0.252000," ","int((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x)","\frac{b C \tan \left(f x +e \right)}{d f}+\frac{d \ln \left(c +d \tan \left(f x +e \right)\right) A a}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A b c}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B a c}{f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,c^{2} b}{f d \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C \,c^{2} a}{f d \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C \,c^{3} b}{f \,d^{2} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b c}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a c}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a C d}{2 f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b c}{2 f \left(c^{2}+d^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a c}{f \left(c^{2}+d^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b d}{f \left(c^{2}+d^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a d}{f \left(c^{2}+d^{2}\right)}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b c}{f \left(c^{2}+d^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a c}{f \left(c^{2}+d^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b d}{f \left(c^{2}+d^{2}\right)}"," ",0,"b*C*tan(f*x+e)/d/f+1/f*d/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*a-1/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*b*c-1/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*a*c+1/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*c^2*b+1/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*C*c^2*a-1/f/d^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*C*c^3*b-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a*d+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*b*c+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a*c+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*b*d+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a*C*d-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*b*c+1/f/(c^2+d^2)*A*arctan(tan(f*x+e))*a*c+1/f/(c^2+d^2)*A*arctan(tan(f*x+e))*b*d+1/f/(c^2+d^2)*B*arctan(tan(f*x+e))*a*d-1/f/(c^2+d^2)*B*arctan(tan(f*x+e))*b*c-1/f/(c^2+d^2)*C*arctan(tan(f*x+e))*a*c-1/f/(c^2+d^2)*C*arctan(tan(f*x+e))*b*d","B"
73,1,234,99,0.255000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x)","\frac{d \ln \left(c +d \tan \left(f x +e \right)\right) A}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B c}{f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) c^{2} C}{f \left(c^{2}+d^{2}\right) d}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B c}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C d}{2 f \left(c^{2}+d^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) d}{f \left(c^{2}+d^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}"," ",0,"1/f/(c^2+d^2)*d*ln(c+d*tan(f*x+e))*A-1/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*c+1/f/(c^2+d^2)/d*ln(c+d*tan(f*x+e))*c^2*C-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*d+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*c+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*d+1/f/(c^2+d^2)*A*arctan(tan(f*x+e))*c+1/f/(c^2+d^2)*B*arctan(tan(f*x+e))*d-1/f/(c^2+d^2)*C*arctan(tan(f*x+e))*c","B"
74,1,647,165,0.517000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x)","-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A \,b^{2}}{f \left(d a -c b \right) \left(a^{2}+b^{2}\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B a b}{f \left(d a -c b \right) \left(a^{2}+b^{2}\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{2} C}{f \left(d a -c b \right) \left(a^{2}+b^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A \,d^{2}}{f \left(d a -c b \right) \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B c d}{f \left(d a -c b \right) \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) c^{2} C}{f \left(d a -c b \right) \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a d}{2 f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b c}{2 f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a c}{2 f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b d}{2 f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a C d}{2 f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b c}{2 f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a c}{f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b d}{f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a d}{f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b c}{f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a c}{f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b d}{f \left(c^{2}+d^{2}\right) \left(a^{2}+b^{2}\right)}"," ",0,"-1/f/(a*d-b*c)/(a^2+b^2)*ln(a+b*tan(f*x+e))*A*b^2+1/f/(a*d-b*c)/(a^2+b^2)*ln(a+b*tan(f*x+e))*B*a*b-1/f/(a*d-b*c)/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^2*C+1/f/(a*d-b*c)/(c^2+d^2)*ln(c+d*tan(f*x+e))*A*d^2-1/f/(a*d-b*c)/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*c*d+1/f/(a*d-b*c)/(c^2+d^2)*ln(c+d*tan(f*x+e))*c^2*C-1/2/f/(c^2+d^2)/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*a*d-1/2/f/(c^2+d^2)/(a^2+b^2)*ln(1+tan(f*x+e)^2)*A*b*c+1/2/f/(c^2+d^2)/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*a*c-1/2/f/(c^2+d^2)/(a^2+b^2)*ln(1+tan(f*x+e)^2)*B*b*d+1/2/f/(c^2+d^2)/(a^2+b^2)*ln(1+tan(f*x+e)^2)*a*C*d+1/2/f/(c^2+d^2)/(a^2+b^2)*ln(1+tan(f*x+e)^2)*C*b*c+1/f/(c^2+d^2)/(a^2+b^2)*A*arctan(tan(f*x+e))*a*c-1/f/(c^2+d^2)/(a^2+b^2)*A*arctan(tan(f*x+e))*b*d+1/f/(c^2+d^2)/(a^2+b^2)*B*arctan(tan(f*x+e))*a*d+1/f/(c^2+d^2)/(a^2+b^2)*B*arctan(tan(f*x+e))*b*c-1/f/(c^2+d^2)/(a^2+b^2)*C*arctan(tan(f*x+e))*a*c+1/f/(c^2+d^2)/(a^2+b^2)*C*arctan(tan(f*x+e))*b*d","B"
75,1,1262,280,0.548000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x)","\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,b^{4} c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{2} b^{2} d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) C a \,b^{3} c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) a b d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) A a \,b^{3} c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) a^{3} b B d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} b^{2} c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) a b d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{B a b}{f \left(d a -c b \right) \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) B c}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} b^{2} d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{d \ln \left(c +d \tan \left(f x +e \right)\right) c^{2} C}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{2} d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{2} d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A \,b^{4} d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{4} C d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{A \,b^{2}}{f \left(d a -c b \right) \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{a^{2} C}{f \left(d a -c b \right) \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) A}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)}"," ",0,"1/f/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*b^4*c+1/f/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^2*b^2*d-2/f/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a*b^3*c+2/f/(a^2+b^2)^2/(c^2+d^2)*C*arctan(tan(f*x+e))*a*b*d+2/f/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a*b^3*c+2/f/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^3*b*B*d-1/f/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^2*b^2*c-1/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a*b*d+1/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*a*b*c-2/f/(a^2+b^2)^2/(c^2+d^2)*A*arctan(tan(f*x+e))*a*b*d+2/f/(a^2+b^2)^2/(c^2+d^2)*B*arctan(tan(f*x+e))*a*b*c-1/f/(a*d-b*c)/(a^2+b^2)/(a+b*tan(f*x+e))*B*a*b-1/f*d^2/(a*d-b*c)^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*c-3/f/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a^2*b^2*d-1/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a*b*c+1/f*d/(a*d-b*c)^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*c^2*C-1/2/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a^2*d+1/2/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*b^2*d+1/2/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a^2*c-1/f/(a^2+b^2)^2/(c^2+d^2)*B*arctan(tan(f*x+e))*b^2*d-1/f/(a^2+b^2)^2/(c^2+d^2)*C*arctan(tan(f*x+e))*a^2*c+1/f/(a^2+b^2)^2/(c^2+d^2)*C*arctan(tan(f*x+e))*b^2*c-1/f/(a^2+b^2)^2/(c^2+d^2)*A*arctan(tan(f*x+e))*b^2*c+1/f/(a^2+b^2)^2/(c^2+d^2)*B*arctan(tan(f*x+e))*a^2*d-1/f/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*b^4*d-1/f/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^4*C*d-1/2/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*b^2*c+1/2/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*a^2*d-1/2/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*b^2*d+1/f/(a^2+b^2)^2/(c^2+d^2)*A*arctan(tan(f*x+e))*a^2*c+1/f/(a*d-b*c)/(a^2+b^2)/(a+b*tan(f*x+e))*A*b^2+1/f/(a*d-b*c)/(a^2+b^2)/(a+b*tan(f*x+e))*a^2*C+1/f*d^3/(a*d-b*c)^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*A","B"
76,1,2298,473,0.523000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x)","\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{3} d}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} C d}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{3} c}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{3} c}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{3} d}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{3} c}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) a^{3} d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{3} c}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{B a b}{2 f \left(d a -c b \right) \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{6 \ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} b^{4} c d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{B \,b^{4} c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{a^{4} C d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) B c}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)}+\frac{d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2} C}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)}+\frac{A \,b^{4} d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A \,b^{6} c^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) A \,b^{6} d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{6} C \,d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) C \,b^{6} c^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} b c}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,b^{2} c}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} b d}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} b c}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{4} b^{2} C \,d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{2} b^{4} c^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{6 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{4} b^{2} d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{C \,a^{2} b^{2} d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{2 C a \,b^{3} c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} b^{4} c^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} b^{4} d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{5} b B \,d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{3} b^{3} c^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{3} b^{3} d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a \,b^{5} B \,c^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) B \,b^{6} c d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{2 a^{3} b B d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{3 A \,a^{2} b^{2} d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{B \,a^{2} b^{2} c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{2 A a \,b^{3} c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{4} b^{2} c d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{8 \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{3} b^{3} c d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{A \,b^{2}}{2 f \left(d a -c b \right) \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{a^{2} C}{2 f \left(d a -c b \right) \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) A}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)}-\frac{8 \ln \left(a +b \tan \left(f x +e \right)\right) C \,a^{3} b^{3} c d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a^3*c+1/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*b^3*d+1/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^3*C*d-1/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*b^3*c+1/f/(a^2+b^2)^3/(c^2+d^2)*A*arctan(tan(f*x+e))*a^3*c+1/f/(a^2+b^2)^3/(c^2+d^2)*A*arctan(tan(f*x+e))*b^3*d+1/f/(a^2+b^2)^3/(c^2+d^2)*B*arctan(tan(f*x+e))*a^3*d-1/f/(a^2+b^2)^3/(c^2+d^2)*B*arctan(tan(f*x+e))*b^3*c-1/f/(a^2+b^2)^3/(c^2+d^2)*C*arctan(tan(f*x+e))*a^3*c-1/f/(a^2+b^2)^3/(c^2+d^2)*C*arctan(tan(f*x+e))*b^3*d-1/2/f/(a*d-b*c)/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a*b+6/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^2*b^4*c*d-1/f/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*b^4*c+1/f/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^4*C*d+1/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*b^3*c-1/f*d^3/(a*d-b*c)^3/(c^2+d^2)*ln(c+d*tan(f*x+e))*B*c+1/f*d^2/(a*d-b*c)^3/(c^2+d^2)*ln(c+d*tan(f*x+e))*c^2*C-1/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a^3*d+1/f/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*b^4*d+1/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*b^6*c^2-1/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*b^6*d^2-1/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^6*C*d^2-1/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*b^6*c^2+3/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^4*b^2*C*d^2+3/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^2*b^4*c^2-6/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^4*b^2*d^2+3/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*a^2*b*c-1/f/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a^2*b^2*d+2/f/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a*b^3*c-3/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^2*b^4*c^2-3/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^2*b^4*d^2+3/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^5*b*B*d^2+1/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^3*b^3*c^2-1/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^3*b^3*d^2-3/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a*b^5*B*c^2-3/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a*b^2*c-3/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*B*a^2*b*d+3/f/(a^2+b^2)^3/(c^2+d^2)*C*arctan(tan(f*x+e))*a^2*b*d+3/f/(a^2+b^2)^3/(c^2+d^2)*C*arctan(tan(f*x+e))*a*b^2*c-3/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a^2*b*c+3/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*A*a*b^2*d+1/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*b^6*c*d-3/f/(a^2+b^2)^3/(c^2+d^2)*B*arctan(tan(f*x+e))*a*b^2*d-2/f/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^3*b*B*d+3/f/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a^2*b^2*d-3/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*C*a*b^2*d-3/f/(a^2+b^2)^3/(c^2+d^2)*A*arctan(tan(f*x+e))*a^2*b*d-3/f/(a^2+b^2)^3/(c^2+d^2)*A*arctan(tan(f*x+e))*a*b^2*c+3/f/(a^2+b^2)^3/(c^2+d^2)*B*arctan(tan(f*x+e))*a^2*b*c+1/f/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^2*b^2*c-2/f/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a*b^3*c-3/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^4*b^2*c*d+8/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^3*b^3*c*d+1/2/f/(a*d-b*c)/(a^2+b^2)/(a+b*tan(f*x+e))^2*A*b^2+1/2/f/(a*d-b*c)/(a^2+b^2)/(a+b*tan(f*x+e))^2*a^2*C+1/f*d^4/(a*d-b*c)^3/(c^2+d^2)*ln(c+d*tan(f*x+e))*A-8/f/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^3*b^3*c*d","B"
77,1,2250,577,0.286000," ","int((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x)","-\frac{4 \ln \left(c +d \tan \left(f x +e \right)\right) B \,b^{3} c^{3}}{f d \left(c^{2}+d^{2}\right)^{2}}-\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) C \,a^{3} c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C \,b^{3} c^{6}}{f \,d^{4} \left(c^{2}+d^{2}\right)^{2}}+\frac{5 \ln \left(c +d \tan \left(f x +e \right)\right) C \,b^{3} c^{4}}{f \,d^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a^{3} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{C \,c^{2} a^{3}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{C \,c^{5} b^{3}}{f \,d^{4} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 A \,a^{2} c b}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{9 \ln \left(c +d \tan \left(f x +e \right)\right) B a \,b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{9 \ln \left(c +d \tan \left(f x +e \right)\right) C \,a^{2} b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) b^{3} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{A \,c^{3} b^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A \,a^{2} b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) b^{3} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{B \,c^{4} b^{3}}{f \,d^{3} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) A \,a^{3} c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) A \,a^{2} b}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A \,b^{3} c^{4}}{f \,d^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) B \,b^{3} c^{5}}{f \,d^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} b \,c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} b \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,b^{2} c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{3} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,b^{2} d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{3} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{3} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} b \,c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{3 A \,c^{2} a \,b^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} b c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C \,a^{2} b \,c^{4}}{f \,d^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{6 \ln \left(c +d \tan \left(f x +e \right)\right) C a \,b^{2} c^{5}}{f \,d^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{12 \ln \left(c +d \tan \left(f x +e \right)\right) C a \,b^{2} c^{3}}{f d \left(c^{2}+d^{2}\right)^{2}}-\frac{6 d \ln \left(c +d \tan \left(f x +e \right)\right) A a \,b^{2} c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{6 A \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{6 B \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{6 C \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B a \,b^{2} c^{4}}{f \,d^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{3 B \,c^{2} a^{2} b}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 B \,c^{3} a \,b^{2}}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 C \,c^{3} a^{2} b}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{3 C \,c^{4} a \,b^{2}}{f \,d^{3} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{6 d \ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{2} b c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} b \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b^{3} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{3} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{a^{3} B c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{b^{3} C \left(\tan^{2}\left(f x +e \right)\right)}{2 f \,d^{2}}+\frac{b^{3} B \tan \left(f x +e \right)}{f \,d^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{3} c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{3} d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{3} c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{3} d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{3} c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{3} d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A \,b^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{d A \,a^{3}}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{3}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 b^{2} C \tan \left(f x +e \right) a}{f \,d^{2}}-\frac{2 b^{3} C c \tan \left(f x +e \right)}{f \,d^{3}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{3} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"-4/f/d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*b^3*c^3-2/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a^3*c+3/f/d^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b^3*c^6+5/f/d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b^3*c^4-3/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*b^2*d^2+2/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a^3*c*d-1/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*C*c^2*a^3+1/f/d^4/(c^2+d^2)/(c+d*tan(f*x+e))*C*c^5*b^3+3/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*b*c^2-3/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*b*d^2-3/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*b^2*c^2+3/f/(c^2+d^2)/(c+d*tan(f*x+e))*A*a^2*c*b+9/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a*b^2*c^2+9/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a^2*b*c^2+2/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*b^3*c*d-3/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a^2*b*c^2+3/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a^2*b*d^2+3/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*b^2*c^2+1/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))*A*c^3*b^3-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a^3*c*d-3/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a^2*b*c^2-2/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*b^3*c*d+3/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*b^2*d^2-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*b^3*c*d+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a^3*c*d-3/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*b*c^2-1/f/d^3/(c^2+d^2)/(c+d*tan(f*x+e))*B*c^4*b^3+3/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*b*d^2-3/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*b^2*c^2+3/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*b^2*d^2+2/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a^3*c+3/f*d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a^2*b+1/f/d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b^3*c^4-2/f/d^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*b^3*c^5-3/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*A*c^2*a*b^2+3/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a*b^2*c*d+3/f/d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a^2*b*c^4-6/f/d^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a*b^2*c^5-12/f/d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a*b^2*c^3-6/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a*b^2*c+3/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*b*c*d-3/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a*b^2*c*d+6/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^2*b*c*d-6/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a*b^2*c*d-6/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^2*b*c*d+3/f/d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a*b^2*c^4-3/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*B*c^2*a^2*b+3/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))*B*c^3*a*b^2+3/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))*C*c^3*a^2*b-3/f/d^3/(c^2+d^2)/(c+d*tan(f*x+e))*C*c^4*a*b^2-6/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a^2*b*c+1/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b^3*c^2-1/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b^3*d^2-1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^3*c^2+1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^3*d^2+1/f/(c^2+d^2)/(c+d*tan(f*x+e))*a^3*B*c+1/f*b^3/d^2*B*tan(f*x+e)+1/2/f*b^3/d^2*C*tan(f*x+e)^2+3/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b^3*c^2-1/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a^3*c^2-1/f*d/(c^2+d^2)/(c+d*tan(f*x+e))*A*a^3+1/f*d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a^3-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b^3*c^2+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b^3*d^2+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^3*c^2-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^3*d^2+3/f*b^2/d^2*C*tan(f*x+e)*a-2/f*b^3/d^3*C*c*tan(f*x+e)+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b^3*c^2-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b^3*d^2+1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^3*c^2-1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^3*d^2","B"
78,1,1554,417,0.267000," ","int((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x)","\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) C a b \,c^{4}}{f \,d^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 C \,c^{3} a b}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{4 d \ln \left(c +d \tan \left(f x +e \right)\right) B a b c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 B a b \,c^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{4 A \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{4 C \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{C \,a^{2} c^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{C \,c^{4} b^{2}}{f \,d^{3} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) A \,a^{2} c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) A a b}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) A \,b^{2} c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,b^{2} c^{4}}{f \,d^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) C \,a^{2} c}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) C \,b^{2} c^{5}}{f \,d^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{4 \ln \left(c +d \tan \left(f x +e \right)\right) C \,b^{2} c^{3}}{f d \left(c^{2}+d^{2}\right)^{2}}+\frac{2 A a b c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{6 \ln \left(c +d \tan \left(f x +e \right)\right) C a b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{A \,b^{2} c^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{B \,c^{3} b^{2}}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) A a b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{d A \,a^{2}}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{B \,a^{2} c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B \,b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{b^{2} C \tan \left(f x +e \right)}{f \,d^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"2/f/d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a*b*c^4+2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*b*c*d+2/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))*C*c^3*a*b-4/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a*b*c-2/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*B*a*b*c^2+4/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*b*c*d-4/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*b*c*d-1/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*C*a^2*c^2-1/f/d^3/(c^2+d^2)/(c+d*tan(f*x+e))*C*c^4*b^2+2/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a^2*c+2/f*d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a*b-2/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b^2*c+1/f/d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*b^2*c^4-2/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a*b*c^2+2/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a*b*d^2-2/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a^2*c-2/f/d^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b^2*c^5-4/f/d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b^2*c^3-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*c*d-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b^2*c*d+2/f/(c^2+d^2)/(c+d*tan(f*x+e))*A*a*b*c+6/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a*b*c^2-2/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b^2*c*d+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b^2*c*d+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*c*d-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a*b*c^2+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a*b*d^2+2/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a^2*c*d-1/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*A*b^2*c^2+1/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))*B*c^3*b^2-2/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a*b*c^2+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a*b*c^2-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a*b*d^2-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*b^2*c^2+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*b^2*d^2-1/f*d/(c^2+d^2)/(c+d*tan(f*x+e))*A*a^2+1/f*d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a^2+1/f/(c^2+d^2)/(c+d*tan(f*x+e))*B*a^2*c-1/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a^2*c^2+3/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*b^2*c^2-1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^2*d^2-1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*b^2*c^2+1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*b^2*d^2-1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^2*c^2+1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^2*d^2+1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^2*c^2+1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*b^2*c^2-1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*b^2*d^2+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*c^2-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*d^2+1/f*b^2*C/d^2*tan(f*x+e)","B"
79,1,948,292,0.270000," ","int((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x)","\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{B a c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) A a c}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) b c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{C \,c^{3} b}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) B b c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) b c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C b \,c^{4}}{f \left(c^{2}+d^{2}\right)^{2} d^{2}}-\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) C a c}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{B b \,c^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{C a \,c^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{d a A}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) B a}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{A b c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) A b}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B a \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*d^2+3/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b*c^2+1/f/(c^2+d^2)/(c+d*tan(f*x+e))*B*a*c+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a*c*d+2/f/(c^2+d^2)^2*d*ln(c+d*tan(f*x+e))*A*a*c-2/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*b*c*d+1/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))*C*c^3*b+2/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a*c*d-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a*c*d+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*b*c*d-2/f/(c^2+d^2)^2*d*ln(c+d*tan(f*x+e))*B*b*c+2/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*b*c*d+1/f/(c^2+d^2)^2/d^2*ln(c+d*tan(f*x+e))*C*b*c^4-2/f/(c^2+d^2)^2*d*ln(c+d*tan(f*x+e))*C*a*c-1/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*B*b*c^2-1/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*C*a*c^2-1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*d^2-1/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b*c^2-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b*d^2-1/f*d/(c^2+d^2)/(c+d*tan(f*x+e))*a*A+1/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b*d^2+1/f/(c^2+d^2)^2*d^2*ln(c+d*tan(f*x+e))*B*a+1/f/(c^2+d^2)/(c+d*tan(f*x+e))*A*b*c+1/f/(c^2+d^2)^2*d^2*ln(c+d*tan(f*x+e))*A*b-1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*c^2-1/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a*c^2+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b*c^2+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*c^2-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*d^2-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b*c^2+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b*d^2-1/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b*c^2+1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*c^2","B"
80,1,438,140,0.296000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x)","-\frac{d A}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{B c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{c^{2} C}{f \left(c^{2}+d^{2}\right) d \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) A c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) c C d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c C d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"-1/f/(c^2+d^2)*d/(c+d*tan(f*x+e))*A+1/f/(c^2+d^2)/(c+d*tan(f*x+e))*B*c-1/f/(c^2+d^2)/d/(c+d*tan(f*x+e))*c^2*C+2/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*c*d-1/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*c^2+1/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*d^2-2/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c*C*d-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*c*d+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*c^2-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*d^2+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*c*C*d+1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*c^2-1/f/(c^2+d^2)^2*A*arctan(tan(f*x+e))*d^2+2/f/(c^2+d^2)^2*B*arctan(tan(f*x+e))*c*d-1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*c^2+1/f/(c^2+d^2)^2*C*arctan(tan(f*x+e))*d^2","B"
81,1,1263,293,0.547000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x)","\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a c d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b c d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a c d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{2 C \arctan \left(\tan \left(f x +e \right)\right) b c d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) A a c \,d^{3}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A b \,c^{2} d^{2}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B a \,c^{2} d^{2}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) B b \,c^{3} d}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) C a c \,d^{3}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C b \,c^{2} d^{2}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a c d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{2 A \arctan \left(\tan \left(f x +e \right)\right) b c d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,d^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,c^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,c^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,d^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,d^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,c^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B a \,d^{4}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C b \,c^{4}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{B c d}{f \left(d a -c b \right) \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,d^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{b \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} C}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A b \,d^{4}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) B a}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)}+\frac{b^{3} \ln \left(a +b \tan \left(f x +e \right)\right) A}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)}-\frac{A \,d^{2}}{f \left(d a -c b \right) \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{c^{2} C}{f \left(d a -c b \right) \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}"," ",0,"-1/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*b*c*d+2/f/(a^2+b^2)/(c^2+d^2)^2*C*arctan(tan(f*x+e))*b*c*d+2/f/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a*c*d^3-3/f/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b*c^2*d^2-1/f/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a*c^2*d^2+2/f/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*b*c^3*d-2/f/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a*c*d^3+1/f/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b*c^2*d^2-1/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a*c*d+2/f/(a^2+b^2)/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a*c*d-2/f/(a^2+b^2)/(c^2+d^2)^2*A*arctan(tan(f*x+e))*b*c*d+1/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a*c*d-1/2/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b*c^2+1/f/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a*d^4-1/f/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b*c^4+1/f/(a*d-b*c)/(c^2+d^2)/(c+d*tan(f*x+e))*B*c*d+1/f/(a^2+b^2)/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b*c^2-1/f/(a^2+b^2)/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b*d^2-1/f/(a^2+b^2)/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*c^2+1/f/(a^2+b^2)/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*d^2-1/2/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*d^2+1/2/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b*c^2+1/2/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*c^2-1/2/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b*d^2+1/f/(a^2+b^2)/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*c^2-1/f/(a^2+b^2)/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*d^2+1/f*b/(a*d-b*c)^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^2*C-1/f/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b*d^4+1/2/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b*d^2-1/f*b^2/(a*d-b*c)^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*B*a+1/f*b^3/(a*d-b*c)^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*A-1/f/(a*d-b*c)/(c^2+d^2)/(c+d*tan(f*x+e))*A*d^2-1/f/(a*d-b*c)/(c^2+d^2)/(c+d*tan(f*x+e))*c^2*C","B"
82,1,2012,508,0.481000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x)","-\frac{4 A \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) A a c}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}-\frac{3 b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) a^{3} B d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}+\frac{b^{3} \ln \left(a +b \tan \left(f x +e \right)\right) B \,a^{2} c}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}+\frac{4 b^{3} \ln \left(a +b \tan \left(f x +e \right)\right) A \,a^{2} d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}-\frac{4 d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) A b \,c^{2}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) B a d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) a^{4} C d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) C a c}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}-\frac{d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) B a \,c^{2}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{3 d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) B b \,c^{3}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) B b c}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) C a c}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) C b \,c^{4}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) A a c}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 B \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{4 C \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a b c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} c^{2}}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,a^{2} d^{2}}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} c^{2}}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,b^{2} d^{2}}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 b^{5} \ln \left(a +b \tan \left(f x +e \right)\right) A d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}-\frac{2 d^{5} \ln \left(c +d \tan \left(f x +e \right)\right) A b}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{d^{5} \ln \left(c +d \tan \left(f x +e \right)\right) B a}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{d^{2} B c}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{d \,c^{2} C}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{b^{5} \ln \left(a +b \tan \left(f x +e \right)\right) B c}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}+\frac{b^{2} B a}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{b \,a^{2} C}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{d^{3} A}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{b^{3} A}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}"," ",0,"-2/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*b*c*d-4/f/(a^2+b^2)^2/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*b*c*d-2/f*b^4/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a*c-3/f*b^2/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^3*B*d+1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b^2*c*d-1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a*b*c^2+1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a*b*d^2+1/f*b^3/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^2*c+4/f*b^3/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a^2*d-4/f*d^3/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b*c^2-1/f*b^4/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a*d+2/f*b/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^4*C*d+2/f*b^4/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a*c-1/f*d^3/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a*c^2+3/f*d^2/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*b*c^3+1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a*b*c^2-1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a*b*d^2-1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b^2*c*d-2/f/(a^2+b^2)^2/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b^2*c*d+1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*c*d+1/f*d^4/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*b*c-2/f*d^4/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a*c-2/f*d/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b*c^4-1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*c*d+2/f*d^4/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a*c+2/f/(a^2+b^2)^2/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a^2*c*d+2/f/(a^2+b^2)^2/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a*b*c^2-2/f/(a^2+b^2)^2/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a*b*d^2+4/f/(a^2+b^2)^2/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*b*c*d+2/f*b^5/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*d-2/f*d^5/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b+1/f*d^5/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a+1/2/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*c^2-1/2/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*d^2-1/f/(a^2+b^2)^2/(c^2+d^2)^2*C*arctan(tan(f*x+e))*b^2*d^2-1/2/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*b^2*c^2+1/2/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*b^2*d^2+1/f/(a^2+b^2)^2/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^2*c^2-1/f/(a^2+b^2)^2/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^2*d^2-1/f/(a^2+b^2)^2/(c^2+d^2)^2*A*arctan(tan(f*x+e))*b^2*c^2+1/f/(a^2+b^2)^2/(c^2+d^2)^2*C*arctan(tan(f*x+e))*b^2*c^2+1/f/(a^2+b^2)^2/(c^2+d^2)^2*A*arctan(tan(f*x+e))*b^2*d^2-1/f/(a^2+b^2)^2/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^2*c^2+1/f/(a^2+b^2)^2/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^2*d^2+1/f*d^2/(a*d-b*c)^2/(c^2+d^2)/(c+d*tan(f*x+e))*B*c-1/f*d/(a*d-b*c)^2/(c^2+d^2)/(c+d*tan(f*x+e))*c^2*C-1/f*b^5/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*c+1/f*b^2/(a*d-b*c)^2/(a^2+b^2)/(a+b*tan(f*x+e))*B*a-1/f*b/(a*d-b*c)^2/(a^2+b^2)/(a+b*tan(f*x+e))*a^2*C-1/f*d^3/(a*d-b*c)^2/(c^2+d^2)/(c+d*tan(f*x+e))*A-1/f*b^3/(a*d-b*c)^2/(a^2+b^2)/(a+b*tan(f*x+e))*A","B"
83,1,3364,838,0.623000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"-1/f*d^2/(a*d-b*c)^3/(c^2+d^2)/(c+d*tan(f*x+e))*c^2*C+1/f/(a^2+b^2)^3/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^3*c^2-1/f/(a^2+b^2)^3/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^3*d^2-1/f/(a^2+b^2)^3/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b^3*c^2+1/f/(a^2+b^2)^3/(c^2+d^2)^2*B*arctan(tan(f*x+e))*b^3*d^2+2/f*b^4/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a*c+3/f*b^2/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^3*B*d-1/f*b^3/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a^2*c+1/f*b^4/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*a*d-2/f*b/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^4*C*d-2/f*b^4/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*C*a*c+10/f*b^3/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^4*d^2-2/f*d^5/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*a*c-3/f*d^2/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b*c^4-1/f*d^4/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*C*b*c^2+2/f*d^5/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*b*c+2/f/(a^2+b^2)^3/(c^2+d^2)^2*A*arctan(tan(f*x+e))*b^3*c*d+2/f/(a^2+b^2)^3/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a^3*c*d+3/f/(a^2+b^2)^3/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a^2*b*c^2-3/f/(a^2+b^2)^3/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a^2*b*d^2+3/f/(a^2+b^2)^3/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*b^2*c^2-3/f/(a^2+b^2)^3/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a*b^2*d^2-2/f/(a^2+b^2)^3/(c^2+d^2)^2*C*arctan(tan(f*x+e))*b^3*c*d-1/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a^3*c*d-3/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*b^2*c^2+3/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a*b^2*d^2+1/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*b^3*c*d+3/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*b*c^2-3/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a^2*b*d^2-3/f/(a^2+b^2)^3/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*b^2*c^2+3/f/(a^2+b^2)^3/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a*b^2*d^2+1/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a^3*c*d-4/f*b^3/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*a^2*d+2/f*d^5/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*a*c-5/f*d^4/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b*c^2-1/f*d^4/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a*c^2+4/f*d^3/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*b*c^3-6/f*b^2/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^5*B*d^2-1/f*b^4/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^3*c^2-3/f*b^4/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^3*d^2+3/f*b^6/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a*B*c^2-1/f*b^6/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a*d^2-2/f*b^7/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*c*d+3/f*b/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^6*C*d^2-1/f*b^3/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^4*C*d^2-3/f*b^5/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^2*c^2-3/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*b*c^2+3/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a^2*b*d^2+3/f*b^5/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^2*c^2+9/f*b^5/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^2*d^2+6/f/(a^2+b^2)^3/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^2*b*c*d-10/f*b^4/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a^3*c*d+4/f*b^3/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^4*c*d-6/f/(a^2+b^2)^3/(c^2+d^2)^2*B*arctan(tan(f*x+e))*a*b^2*c*d-3/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*a*b^2*c*d-2/f*b^6/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*a*c*d+3/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*a*b^2*c*d-3/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^2*b*c*d-6/f/(a^2+b^2)^3/(c^2+d^2)^2*A*arctan(tan(f*x+e))*a^2*b*c*d+10/f*b^4/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a^3*c*d-6/f*b^5/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*B*a^2*c*d+3/f*b^7/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*d^2+1/f*b^7/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*c^2+1/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b^3*c^2-1/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*A*b^3*d^2+1/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^3*c^2-1/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*B*a^3*d^2-1/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b^3*c^2+1/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*C*b^3*d^2+1/2/f*b^2/(a*d-b*c)^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*B*a-1/2/f*b/(a*d-b*c)^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*a^2*C-3/f*d^6/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*A*b+1/f*d^6/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*B*a+1/f*d^3/(a*d-b*c)^3/(c^2+d^2)/(c+d*tan(f*x+e))*B*c-1/f/(a^2+b^2)^3/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^3*c^2+1/f/(a^2+b^2)^3/(c^2+d^2)^2*C*arctan(tan(f*x+e))*a^3*d^2-2/f*b^5/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*A*d+1/f*b^5/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*B*c-1/f*b^7/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*A*c^2+2/f*b^6/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*C*a*c*d-1/2/f*b^3/(a*d-b*c)^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*A-1/f*d^4/(a*d-b*c)^3/(c^2+d^2)/(c+d*tan(f*x+e))*A","B"
84,1,3522,800,0.294000," ","int((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"3/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^3*c^2*d-3/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^2*b*c^3+3/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*b^2*d^3-1/f/d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*b^3*c^4-1/2/f/d^3/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*c^4*b^3-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*b^2*d^3+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b^3*c*d^2+1/2/f/d^4/(c^2+d^2)/(c+d*tan(f*x+e))^2*C*c^5*b^3+3/f*d^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^3*c-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b^3*c*d^2+6/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a^2*b*c-3/f/d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a*b^2*c^4-3/f/d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a^2*b*c^4+6/f/d^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a*b^2*c^5+12/f/d/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a*b^2*c^3+9/f*d^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a^2*b*c+18/f*d/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a*b^2*c^2-9/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*b*c*d^2+9/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*b^2*c^2*d+9/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*b*c^2*d-9/f*d/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a*b^2*c^2-9/f*d/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^2*b*c^2+9/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*b*c*d^2-9/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*b^2*c^2*d+9/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a^2*b*c^2*d+9/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*b^2*c*d^2+9/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^2*b*c*d^2-9/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*b^2*c^2*d-9/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a^2*b*c^2*d-9/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*b^2*c*d^2-3/2/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*A*a*b^2*c^2+9/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*b^2*c*d^2-9/f*d^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b^2*c-3/2/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*a^2*b*c^2+3/2/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*a*b^2*c^3+3/2/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*C*a^2*b*c^3-3/2/f/d^3/(c^2+d^2)/(c+d*tan(f*x+e))^2*C*c^4*a*b^2+6/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*a*b^2*c-9/f*d^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a^2*b*c+3/f/d^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a*b^2*c^6+9/f/d/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a*b^2*c^4+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a^3*c^2*d-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*b*c^3+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*b^2*d^3+1/2/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*A*b^3*c^3+1/f*b^3*C/d^3*tan(f*x+e)+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a^2*b*c^3+3/2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*A*a^2*b*c+3/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*a^2*b*c^2+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b^2*c^3-3/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a^3*c*d^2-3/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a^2*b*d^3-3/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*b^2*c^3-3/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b^3*c^2*d+6/f*d/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^3*c^2-3/f*d/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a^3*c^2-3/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b^3*c*d^2-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^3*c^2*d+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*b*c^3+3/f/d/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^3*c^4+3/f*d^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^2*b+1/f/d^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^3*c^6-9/f/d^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b^3*c^5-1/f*d^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a^3-1/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a^3*c^3-1/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b^3*d^3+1/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a^3*c^2+1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^3*c^3-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*b*d^3-9/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a*b^2*c^2-9/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a^2*b*c^2-3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a^2*b*c^3-1/2/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*C*a^3*c^2-2/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*a^3*c-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*b^2*c^3+3/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a^3*c*d^2+3/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a^2*b*d^3+3/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*b^2*c^3+2/f/d^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*b^3*c^5+4/f/d/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*b^3*c^3+2/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a^3*c+3/f*d/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a^3*c^2-3/f*d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*a^2*b-3/f*d^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^3*c-3/f/d^4/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*b^3*c^6-5/f/d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*b^3*c^4-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^3*c*d^2+1/f*d^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a^3+1/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a^3*c^3+1/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b^3*d^3-1/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^3*d^3-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b^3*c^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^3*c^3+1/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b^3*c^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b^3*d^3-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^3*C*d^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b^3*c^3-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^3*c^3-10/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b^3*c^3-3/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*b^3*c^2+1/2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*a^3*c+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^3*d^3-1/2/f*d/(c^2+d^2)/(c+d*tan(f*x+e))^2*A*a^3-1/f*d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a^3-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b^3*c^2*d+3/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b^3*c^2*d+3/f*d^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a*b^2-3/f/d^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b^3*c^7","B"
85,1,2465,595,0.320000," ","int((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"1/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*C*a*b*c^3-1/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*c^2*a*b+4/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a*b*c-2/f/d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a*b*c^4+6/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*b*c*d^2-6/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*b*c^2*d-3/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*b*c*d^2+3/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*b*c^2*d+3/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*b*c*d^2+6/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*b*c^2*d+6/f/(c^2+d^2)^3*d^2*ln(c+d*tan(f*x+e))*A*a*b*c-6/f/(c^2+d^2)^3*d*ln(c+d*tan(f*x+e))*B*a*b*c^2-6/f/(c^2+d^2)^3*d^2*ln(c+d*tan(f*x+e))*C*a*b*c-2/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a*b*c^3+2/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*a*b*c^2-6/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a*b*c^2+1/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*A*a*c*b-1/f/d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*b^2*c^4+2/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a^2*c-1/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^2*d^3+1/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b^2*d^3-1/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a^2*c^3+1/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b^2*c^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*d^3-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b^2*d^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*c^3-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b^2*c^3-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*d^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b^2*d^3-1/2/f*d/(c^2+d^2)/(c+d*tan(f*x+e))^2*a^2*A-1/f*d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a^2-1/f/(c^2+d^2)^3*d^3*ln(c+d*tan(f*x+e))*A*a^2+1/f/(c^2+d^2)^3*d^3*ln(c+d*tan(f*x+e))*A*b^2+1/f/(c^2+d^2)^3*d^3*ln(c+d*tan(f*x+e))*C*a^2-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^2*c^3+1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^2*c^3+1/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a^2*c^2-3/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*b^2*c^2+1/2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*a^2*c+1/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a^2*c^3-1/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b^2*c^3-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*c^2*d+1/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*b*c^3+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b^2*c^2*d-1/2/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*A*c^2*b^2+2/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a*b*c^3+2/f/d^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*b^2*c^5+4/f/d/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*b^2*c^3+1/2/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*b^2*c^3+3/f/(c^2+d^2)^3*d*ln(c+d*tan(f*x+e))*A*a^2*c^2-3/f/(c^2+d^2)^3*d*ln(c+d*tan(f*x+e))*A*b^2*c^2+3/f/(c^2+d^2)^3*d^2*ln(c+d*tan(f*x+e))*B*a^2*c+2/f/(c^2+d^2)^3*d^3*ln(c+d*tan(f*x+e))*B*a*b-3/f/(c^2+d^2)^3*d^2*ln(c+d*tan(f*x+e))*B*b^2*c-3/f/(c^2+d^2)^3*d*ln(c+d*tan(f*x+e))*C*a^2*c^2+1/f/(c^2+d^2)^3/d^3*ln(c+d*tan(f*x+e))*C*b^2*c^6+3/f/(c^2+d^2)^3/d*ln(c+d*tan(f*x+e))*C*b^2*c^4-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*c*d^2-1/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*b*d^3-1/2/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*C*c^2*a^2-1/2/f/d^3/(c^2+d^2)/(c+d*tan(f*x+e))^2*b^2*C*c^4-3/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a^2*c*d^2-2/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*b*d^3+3/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b^2*c*d^2+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*c^2*d-1/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*b*c^3-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b^2*c^2*d+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b^2*c*d^2-2/f*d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*a*b+2/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*b^2*c+3/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a^2*c*d^2+2/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*b*d^3-3/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b^2*c*d^2+3/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^2*c^2*d-2/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*b*c^3-3/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b^2*c^2*d+6/f/(c^2+d^2)^3*d*ln(c+d*tan(f*x+e))*C*b^2*c^2-2/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*a^2*c","B"
86,1,1513,351,0.333000," ","int((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x)","\frac{A b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{d^{2} B a}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{3 C b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B a \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B b \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C a \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C b \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{2 d C a c}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 d B b c}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{C b \,c^{3}}{2 f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C a \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C b c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B b \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{B b \,c^{2}}{2 f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{C a \,c^{2}}{2 f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{2 d A a c}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B b \,c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A b c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) b c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{C b \,c^{4}}{f \left(c^{2}+d^{2}\right)^{2} d^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A a \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A b c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B a c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,c^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b \,d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C b c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A a \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A b \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{B a \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{d^{2} A b}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,c^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,c^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{A b c}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{B a c}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{d A a}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{A \arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) a \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{C \arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}"," ",0,"1/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*b*c^2-1/f/(c^2+d^2)^2*d^2/(c+d*tan(f*x+e))*B*a-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b*c^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b*c^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*c^3-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b*d^3-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*d^3-3/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*b*c^2-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*c^3+1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b*d^3+1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a*d^3+1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b*c^3+2/f/(c^2+d^2)^2*d/(c+d*tan(f*x+e))*C*a*c+2/f/(c^2+d^2)^2*d/(c+d*tan(f*x+e))*B*b*c+3/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*c*d^2-3/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b*c^2*d+1/2/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*C*b*c^3-3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a*c^2*d-3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b*c*d^2-3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b*c^2*d-1/2/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*b*c^2-1/2/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*C*a*c^2+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b*c^2*d-2/f/(c^2+d^2)^2*d/(c+d*tan(f*x+e))*A*a*c-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b*c*d^2-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*c*d^2+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*c^2*d+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b*c*d^2-3/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*c*d^2+3/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b*c^2*d+3/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*c^2*d+3/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b*c*d^2-1/f/(c^2+d^2)^2/d^2/(c+d*tan(f*x+e))*C*b*c^4-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*c^2*d+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a*c^2*d+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b*c*d^2+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*c*d^2+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*d^3+1/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*c^3-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a*d^3-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b*c^3+1/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a*c^2-1/f/(c^2+d^2)^2*d^2/(c+d*tan(f*x+e))*A*b+1/2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*A*b*c+1/2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*a*c-1/2/f*d/(c^2+d^2)/(c+d*tan(f*x+e))^2*A*a-1/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b*d^3-1/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*d^3-1/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b*c^3-1/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*c^3+1/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b*d^3","B"
87,1,713,206,0.292000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x)","-\frac{d A}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{B c}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{B \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A \,d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{d^{2} B}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B \,c^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{c^{2} C}{2 f \left(c^{2}+d^{2}\right) d \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{2 A c d}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 c C d}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C \,c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}"," ",0,"-1/2/f/(c^2+d^2)*d/(c+d*tan(f*x+e))^2*A+1/2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*c-1/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*d^3-1/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*c^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*d^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*c^3-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*d^3-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*d^3-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*c^3+1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*d^3+1/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*c^2+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*c^2*d+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*c*d^2-3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*c^2*d-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*c^2*d-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*c*d^2+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*c^2*d-3/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*c*d^2+1/f/(c^2+d^2)^3*A*arctan(tan(f*x+e))*c^3-1/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*d^2*B+3/f/(c^2+d^2)^3*B*arctan(tan(f*x+e))*c^2*d+3/f/(c^2+d^2)^3*C*arctan(tan(f*x+e))*c*d^2-1/2/f/(c^2+d^2)/d/(c+d*tan(f*x+e))^2*c^2*C-2/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*c*d+2/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*c*C*d","B"
88,1,2298,485,0.528000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x)","-\frac{8 \ln \left(c +d \tan \left(f x +e \right)\right) A a b \,c^{3} d^{3}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{b^{3} \ln \left(a +b \tan \left(f x +e \right)\right) B a}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)}-\frac{b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} C}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{A b \,d^{4}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{B a \,d^{4}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{C b \,c^{4}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A \,a^{2} d^{6}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,c^{2} d}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B b \,c^{2} d}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B \,b^{2} c^{5} d}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,b^{2} c^{3} d^{3}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C \,a^{2} c^{2} d^{4}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) C \,b^{2} c^{4} d^{2}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) A b c \,d^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) B a c \,d^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,c^{2} d}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) C b c \,d^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{C b \,c^{2} d^{2}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{2 A a c \,d^{3}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 A b \,c^{2} d^{2}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{B a \,c^{2} d^{2}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{2 B b \,c^{3} d}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{3 C \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) a \,c^{2} d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{2 C a c \,d^{3}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{3 A \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A \,a^{2} c^{2} d^{4}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{6 \ln \left(c +d \tan \left(f x +e \right)\right) A \,b^{2} c^{4} d^{2}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) A \,b^{2} c^{2} d^{4}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{2} c^{3} d^{3}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B \,a^{2} c \,d^{5}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) B a b \,d^{6}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{3 B \arctan \left(\tan \left(f x +e \right)\right) b c \,d^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) A \,b^{2} d^{6}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C \,a^{2} d^{6}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) C \,b^{2} c^{6}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{B c d}{2 f \left(d a -c b \right) \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{A \arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{B \arctan \left(\tan \left(f x +e \right)\right) a \,d^{3}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{B \arctan \left(\tan \left(f x +e \right)\right) b \,c^{3}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{C \arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A b \,c^{3}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B a \,c^{3}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) B b \,d^{3}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C a \,d^{3}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) C b \,c^{3}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) A a \,d^{3}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{A \,d^{2}}{2 f \left(d a -c b \right) \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{c^{2} C}{2 f \left(d a -c b \right) \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) A}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) B a b \,c^{4} d^{2}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{6 \ln \left(c +d \tan \left(f x +e \right)\right) B a b \,c^{2} d^{4}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{8 \ln \left(c +d \tan \left(f x +e \right)\right) C a b \,c^{3} d^{3}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}"," ",0,"-8/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a*b*c^3*d^3+1/f*b^3/(a*d-b*c)^3/(a^2+b^2)*ln(a+b*tan(f*x+e))*B*a-1/f*b^2/(a*d-b*c)^3/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^2*C+1/f/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*b*d^4-1/f/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a*d^4+1/f/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*b*c^4-1/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a^2*d^6-1/f/(a^2+b^2)/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b*d^3-3/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b*c^2*d-3/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^2*c^5*d+1/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^2*c^3*d^3-3/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a^2*c^2*d^4-3/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b^2*c^4*d^2-3/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*c^2*d+3/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b*c*d^2-3/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*c*d^2-1/f/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*b*c^2*d^2-2/f/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*a*c*d^3+3/f/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*b*c^2*d^2+1/f/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a*c^2*d^2-2/f/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*b*c^3*d+3/f/(a^2+b^2)/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*c*d^2+3/f/(a^2+b^2)/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b*c^2*d-3/f/(a^2+b^2)/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b*c^2*d+3/f/(a^2+b^2)/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*c^2*d+3/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*c^2*d+2/f/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a*c*d^3-3/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b*c*d^2-3/f/(a^2+b^2)/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*c*d^2+3/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a^2*c^2*d^4+6/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^2*c^4*d^2+3/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^2*c^2*d^4-1/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^2*c^3*d^3+3/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^2*c*d^5-1/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b*d^6-3/f/(a^2+b^2)/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b*c*d^2+1/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^2*d^6+1/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a^2*d^6+1/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b^2*c^6+1/2/f/(a*d-b*c)/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*c*d+1/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*d^3-1/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b*c^3+1/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*c^3+1/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b*d^3-1/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*d^3+1/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b*c^3+1/f/(a^2+b^2)/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*c^3+1/f/(a^2+b^2)/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b*d^3-1/f/(a^2+b^2)/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*d^3+1/f/(a^2+b^2)/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b*c^3-1/f/(a^2+b^2)/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*c^3-1/2/f/(a*d-b*c)/(c^2+d^2)/(c+d*tan(f*x+e))^2*A*d^2-1/2/f/(a*d-b*c)/(c^2+d^2)/(c+d*tan(f*x+e))^2*c^2*C-1/f*b^4/(a*d-b*c)^3/(a^2+b^2)*ln(a+b*tan(f*x+e))*A+3/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b*c^4*d^2-6/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b*c^2*d^4+8/f/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a*b*c^3*d^3","B"
89,1,3364,858,0.620000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"2/f*d^4/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a*c+2/f*d/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*b*c^4+3/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a^2*c^2-3/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a^2*c^2+3/f*d/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b^2*c^6-1/f*d^3/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b^2*c^4-5/f*b^4/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a^2*d-3/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a^2*c*d^2+2/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*b*d^3+3/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b^2*c*d^2+3/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^2*c^2*d-1/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*b*c^3+3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b^2*c^2*d-3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*c*d^2+1/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*b*d^3+10/f*d^3/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^2*c^4+9/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^2*c^2-1/f*d^4/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^2*c^3-1/f*b^4/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a^2*d-2/f*b^5/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a*c-2/f*d^4/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*a*c+4/f*d^3/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*b*c^2+1/f*d^3/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a*c^2-3/f*d^2/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*b*c^3-1/f*d^4/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*b*c-3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*c^2*d+3/f/(a^2+b^2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a^2*c*d^2-2/f/(a^2+b^2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*b*d^3-3/f/(a^2+b^2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b^2*c*d^2+2/f*b^5/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a*c+4/f*b^3/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^3*B*d-1/f*b^4/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^2*c+2/f*b^5/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a*d-3/f*b^2/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^4*C*d+3/f*d^6/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^2*c-2/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b-6/f*d^2/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^2*c^5-3/f*d^4/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^2*c^3-1/f*d^6/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^2*c+2/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*b*c^3-3/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b^2*c^2*d-3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b^2*c^2*d+3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b^2*c*d^2+3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*c^2*d+1/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*b*c^3-3/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*b*c*d^2+6/f/(a^2+b^2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*b*c^2*d-3/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*b*c^2*d-1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b^2*c^3-1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*d^3-3/f*b^6/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*d+1/f*b^6/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*c-1/f*b^3/(a*d-b*c)^3/(a^2+b^2)/(a+b*tan(f*x+e))*B*a+1/f*b^2/(a*d-b*c)^3/(a^2+b^2)/(a+b*tan(f*x+e))*a^2*C+2/f*d^5/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*b-1/f*d^5/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a-1/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a^2+3/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^2+1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b^2*d^3+1/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a^2*c^3-1/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arctan(tan(f*x+e))*b^2*c^3-1/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^2*d^3+1/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b^2*d^3-1/f/(a^2+b^2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a^2*c^3+1/f/(a^2+b^2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b^2*c^3+1/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a^2+1/2/f*d^2/(a*d-b*c)^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*c-1/2/f*d/(a*d-b*c)^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*c^2*C+1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*d^3-1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b^2*d^3+1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*c^3-2/f*d^6/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a*b*c+4/f*d^3/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b*c^4+2/f*d^6/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a*b*c-6/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b*c^2+10/f*d^4/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a*b*c^3-6/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*b*c*d^2-10/f*d^4/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a*b*c^3-6/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*b*c^2*d-1/2/f*d^3/(a*d-b*c)^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*A+1/f*b^4/(a*d-b*c)^3/(a^2+b^2)/(a+b*tan(f*x+e))*A+3/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*b*c*d^2","B"
90,1,6661,424,0.618000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
91,1,4775,291,0.455000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\text{output too large to display}"," ",0,"-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)*a*b+2/f*B*a^2*(c+d*tan(f*x+e))^(1/2)-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a*b*c-2/f*B*b^2*(c+d*tan(f*x+e))^(1/2)-1/2/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c+1/2/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b+1/2/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c-1/2/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b+2/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a*b+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c-2/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a*b-4/3/f/d^2*C*(c+d*tan(f*x+e))^(3/2)*a*b*c+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a*b*c-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)*a*b+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)*a*b+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a*b*c-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)*a*b+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a*b*c-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a^2+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a^2-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b^2+2/3/f/d^3*C*(c+d*tan(f*x+e))^(3/2)*b^2*c^2-4/5/f/d^3*C*(c+d*tan(f*x+e))^(5/2)*b^2*c+4/3/f/d*B*(c+d*tan(f*x+e))^(3/2)*a*b-2/3/f/d^2*B*(c+d*tan(f*x+e))^(3/2)*b^2*c+4/5/f/d^2*C*(c+d*tan(f*x+e))^(5/2)*a*b+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b^2-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a^2+1/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a^2*c+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b^2*c+1/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b-1/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*a^2-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*b^2+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a^2*c-1/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*a^2+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*b^2-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b^2*c+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b^2+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a^2-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b^2+2/7/f/d^3*b^2*C*(c+d*tan(f*x+e))^(7/2)+2/3/f/d*C*(c+d*tan(f*x+e))^(3/2)*a^2-2/3/f/d*C*(c+d*tan(f*x+e))^(3/2)*b^2+2/5/f/d^2*B*(c+d*tan(f*x+e))^(5/2)*b^2+2/3/f/d*A*(c+d*tan(f*x+e))^(3/2)*b^2+4/f*A*a*b*(c+d*tan(f*x+e))^(1/2)-4/f*C*a*b*(c+d*tan(f*x+e))^(1/2)+1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2-1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2-1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2+1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2","B"
92,1,3028,194,0.500000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\text{output too large to display}"," ",0,"1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*a+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b*c+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b*c-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a*c+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a*c+1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a-1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+2/3/f/d*B*(c+d*tan(f*x+e))^(3/2)*b+2/5/f/d^2*C*b*(c+d*tan(f*x+e))^(5/2)+2/3/f/d*C*(c+d*tan(f*x+e))^(3/2)*a-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*a+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)*b+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)*b+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a-2/3/f/d^2*C*(c+d*tan(f*x+e))^(3/2)*b*c-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b*c-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)*b-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b*c-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)*b-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a+2/f*A*(c+d*tan(f*x+e))^(1/2)*b+2/f*B*(c+d*tan(f*x+e))^(1/2)*a-2/f*C*b*(c+d*tan(f*x+e))^(1/2)","B"
93,1,1472,130,0.436000," ","int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\frac{2 C \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 d f}+\frac{2 B \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) A}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) C}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) A}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) C}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{4 d f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{4 d f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{4 d f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{4 d f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B \sqrt{c^{2}+d^{2}}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B \sqrt{c^{2}+d^{2}}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{4 d f}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{4 d f}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{4 d f}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{4 d f}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) B \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{4 f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) B \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{4 f}"," ",0,"2/3*C*(c+d*tan(f*x+e))^(3/2)/d/f+2*B*(c+d*tan(f*x+e))^(1/2)/f+d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A-d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C-d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A+d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*c-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*c-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)","B"
94,1,3576,200,0.749000," ","int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"-2/f*b/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*B*a*c-2/f/b/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^3*C*d+1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a+1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b-1/4/f/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+2*C*(c+d*tan(f*x+e))^(1/2)/b/f+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*a+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)*b-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)*b+1/f/(a^2+b^2)*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b*c+2/f*b^2/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*A*c+2/f/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*B*a^2*d+2/f/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*C*a^2*c+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b*c+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)*b+1/f/(a^2+b^2)*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a-1/f/(a^2+b^2)*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*a+1/f/(a^2+b^2)*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b-1/f/(a^2+b^2)*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a-1/f/(a^2+b^2)*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b*c-1/4/f/(a^2+b^2)/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b+1/4/f/(a^2+b^2)/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+1/4/f/(a^2+b^2)/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c+1/4/f/(a^2+b^2)/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/(a^2+b^2)/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-2/f*b/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*A*a*d-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a*c+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b*c+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a*c-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)*b-1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/(a^2+b^2)/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/4/f/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/4/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/4/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/4/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/4/f/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b","B"
95,1,5778,284,0.873000," ","int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
96,1,9797,503,0.881000," ","int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
97,1,11056,507,0.640000," ","int((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
98,1,8031,357,0.603000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
99,1,5149,239,0.546000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
100,1,2517,158,0.407000," ","int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{4 d f}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{4 d f}-\frac{2 d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) A c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) A \sqrt{c^{2}+d^{2}}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) C \sqrt{c^{2}+d^{2}}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) C c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) C \sqrt{c^{2}+d^{2}}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B \sqrt{c^{2}+d^{2}}\, c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B \sqrt{c^{2}+d^{2}}\, c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{4 d f}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) B \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{2 f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) B \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{4 f}+\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B \,c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B \,c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, c}{4 d f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, c}{4 d f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, c}{4 d f}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) B \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{4 f}+\frac{2 d A \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{2 d C \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{2 B c \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) B \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{2 f}-\frac{d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{4 f}+\frac{d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{4 f}-\frac{d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) B}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{4 f}+\frac{d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) A \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{4 f}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, c}{4 d f}+\frac{2 C \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) C \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{4 d f}-\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) A \sqrt{c^{2}+d^{2}}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) C c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) A c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 B \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}"," ",0,"1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2-2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*c+d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)-d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)+2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*c+d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*c+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*c-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2-1/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*c^2-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*c^2-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c+1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+2*d/f*A*(c+d*tan(f*x+e))^(1/2)-2*d/f*C*(c+d*tan(f*x+e))^(1/2)+2/f*B*c*(c+d*tan(f*x+e))^(1/2)+1/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-1/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+1/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B+d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B-1/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+1/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c+2/5*C*(c+d*tan(f*x+e))^(5/2)/d/f+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2-d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)-2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*c+2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*c+2/3*B*(c+d*tan(f*x+e))^(3/2)/f","B"
101,1,6055,234,0.830000," ","int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
102,1,9865,337,0.831000," ","int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
103,1,14441,492,0.829000," ","int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
104,1,11478,459,0.595000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
105,1,7402,315,0.519000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
106,1,3614,196,0.408000," ","int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\text{output too large to display}"," ",0,"1/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)-3/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c+d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)+3*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*c^2-3*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*c^2+1/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*c^2+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)*c^2-1/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c-1/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^3+2/5*B*(c+d*tan(f*x+e))^(5/2)/f-2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)*c+2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)*c+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c^2-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c^2-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c^2-2*d^2/f*B*(c+d*tan(f*x+e))^(1/2)-2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*(c^2+d^2)^(1/2)*c+2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)*c+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*c^2+2/3*d/f*A*(c+d*tan(f*x+e))^(3/2)-2/3*d/f*C*(c+d*tan(f*x+e))^(3/2)+2/3/f*B*(c+d*tan(f*x+e))^(3/2)*c+2/f*B*c^2*(c+d*tan(f*x+e))^(1/2)+2/7*C*(c+d*tan(f*x+e))^(7/2)/d/f+d^3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C-d^3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A-d^3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C+1/4*d^2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^3+4*d/f*A*c*(c+d*tan(f*x+e))^(1/2)-3/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*c^3+d^3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A+3/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-3*d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*c+3*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*c^2+3*d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*c-1/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+3/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c+1/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)-3/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-3*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*c^2-4*d/f*c*C*(c+d*tan(f*x+e))^(1/2)-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*c^3+3/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2-1/4*d^2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*(c^2+d^2)^(1/2)+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^3-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^3","B"
107,1,8698,294,0.842000," ","int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
108,1,14119,434,0.874000," ","int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
109,1,20663,599,0.839000," ","int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
110,1,25426,371,0.465000," ","int((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
111,1,18289,254,0.412000," ","int((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
112,1,4138,166,0.396000," ","int((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-2/f/d^2*C*b*c*(c+d*tan(f*x+e))^(1/2)+1/4/f/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/4/f/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/4/f/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a-1/4/f/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/4/f/d/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+1/f/d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a*c^2-1/f/d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a*c^2+1/4/f/d/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-1/4/f/d/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-1/4/f/d/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/f/d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b*c^2+1/f/d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b*c^2+1/f/d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a*c^2+1/4/f/d/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+1/4/f/d/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/f/d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a*c^2-1/f/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b*c+1/f/d*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b-1/f/d*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a-2/f*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*A+2/f/d*C*(c+d*tan(f*x+e))^(1/2)*a+2/f*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b-1/f/d*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b-1/f/d*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a+1/f/d*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a+1/f/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a*c-1/f/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b*c+1/f/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b*c-1/f/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a*c+1/f/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b*c+2/f*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*A-2/f*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b-2/f*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*C+1/f/d*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*a+2/f*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*C+2/f/d*B*(c+d*tan(f*x+e))^(1/2)*b+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b+2/3/f/d^2*C*b*(c+d*tan(f*x+e))^(3/2)-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*C*b+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*b-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a-1/4/f/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/4/f/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a","B"
113,1,5570,112,0.372000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
114,1,13474,179,0.522000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
115,1,20870,294,0.643000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
116,1,49725,476,0.578000," ","int((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
117,1,36710,312,0.464000," ","int((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
118,1,23472,177,0.436000," ","int((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
119,1,11427,136,0.360000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
120,1,26343,229,0.625000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
121,1,40619,411,0.719000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
122,1,85156,550,0.615000," ","int((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
123,1,61833,325,0.519000," ","int((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
124,1,40201,246,0.611000," ","int((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
125,1,20647,184,0.395000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
126,1,45119,328,0.674000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
127,1,67570,639,0.850000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
128,-1,0,606,180.000000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \sqrt{c +d \tan \left(f x +e \right)}\, \left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
129,-1,0,437,180.000000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \sqrt{c +d \tan \left(f x +e \right)}\, \left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
130,-1,0,320,180.000000," ","int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \sqrt{a +b \tan \left(f x +e \right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
131,-1,0,236,180.000000," ","int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2),x)","\int \frac{\sqrt{c +d \tan \left(f x +e \right)}\, \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\sqrt{a +b \tan \left(f x +e \right)}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2),x)","F"
132,-1,0,249,180.000000," ","int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2),x)","\int \frac{\sqrt{c +d \tan \left(f x +e \right)}\, \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2),x)","F"
133,-1,0,323,180.000000," ","int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2),x)","\int \frac{\sqrt{c +d \tan \left(f x +e \right)}\, \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2),x)","F"
134,-1,0,544,180.000000," ","int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(7/2),x)","\int \frac{\sqrt{c +d \tan \left(f x +e \right)}\, \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(7/2),x)","F"
135,-1,0,610,180.000000," ","int((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
136,-1,0,441,180.000000," ","int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \sqrt{a +b \tan \left(f x +e \right)}\, \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
137,-1,0,322,180.000000," ","int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\sqrt{a +b \tan \left(f x +e \right)}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2),x)","F"
138,-1,0,327,180.000000," ","int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2),x)","F"
139,-1,0,345,180.000000," ","int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2),x)","F"
140,-1,0,533,180.000000," ","int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(7/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(7/2),x)","F"
141,-1,0,623,180.000000," ","int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \sqrt{a +b \tan \left(f x +e \right)}\, \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
142,-1,0,438,180.000000," ","int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\sqrt{a +b \tan \left(f x +e \right)}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2),x)","F"
143,-1,0,470,180.000000," ","int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2),x)","F"
144,-1,0,482,180.000000," ","int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2),x)","F"
145,-1,0,527,180.000000," ","int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(7/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(7/2),x)","F"
146,-1,0,887,180.000000," ","int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(9/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{9}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(9/2),x)","F"
147,-1,0,438,180.000000," ","int((a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","F"
148,-1,0,321,180.000000," ","int((a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","F"
149,-1,0,238,180.000000," ","int((a+b*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{\sqrt{a +b \tan \left(f x +e \right)}\, \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x)","F"
150,-1,0,192,180.000000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)}{\sqrt{a +b \tan \left(f x +e \right)}\, \sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x)","F"
151,-1,0,212,180.000000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x)","\int \frac{A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)}{\sqrt{c +d \tan \left(f x +e \right)}\, \left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x)","F"
152,-1,0,328,180.000000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x)","\int \frac{A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)}{\sqrt{c +d \tan \left(f x +e \right)}\, \left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x)","F"
153,-1,0,463,180.000000," ","int((a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","F"
154,-1,0,325,180.000000," ","int((a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","F"
155,-1,0,248,180.000000," ","int((a+b*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{\sqrt{a +b \tan \left(f x +e \right)}\, \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)","F"
156,-1,0,212,180.000000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)}{\sqrt{a +b \tan \left(f x +e \right)}\, \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
157,-1,0,340,180.000000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
158,-1,0,545,180.000000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
159,-1,0,486,180.000000," ","int((a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","F"
160,-1,0,350,180.000000," ","int((a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","F"
161,-1,0,326,180.000000," ","int((a+b*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\sqrt{a +b \tan \left(f x +e \right)}\, \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x)","F"
162,-1,0,332,180.000000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)}{\sqrt{a +b \tan \left(f x +e \right)}\, \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
163,-1,0,600,180.000000," ","int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
164,0,0,368,4.344000," ","int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{n} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
165,0,0,552,2.622000," ","int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{3} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
166,0,0,354,2.191000," ","int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{2} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
167,0,0,239,1.735000," ","int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right) \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
168,0,0,171,1.366000," ","int((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x)","F"
169,0,0,251,4.918000," ","int((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{m} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{c +d \tan \left(f x +e \right)}\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x)","F"
170,0,0,396,4.555000," ","int((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{m} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(c +d \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x)","F"
171,0,0,690,5.038000," ","int((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{m} \left(A +B \tan \left(f x +e \right)+C \left(\tan^{2}\left(f x +e \right)\right)\right)}{\left(c +d \tan \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x)","F"