1,1,141,82,0.022000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{i a B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{i a A \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{i a B \tan \left(d x +c \right)}{d}+\frac{a B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a A \tan \left(d x +c \right)}{d}-\frac{i a \ln \left(1+\tan^{2}\left(d x +c \right)\right) A}{2 d}-\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right) B}{2 d}+\frac{i a B \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{a A \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/3*I*a*B*tan(d*x+c)^3/d+1/2*I/d*a*A*tan(d*x+c)^2-I/d*a*B*tan(d*x+c)+1/2/d*a*B*tan(d*x+c)^2+a*A*tan(d*x+c)/d-1/2*I/d*a*ln(1+tan(d*x+c)^2)*A-1/2/d*a*ln(1+tan(d*x+c)^2)*B+I/d*a*B*arctan(tan(d*x+c))-1/d*a*A*arctan(tan(d*x+c))","A"
2,1,110,63,0.022000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{i a B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{i a A \tan \left(d x +c \right)}{d}+\frac{a B \tan \left(d x +c \right)}{d}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right) A}{2 d}-\frac{i a \ln \left(1+\tan^{2}\left(d x +c \right)\right) B}{2 d}-\frac{i a A \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{a B \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2*I*a*B*tan(d*x+c)^2/d+I/d*a*A*tan(d*x+c)+1/d*a*B*tan(d*x+c)+1/2/d*a*ln(1+tan(d*x+c)^2)*A-1/2*I/d*a*ln(1+tan(d*x+c)^2)*B-I/d*a*A*arctan(tan(d*x+c))-1/d*a*B*arctan(tan(d*x+c))","A"
3,1,81,43,0.023000," ","int((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{i a B \tan \left(d x +c \right)}{d}+\frac{i a \ln \left(1+\tan^{2}\left(d x +c \right)\right) A}{2 d}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right) B}{2 d}-\frac{i a B \arctan \left(\tan \left(d x +c \right)\right)}{d}+\frac{a A \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"I*a*B*tan(d*x+c)/d+1/2*I/d*a*ln(1+tan(d*x+c)^2)*A+1/2/d*a*ln(1+tan(d*x+c)^2)*B-I/d*a*B*arctan(tan(d*x+c))+1/d*a*A*arctan(tan(d*x+c))","A"
4,1,56,38,0.424000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","i A a x +\frac{i A a c}{d}-\frac{i a B \ln \left(\cos \left(d x +c \right)\right)}{d}+a B x +\frac{a A \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{B a c}{d}"," ",0,"I*A*a*x+I/d*A*a*c-I*a*B*ln(cos(d*x+c))/d+a*B*x+a*A*ln(sin(d*x+c))/d+1/d*B*a*c","A"
5,1,71,42,0.338000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","i B a x +\frac{i A a \ln \left(\sin \left(d x +c \right)\right)}{d}-a A x +\frac{i B a c}{d}-\frac{a A \cot \left(d x +c \right)}{d}-\frac{A a c}{d}+\frac{a B \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"I*B*a*x+I/d*A*a*ln(sin(d*x+c))-a*A*x+I/d*B*a*c-a*A*cot(d*x+c)/d-1/d*A*a*c+1/d*a*B*ln(sin(d*x+c))","A"
6,1,101,63,0.448000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-i A a x -\frac{i A \cot \left(d x +c \right) a}{d}-\frac{i A a c}{d}+\frac{i B a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a A \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a A \ln \left(\sin \left(d x +c \right)\right)}{d}-a B x -\frac{B \cot \left(d x +c \right) a}{d}-\frac{B a c}{d}"," ",0,"-I*A*a*x-I/d*A*cot(d*x+c)*a-I/d*A*a*c+I/d*B*a*ln(sin(d*x+c))-1/2*a*A*cot(d*x+c)^2/d-a*A*ln(sin(d*x+c))/d-a*B*x-1/d*B*cot(d*x+c)*a-1/d*B*a*c","A"
7,1,129,81,0.387000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-\frac{i A a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{i A a \ln \left(\sin \left(d x +c \right)\right)}{d}-i B a x -\frac{i B \cot \left(d x +c \right) a}{d}-\frac{i B a c}{d}-\frac{a A \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a A \cot \left(d x +c \right)}{d}+a A x +\frac{A a c}{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}"," ",0,"-1/2*I/d*A*a*cot(d*x+c)^2-I/d*A*a*ln(sin(d*x+c))-I*B*a*x-I/d*B*cot(d*x+c)*a-I/d*B*a*c-1/3*a*A*cot(d*x+c)^3/d+a*A*cot(d*x+c)/d+a*A*x+1/d*A*a*c-1/2/d*a*B*cot(d*x+c)^2-1/d*a*B*ln(sin(d*x+c))","A"
8,1,159,100,0.428000," ","int(cot(d*x+c)^5*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-\frac{i A a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{i A \cot \left(d x +c \right) a}{d}+i A a x +\frac{i A a c}{d}-\frac{i B a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{i B a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a A \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a A \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a A \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{B \cot \left(d x +c \right) a}{d}+a B x +\frac{B a c}{d}"," ",0,"-1/3*I/d*A*a*cot(d*x+c)^3+I/d*A*a*cot(d*x+c)+I*A*a*x+I/d*A*a*c-1/2*I/d*B*a*cot(d*x+c)^2-I/d*B*a*ln(sin(d*x+c))-1/4*a*A*cot(d*x+c)^4/d+1/2*a*A*cot(d*x+c)^2/d+a*A*ln(sin(d*x+c))/d-1/3/d*a*B*cot(d*x+c)^3+1/d*B*cot(d*x+c)*a+a*B*x+1/d*B*a*c","A"
9,1,193,130,0.026000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\frac{2 i a^{2} B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} B \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{i a^{2} A \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{a^{2} A \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 i a^{2} B \tan \left(d x +c \right)}{d}+\frac{a^{2} B \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{2} A \tan \left(d x +c \right)}{d}-\frac{i a^{2} A \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{a^{2} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{2 i a^{2} B \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{2 a^{2} A \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"2/3*I/d*a^2*B*tan(d*x+c)^3-1/4/d*a^2*B*tan(d*x+c)^4+I/d*a^2*A*tan(d*x+c)^2-1/3/d*a^2*A*tan(d*x+c)^3-2*I/d*a^2*B*tan(d*x+c)+1/d*a^2*B*tan(d*x+c)^2+2*a^2*A*tan(d*x+c)/d-I/d*a^2*A*ln(1+tan(d*x+c)^2)-1/d*a^2*B*ln(1+tan(d*x+c)^2)+2*I/d*a^2*B*arctan(tan(d*x+c))-2/d*a^2*A*arctan(tan(d*x+c))","A"
10,1,158,97,0.023000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\frac{i a^{2} B \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{a^{2} B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 i a^{2} A \tan \left(d x +c \right)}{d}-\frac{a^{2} A \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 a^{2} B \tan \left(d x +c \right)}{d}-\frac{i a^{2} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{a^{2} A \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 i a^{2} A \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{2 a^{2} B \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"I/d*a^2*B*tan(d*x+c)^2-1/3/d*a^2*B*tan(d*x+c)^3+2*I/d*a^2*A*tan(d*x+c)-1/2/d*a^2*A*tan(d*x+c)^2+2*a^2*B*tan(d*x+c)/d-I/d*a^2*B*ln(1+tan(d*x+c)^2)+1/d*a^2*A*ln(1+tan(d*x+c)^2)-2*I/d*a^2*A*arctan(tan(d*x+c))-2/d*a^2*B*arctan(tan(d*x+c))","A"
11,1,123,74,0.021000," ","int((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{a^{2} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} A \tan \left(d x +c \right)}{d}+\frac{2 i a^{2} B \tan \left(d x +c \right)}{d}+\frac{i a^{2} A \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{a^{2} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 i a^{2} B \arctan \left(\tan \left(d x +c \right)\right)}{d}+\frac{2 a^{2} A \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^2*B*tan(d*x+c)^2-a^2*A*tan(d*x+c)/d+2*I/d*a^2*B*tan(d*x+c)+I/d*a^2*A*ln(1+tan(d*x+c)^2)+1/d*a^2*B*ln(1+tan(d*x+c)^2)-2*I/d*a^2*B*arctan(tan(d*x+c))+2/d*a^2*A*arctan(tan(d*x+c))","A"
12,1,100,71,0.443000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","2 i A \,a^{2} x +\frac{2 i A \,a^{2} c}{d}-\frac{2 i B \,a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+2 a^{2} B x +\frac{a^{2} A \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} A \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} B \tan \left(d x +c \right)}{d}+\frac{2 B \,a^{2} c}{d}"," ",0,"2*I*A*a^2*x+2*I/d*A*a^2*c-2*I/d*B*a^2*ln(cos(d*x+c))+2*a^2*B*x+1/d*a^2*A*ln(cos(d*x+c))+a^2*A*ln(sin(d*x+c))/d-a^2*B*tan(d*x+c)/d+2/d*B*a^2*c","A"
13,1,100,76,0.416000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","2 i B \,a^{2} x +\frac{2 i A \,a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-2 a^{2} A x +\frac{2 i B \,a^{2} c}{d}-\frac{a^{2} A \cot \left(d x +c \right)}{d}-\frac{2 A \,a^{2} c}{d}+\frac{a^{2} B \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"2*I*B*a^2*x+2*I/d*A*a^2*ln(sin(d*x+c))-2*a^2*A*x+2*I/d*B*a^2*c-a^2*A*cot(d*x+c)/d-2/d*A*a^2*c+a^2*B*ln(cos(d*x+c))/d+1/d*a^2*B*ln(sin(d*x+c))","A"
14,1,119,86,0.469000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{2 a^{2} A \ln \left(\sin \left(d x +c \right)\right)}{d}-2 a^{2} B x -\frac{2 B \,a^{2} c}{d}-2 i A \,a^{2} x -\frac{2 i A \cot \left(d x +c \right) a^{2}}{d}-\frac{2 i A \,a^{2} c}{d}+\frac{2 i B \,a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} A \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{B \cot \left(d x +c \right) a^{2}}{d}"," ",0,"-2*a^2*A*ln(sin(d*x+c))/d-2*a^2*B*x-2/d*B*a^2*c-2*I*A*x*a^2-2*I/d*A*cot(d*x+c)*a^2-2*I/d*A*a^2*c+2*I/d*B*a^2*ln(sin(d*x+c))-1/2*a^2*A*cot(d*x+c)^2/d-1/d*B*cot(d*x+c)*a^2","A"
15,1,154,108,0.416000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","2 a^{2} A x +\frac{2 a^{2} A \cot \left(d x +c \right)}{d}+\frac{2 A \,a^{2} c}{d}-\frac{2 a^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{i A \,a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{2 i A \,a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-2 i B \,a^{2} x -\frac{2 i B \cot \left(d x +c \right) a^{2}}{d}-\frac{2 i B \,a^{2} c}{d}-\frac{a^{2} A \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"2*a^2*A*x+2*a^2*A*cot(d*x+c)/d+2/d*A*a^2*c-2/d*a^2*B*ln(sin(d*x+c))-I/d*A*a^2*cot(d*x+c)^2-2*I/d*A*a^2*ln(sin(d*x+c))-2*I*B*x*a^2-2*I/d*B*cot(d*x+c)*a^2-2*I/d*B*a^2*c-1/3*a^2*A*cot(d*x+c)^3/d-1/2/d*a^2*B*cot(d*x+c)^2","A"
16,1,188,129,0.484000," ","int(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\frac{a^{2} A \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{2} A \ln \left(\sin \left(d x +c \right)\right)}{d}+2 a^{2} B x +\frac{2 B \cot \left(d x +c \right) a^{2}}{d}+\frac{2 B \,a^{2} c}{d}+\frac{2 i A \,a^{2} c}{d}-\frac{2 i A \,a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 i B \,a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{i B \,a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}+2 i A \,a^{2} x +\frac{2 i A \cot \left(d x +c \right) a^{2}}{d}-\frac{a^{2} A \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"a^2*A*cot(d*x+c)^2/d+2*a^2*A*ln(sin(d*x+c))/d+2*a^2*B*x+2/d*B*cot(d*x+c)*a^2+2/d*B*a^2*c+2*I/d*A*a^2*c-2/3*I/d*A*a^2*cot(d*x+c)^3-2*I/d*B*a^2*ln(sin(d*x+c))-I/d*B*a^2*cot(d*x+c)^2+2*I*A*a^2*x+2*I/d*A*a^2*cot(d*x+c)-1/4*a^2*A*cot(d*x+c)^4/d-1/3/d*a^2*B*cot(d*x+c)^3","A"
17,1,230,167,0.025000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{i a^{3} B \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{i a^{3} A \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{4 i a^{3} B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{3 a^{3} B \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{2 i a^{3} A \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{a^{3} A \left(\tan^{3}\left(d x +c \right)\right)}{d}-\frac{4 i a^{3} B \tan \left(d x +c \right)}{d}+\frac{2 a^{3} B \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 A \,a^{3} \tan \left(d x +c \right)}{d}-\frac{2 i a^{3} A \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 a^{3} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 i a^{3} B \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{4 a^{3} A \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/5*I/d*a^3*B*tan(d*x+c)^5-1/4*I/d*a^3*A*tan(d*x+c)^4+4/3*I/d*a^3*B*tan(d*x+c)^3-3/4/d*a^3*B*tan(d*x+c)^4+2*I/d*a^3*A*tan(d*x+c)^2-1/d*a^3*A*tan(d*x+c)^3-4*I/d*a^3*B*tan(d*x+c)+2/d*a^3*B*tan(d*x+c)^2+4/d*A*a^3*tan(d*x+c)-2*I/d*a^3*A*ln(1+tan(d*x+c)^2)-2/d*a^3*B*ln(1+tan(d*x+c)^2)+4*I/d*a^3*B*arctan(tan(d*x+c))-4/d*a^3*A*arctan(tan(d*x+c))","A"
18,1,195,124,0.025000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{i a^{3} B \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{i a^{3} A \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 i a^{3} B \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{a^{3} B \left(\tan^{3}\left(d x +c \right)\right)}{d}+\frac{4 i a^{3} A \tan \left(d x +c \right)}{d}-\frac{3 a^{3} A \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{4 a^{3} B \tan \left(d x +c \right)}{d}-\frac{2 i a^{3} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{3} A \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{4 i a^{3} A \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{4 a^{3} B \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/4*I/d*a^3*B*tan(d*x+c)^4-1/3*I/d*a^3*A*tan(d*x+c)^3+2*I/d*a^3*B*tan(d*x+c)^2-1/d*a^3*B*tan(d*x+c)^3+4*I/d*a^3*A*tan(d*x+c)-3/2/d*a^3*A*tan(d*x+c)^2+4/d*a^3*B*tan(d*x+c)-2*I/d*a^3*B*ln(1+tan(d*x+c)^2)+2/d*a^3*A*ln(1+tan(d*x+c)^2)-4*I/d*a^3*A*arctan(tan(d*x+c))-4/d*a^3*B*arctan(tan(d*x+c))","A"
19,1,160,100,0.023000," ","int((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{i a^{3} B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{i a^{3} A \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{4 i a^{3} B \tan \left(d x +c \right)}{d}-\frac{3 a^{3} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 A \,a^{3} \tan \left(d x +c \right)}{d}+\frac{2 i a^{3} A \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{3} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{4 i a^{3} B \arctan \left(\tan \left(d x +c \right)\right)}{d}+\frac{4 a^{3} A \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/3*I/d*a^3*B*tan(d*x+c)^3-1/2*I/d*a^3*A*tan(d*x+c)^2+4*I/d*a^3*B*tan(d*x+c)-3/2/d*a^3*B*tan(d*x+c)^2-3/d*A*a^3*tan(d*x+c)+2*I/d*a^3*A*ln(1+tan(d*x+c)^2)+2/d*a^3*B*ln(1+tan(d*x+c)^2)-4*I/d*a^3*B*arctan(tan(d*x+c))+4/d*a^3*A*arctan(tan(d*x+c))","A"
20,1,135,99,0.456000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","4 i A x \,a^{3}-\frac{i a^{3} A \tan \left(d x +c \right)}{d}+\frac{4 i A \,a^{3} c}{d}-\frac{i a^{3} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{4 i a^{3} B \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 A \,a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+4 a^{3} B x -\frac{3 a^{3} B \tan \left(d x +c \right)}{d}+\frac{4 a^{3} B c}{d}+\frac{a^{3} A \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"4*I*A*x*a^3-I/d*A*tan(d*x+c)*a^3+4*I/d*A*a^3*c-1/2*I/d*a^3*B*tan(d*x+c)^2-4*I/d*a^3*B*ln(cos(d*x+c))+3/d*A*a^3*ln(cos(d*x+c))+4*a^3*B*x-3/d*a^3*B*tan(d*x+c)+4/d*a^3*B*c+a^3*A*ln(sin(d*x+c))/d","A"
21,1,134,110,0.387000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","4 i B x \,a^{3}+\frac{i A \,a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 i A \,a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-4 A \,a^{3} x -\frac{i a^{3} B \tan \left(d x +c \right)}{d}+\frac{4 i B \,a^{3} c}{d}-\frac{A \cot \left(d x +c \right) a^{3}}{d}-\frac{4 A \,a^{3} c}{d}+\frac{3 a^{3} B \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"4*I*B*x*a^3+I/d*A*a^3*ln(cos(d*x+c))+3*I/d*A*a^3*ln(sin(d*x+c))-4*A*a^3*x-I/d*B*tan(d*x+c)*a^3+4*I/d*B*a^3*c-1/d*A*cot(d*x+c)*a^3-4/d*A*a^3*c+3/d*a^3*B*ln(cos(d*x+c))+1/d*a^3*B*ln(sin(d*x+c))","A"
22,1,136,115,0.498000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-4 i A x \,a^{3}-\frac{4 i A \,a^{3} c}{d}+\frac{i a^{3} B \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{4 a^{3} A \ln \left(\sin \left(d x +c \right)\right)}{d}-4 a^{3} B x -\frac{4 a^{3} B c}{d}-\frac{3 i A \cot \left(d x +c \right) a^{3}}{d}+\frac{3 i a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{A \,a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{B \cot \left(d x +c \right) a^{3}}{d}"," ",0,"-4*I*A*x*a^3-4*I/d*A*a^3*c+I*a^3*B*ln(cos(d*x+c))/d-4*a^3*A*ln(sin(d*x+c))/d-4*a^3*B*x-4/d*a^3*B*c-3*I/d*A*cot(d*x+c)*a^3+3*I/d*a^3*B*ln(sin(d*x+c))-1/2/d*A*a^3*cot(d*x+c)^2-1/d*B*cot(d*x+c)*a^3","A"
23,1,154,122,0.437000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{4 i A \,a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-4 i B x \,a^{3}-\frac{3 i A \,a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+4 A \,a^{3} x +\frac{4 A \cot \left(d x +c \right) a^{3}}{d}+\frac{4 A \,a^{3} c}{d}-\frac{4 a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 i B \,a^{3} c}{d}-\frac{3 i B \cot \left(d x +c \right) a^{3}}{d}-\frac{A \,a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{3} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-4*I/d*A*a^3*ln(sin(d*x+c))-4*I*B*x*a^3-3/2*I/d*A*a^3*cot(d*x+c)^2+4*A*a^3*x+4/d*A*cot(d*x+c)*a^3+4/d*A*a^3*c-4/d*a^3*B*ln(sin(d*x+c))-4*I/d*B*a^3*c-3*I/d*B*cot(d*x+c)*a^3-1/3/d*A*a^3*cot(d*x+c)^3-1/2/d*a^3*B*cot(d*x+c)^2","A"
24,1,189,144,0.469000," ","int(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\frac{4 i A \,a^{3} c}{d}-\frac{4 i a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 i A \cot \left(d x +c \right) a^{3}}{d}+4 i A x \,a^{3}+\frac{2 A \,a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{4 a^{3} A \ln \left(\sin \left(d x +c \right)\right)}{d}+4 a^{3} B x +\frac{4 B \cot \left(d x +c \right) a^{3}}{d}+\frac{4 a^{3} B c}{d}-\frac{3 i a^{3} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{i A \,a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{A \,a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"4*I/d*A*a^3*c-4*I/d*a^3*B*ln(sin(d*x+c))+4*I/d*A*cot(d*x+c)*a^3+4*I*A*x*a^3+2/d*A*a^3*cot(d*x+c)^2+4*a^3*A*ln(sin(d*x+c))/d+4*a^3*B*x+4/d*B*cot(d*x+c)*a^3+4/d*a^3*B*c-3/2*I/d*a^3*B*cot(d*x+c)^2-I/d*A*a^3*cot(d*x+c)^3-1/4/d*A*a^3*cot(d*x+c)^4-1/3/d*a^3*B*cot(d*x+c)^3","A"
25,1,224,166,0.480000," ","int(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\frac{4 a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}-4 A \,a^{3} x +\frac{4 i A \,a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 i B \,a^{3} c}{d}+4 i B x \,a^{3}-\frac{3 i A \,a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{4 i B \cot \left(d x +c \right) a^{3}}{d}-\frac{i a^{3} B \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{4 A \,a^{3} c}{d}+\frac{4 A \,a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{4 A \cot \left(d x +c \right) a^{3}}{d}+\frac{2 a^{3} B \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{A \,a^{3} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{3} B \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{2 i A \,a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{d}"," ",0,"4/d*a^3*B*ln(sin(d*x+c))-4*A*a^3*x+4*I/d*A*a^3*ln(sin(d*x+c))+4*I/d*B*a^3*c+4*I*B*x*a^3-3/4*I/d*A*a^3*cot(d*x+c)^4+4*I/d*B*cot(d*x+c)*a^3-I/d*a^3*B*cot(d*x+c)^3-4/d*A*a^3*c+4/3/d*A*a^3*cot(d*x+c)^3-4/d*A*cot(d*x+c)*a^3+2/d*a^3*B*cot(d*x+c)^2-1/5/d*A*a^3*cot(d*x+c)^5-1/4/d*a^3*B*cot(d*x+c)^4+2*I/d*A*a^3*cot(d*x+c)^2","A"
26,1,264,206,0.026000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{4 i a^{4} B \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{4} B \left(\tan^{6}\left(d x +c \right)\right)}{6 d}-\frac{i a^{4} A \left(\tan^{4}\left(d x +c \right)\right)}{d}+\frac{a^{4} A \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{8 i a^{4} B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{7 a^{4} B \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{4 i a^{4} A \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{7 a^{4} A \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{8 i a^{4} B \tan \left(d x +c \right)}{d}+\frac{4 a^{4} B \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{8 A \,a^{4} \tan \left(d x +c \right)}{d}-\frac{4 i a^{4} A \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{4 a^{4} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{8 i a^{4} B \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{8 a^{4} A \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-4/5*I/d*a^4*B*tan(d*x+c)^5+1/6/d*a^4*B*tan(d*x+c)^6-I/d*a^4*A*tan(d*x+c)^4+1/5/d*a^4*A*tan(d*x+c)^5+8/3*I/d*a^4*B*tan(d*x+c)^3-7/4/d*a^4*B*tan(d*x+c)^4+4*I/d*a^4*A*tan(d*x+c)^2-7/3/d*a^4*A*tan(d*x+c)^3-8*I/d*a^4*B*tan(d*x+c)+4/d*a^4*B*tan(d*x+c)^2+8/d*A*a^4*tan(d*x+c)-4*I/d*a^4*A*ln(1+tan(d*x+c)^2)-4/d*a^4*B*ln(1+tan(d*x+c)^2)+8*I/d*a^4*B*arctan(tan(d*x+c))-8/d*a^4*A*arctan(tan(d*x+c))","A"
27,1,229,152,0.021000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{i a^{4} B \left(\tan^{4}\left(d x +c \right)\right)}{d}+\frac{a^{4} B \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{4 i a^{4} A \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} A \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{4 i a^{4} B \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{7 a^{4} B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{8 i a^{4} A \tan \left(d x +c \right)}{d}-\frac{7 a^{4} A \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{8 a^{4} B \tan \left(d x +c \right)}{d}-\frac{4 i a^{4} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 a^{4} A \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{8 i a^{4} A \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{8 a^{4} B \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-I/d*a^4*B*tan(d*x+c)^4+1/5/d*a^4*B*tan(d*x+c)^5-4/3*I/d*a^4*A*tan(d*x+c)^3+1/4/d*a^4*A*tan(d*x+c)^4+4*I/d*a^4*B*tan(d*x+c)^2-7/3/d*a^4*B*tan(d*x+c)^3+8*I/d*a^4*A*tan(d*x+c)-7/2/d*a^4*A*tan(d*x+c)^2+8/d*a^4*B*tan(d*x+c)-4*I/d*a^4*B*ln(1+tan(d*x+c)^2)+4/d*a^4*A*ln(1+tan(d*x+c)^2)-8*I/d*a^4*A*arctan(tan(d*x+c))-8/d*a^4*B*arctan(tan(d*x+c))","A"
28,1,194,128,0.022000," ","int((a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{4 i a^{4} B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} B \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{2 i a^{4} A \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{a^{4} A \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{8 i a^{4} B \tan \left(d x +c \right)}{d}-\frac{7 a^{4} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{7 A \,a^{4} \tan \left(d x +c \right)}{d}+\frac{4 i a^{4} A \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 a^{4} B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{8 i a^{4} B \arctan \left(\tan \left(d x +c \right)\right)}{d}+\frac{8 a^{4} A \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-4/3*I/d*a^4*B*tan(d*x+c)^3+1/4/d*a^4*B*tan(d*x+c)^4-2*I/d*a^4*A*tan(d*x+c)^2+1/3/d*a^4*A*tan(d*x+c)^3+8*I/d*a^4*B*tan(d*x+c)-7/2/d*a^4*B*tan(d*x+c)^2-7/d*A*a^4*tan(d*x+c)+4*I/d*a^4*A*ln(1+tan(d*x+c)^2)+4/d*a^4*B*ln(1+tan(d*x+c)^2)-8*I/d*a^4*B*arctan(tan(d*x+c))+8/d*a^4*A*arctan(tan(d*x+c))","A"
29,1,169,130,0.472000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","\frac{a^{4} A \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{7 A \,a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{4} B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{7 a^{4} B \tan \left(d x +c \right)}{d}+8 a^{4} B x +\frac{8 a^{4} B c}{d}-\frac{8 i B \,a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{2 i a^{4} B \left(\tan^{2}\left(d x +c \right)\right)}{d}+8 i A x \,a^{4}+\frac{8 i A \,a^{4} c}{d}-\frac{4 i a^{4} A \tan \left(d x +c \right)}{d}+\frac{a^{4} A \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*a^4*A*tan(d*x+c)^2+7/d*A*a^4*ln(cos(d*x+c))+1/3/d*a^4*B*tan(d*x+c)^3-7/d*a^4*B*tan(d*x+c)+8*a^4*B*x+8/d*a^4*B*c-8*I/d*B*a^4*ln(cos(d*x+c))-2*I/d*B*a^4*tan(d*x+c)^2+8*I*A*x*a^4+8*I/d*A*a^4*c-4*I/d*A*tan(d*x+c)*a^4+a^4*A*ln(sin(d*x+c))/d","A"
30,1,165,135,0.403000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-8 A \,a^{4} x +\frac{A \,a^{4} \tan \left(d x +c \right)}{d}-\frac{8 A \,a^{4} c}{d}+\frac{a^{4} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{7 a^{4} B \ln \left(\cos \left(d x +c \right)\right)}{d}+8 i B x \,a^{4}+\frac{4 i A \,a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 i A \,a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{4 i a^{4} B \tan \left(d x +c \right)}{d}+\frac{8 i B \,a^{4} c}{d}-\frac{A \cot \left(d x +c \right) a^{4}}{d}+\frac{a^{4} B \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-8*A*a^4*x+1/d*A*a^4*tan(d*x+c)-8/d*A*a^4*c+1/2/d*a^4*B*tan(d*x+c)^2+7*a^4*B*ln(cos(d*x+c))/d+8*I*B*x*a^4+4*I/d*A*a^4*ln(sin(d*x+c))+4*I/d*A*a^4*ln(cos(d*x+c))-4*I/d*B*tan(d*x+c)*a^4+8*I/d*B*a^4*c-1/d*A*cot(d*x+c)*a^4+1/d*a^4*B*ln(sin(d*x+c))","A"
31,1,166,145,0.442000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{A \,a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}-8 a^{4} B x +\frac{a^{4} B \tan \left(d x +c \right)}{d}-\frac{8 a^{4} B c}{d}-\frac{8 i A \,a^{4} c}{d}-8 i A x \,a^{4}+\frac{4 i B \,a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{7 a^{4} A \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 i A \cot \left(d x +c \right) a^{4}}{d}+\frac{4 i B \,a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{A \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{B \cot \left(d x +c \right) a^{4}}{d}"," ",0,"-1/d*A*a^4*ln(cos(d*x+c))-8*a^4*B*x+1/d*a^4*B*tan(d*x+c)-8/d*a^4*B*c-8*I/d*A*a^4*c-8*I*A*x*a^4+4*I/d*B*a^4*ln(cos(d*x+c))-7*a^4*A*ln(sin(d*x+c))/d-4*I/d*A*cot(d*x+c)*a^4+4*I/d*B*a^4*ln(sin(d*x+c))-1/2/d*A*a^4*cot(d*x+c)^2-1/d*B*cot(d*x+c)*a^4","A"
32,1,170,152,0.447000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","8 A \,a^{4} x +\frac{8 A \,a^{4} c}{d}-\frac{a^{4} B \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{8 i B \,a^{4} c}{d}-\frac{2 i A \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{8 i A \,a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{7 A \cot \left(d x +c \right) a^{4}}{d}-\frac{7 a^{4} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 i B \cot \left(d x +c \right) a^{4}}{d}-8 i B x \,a^{4}-\frac{A \,a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{4} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"8*A*a^4*x+8/d*A*a^4*c-a^4*B*ln(cos(d*x+c))/d-8*I/d*B*a^4*c-2*I/d*A*a^4*cot(d*x+c)^2-8*I/d*A*a^4*ln(sin(d*x+c))+7/d*A*cot(d*x+c)*a^4-7/d*a^4*B*ln(sin(d*x+c))-4*I/d*B*cot(d*x+c)*a^4-8*I*B*x*a^4-1/3/d*A*a^4*cot(d*x+c)^3-1/2/d*a^4*B*cot(d*x+c)^2","A"
33,1,189,161,0.451000," ","int(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","\frac{7 A \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{8 a^{4} B c}{d}+\frac{7 B \cot \left(d x +c \right) a^{4}}{d}+8 i A x \,a^{4}+8 a^{4} B x +\frac{8 i A \cot \left(d x +c \right) a^{4}}{d}+\frac{8 i A \,a^{4} c}{d}-\frac{8 i B \,a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 i A \,a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 i B \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{A \,a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{4} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{8 a^{4} A \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"7/2/d*A*a^4*cot(d*x+c)^2+8/d*a^4*B*c+7/d*B*cot(d*x+c)*a^4+8*I*A*x*a^4+8*a^4*B*x+8*I/d*A*cot(d*x+c)*a^4+8*I/d*A*a^4*c-8*I/d*B*a^4*ln(sin(d*x+c))-4/3*I/d*A*a^4*cot(d*x+c)^3-2*I/d*B*a^4*cot(d*x+c)^2-1/4/d*A*a^4*cot(d*x+c)^4-1/3/d*a^4*B*cot(d*x+c)^3+8*a^4*A*ln(sin(d*x+c))/d","A"
34,1,224,183,0.461000," ","int(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","\frac{8 i B \,a^{4} c}{d}+8 i B x \,a^{4}-\frac{4 i B \,a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{8 A \,a^{4} c}{d}-\frac{8 A \cot \left(d x +c \right) a^{4}}{d}-8 A \,a^{4} x +\frac{8 i A \,a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{A \,a^{4} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{4 i A \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{8 a^{4} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{4} B \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{8 i B \cot \left(d x +c \right) a^{4}}{d}+\frac{7 A \,a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{7 a^{4} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{i A \,a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{d}"," ",0,"8*I/d*B*a^4*c+8*I*B*x*a^4-4/3*I/d*B*a^4*cot(d*x+c)^3-8/d*A*a^4*c-8/d*A*cot(d*x+c)*a^4-8*A*a^4*x+8*I/d*A*a^4*ln(sin(d*x+c))-1/5/d*A*a^4*cot(d*x+c)^5+4*I/d*A*a^4*cot(d*x+c)^2+8/d*a^4*B*ln(sin(d*x+c))-1/4/d*a^4*B*cot(d*x+c)^4+8*I/d*B*cot(d*x+c)*a^4+7/3/d*A*a^4*cot(d*x+c)^3+7/2/d*a^4*B*cot(d*x+c)^2-I/d*A*a^4*cot(d*x+c)^4","A"
35,1,259,205,0.499000," ","int(cot(d*x+c)^7*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{4 A \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{7 a^{4} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{8 a^{4} B c}{d}-\frac{8 B \cot \left(d x +c \right) a^{4}}{d}+\frac{7 A \,a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{i B \,a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{d}-\frac{8 i A \cot \left(d x +c \right) a^{4}}{d}+\frac{8 i B \,a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 i B \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{8 i A \,a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{8 i A \,a^{4} c}{d}-\frac{4 i A \,a^{4} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}-8 i A x \,a^{4}-8 a^{4} B x -\frac{8 a^{4} A \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{A \,a^{4} \left(\cot^{6}\left(d x +c \right)\right)}{6 d}-\frac{a^{4} B \left(\cot^{5}\left(d x +c \right)\right)}{5 d}"," ",0,"-4/d*A*a^4*cot(d*x+c)^2+7/3/d*a^4*B*cot(d*x+c)^3-8/d*a^4*B*c-8/d*B*cot(d*x+c)*a^4+7/4/d*A*a^4*cot(d*x+c)^4-I/d*B*a^4*cot(d*x+c)^4-8*I/d*A*a^4*cot(d*x+c)+8*I/d*B*a^4*ln(sin(d*x+c))+4*I/d*B*a^4*cot(d*x+c)^2+8/3*I/d*A*a^4*cot(d*x+c)^3-8*I/d*A*a^4*c-4/5*I/d*A*a^4*cot(d*x+c)^5-8*I*A*x*a^4-8*a^4*B*x-8*a^4*A*ln(sin(d*x+c))/d-1/6/d*A*a^4*cot(d*x+c)^6-1/5/d*a^4*B*cot(d*x+c)^5","A"
36,1,169,115,0.191000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{B \tan \left(d x +c \right)}{d a}-\frac{i B \left(\tan^{2}\left(d x +c \right)\right)}{2 d a}-\frac{i A \tan \left(d x +c \right)}{d a}-\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{5 \ln \left(\tan \left(d x +c \right)-i\right) A}{4 d a}+\frac{7 i \ln \left(\tan \left(d x +c \right)-i\right) B}{4 d a}-\frac{i A}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{B}{2 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"B*tan(d*x+c)/d/a-1/2*I/d/a*B*tan(d*x+c)^2-I/d/a*A*tan(d*x+c)-1/4/d/a*A*ln(tan(d*x+c)+I)+1/4*I/d/a*B*ln(tan(d*x+c)+I)+5/4/d/a*ln(tan(d*x+c)-I)*A+7/4*I/d/a*ln(tan(d*x+c)-I)*B-1/2*I/d/a/(tan(d*x+c)-I)*A+1/2/d/a/(tan(d*x+c)-I)*B","A"
37,1,137,90,0.172000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","-\frac{i B \tan \left(d x +c \right)}{d a}-\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{A}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{i B}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{3 i \ln \left(\tan \left(d x +c \right)-i\right) A}{4 d a}+\frac{5 \ln \left(\tan \left(d x +c \right)-i\right) B}{4 d a}"," ",0,"-I/d/a*B*tan(d*x+c)-1/4/d/a*B*ln(tan(d*x+c)+I)-1/4*I/d/a*A*ln(tan(d*x+c)+I)-1/2/d/a/(tan(d*x+c)-I)*A-1/2*I/d/a/(tan(d*x+c)-I)*B-3/4*I/d/a*ln(tan(d*x+c)-I)*A+5/4/d/a*ln(tan(d*x+c)-I)*B","A"
38,1,121,61,0.205000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{\ln \left(\tan \left(d x +c \right)-i\right) A}{4 d a}-\frac{3 i \ln \left(\tan \left(d x +c \right)-i\right) B}{4 d a}+\frac{i A}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{B}{2 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/4/d/a*A*ln(tan(d*x+c)+I)-1/4*I/d/a*B*ln(tan(d*x+c)+I)-1/4/d/a*ln(tan(d*x+c)-I)*A-3/4*I/d/a*ln(tan(d*x+c)-I)*B+1/2*I/d/a/(tan(d*x+c)-I)*A-1/2/d/a/(tan(d*x+c)-I)*B","A"
39,1,121,40,0.198000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{A}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{i B}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) A}{4 d a}-\frac{\ln \left(\tan \left(d x +c \right)-i\right) B}{4 d a}"," ",0,"1/4/d/a*B*ln(tan(d*x+c)+I)+1/4*I/d/a*A*ln(tan(d*x+c)+I)+1/2/d/a/(tan(d*x+c)-I)*A+1/2*I/d/a/(tan(d*x+c)-I)*B-1/4*I/d/a*ln(tan(d*x+c)-I)*A-1/4/d/a*ln(tan(d*x+c)-I)*B","B"
40,1,136,55,0.767000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","-\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{A \ln \left(\tan \left(d x +c \right)\right)}{d a}-\frac{i A}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{B}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{3 \ln \left(\tan \left(d x +c \right)-i\right) A}{4 d a}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) B}{4 d a}"," ",0,"-1/4/d/a*A*ln(tan(d*x+c)+I)+1/4*I/d/a*B*ln(tan(d*x+c)+I)+1/d/a*A*ln(tan(d*x+c))-1/2*I/d/a/(tan(d*x+c)-I)*A+1/2/d/a/(tan(d*x+c)-I)*B-3/4/d/a*ln(tan(d*x+c)-I)*A-1/4*I/d/a*ln(tan(d*x+c)-I)*B","B"
41,1,170,91,0.582000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","-\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{i A \ln \left(\tan \left(d x +c \right)\right)}{a d}+\frac{B \ln \left(\tan \left(d x +c \right)\right)}{a d}-\frac{A}{a d \tan \left(d x +c \right)}-\frac{A}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{i B}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{5 i \ln \left(\tan \left(d x +c \right)-i\right) A}{4 d a}-\frac{3 \ln \left(\tan \left(d x +c \right)-i\right) B}{4 d a}"," ",0,"-1/4/d/a*B*ln(tan(d*x+c)+I)-1/4*I/d/a*A*ln(tan(d*x+c)+I)-I/a/d*A*ln(tan(d*x+c))+1/a/d*B*ln(tan(d*x+c))-1/a/d*A/tan(d*x+c)-1/2/d/a/(tan(d*x+c)-I)*A-1/2*I/d/a/(tan(d*x+c)-I)*B+5/4*I/a/d*ln(tan(d*x+c)-I)*A-3/4/d/a*ln(tan(d*x+c)-I)*B","A"
42,1,206,117,0.722000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{A}{2 a d \tan \left(d x +c \right)^{2}}-\frac{i B \ln \left(\tan \left(d x +c \right)\right)}{a d}-\frac{2 A \ln \left(\tan \left(d x +c \right)\right)}{d a}+\frac{i A}{a d \tan \left(d x +c \right)}-\frac{B}{a d \tan \left(d x +c \right)}+\frac{i A}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{B}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{7 \ln \left(\tan \left(d x +c \right)-i\right) A}{4 d a}+\frac{5 i \ln \left(\tan \left(d x +c \right)-i\right) B}{4 d a}"," ",0,"1/4/d/a*A*ln(tan(d*x+c)+I)-1/4*I/d/a*B*ln(tan(d*x+c)+I)-1/2/a/d*A/tan(d*x+c)^2-I/a/d*B*ln(tan(d*x+c))-2/d/a*A*ln(tan(d*x+c))+I/a/d/tan(d*x+c)*A-1/a/d/tan(d*x+c)*B+1/2*I/d/a/(tan(d*x+c)-I)*A-1/2/d/a/(tan(d*x+c)-I)*B+7/4/d/a*ln(tan(d*x+c)-I)*A+5/4*I/a/d*ln(tan(d*x+c)-I)*B","A"
43,1,241,140,0.656000," ","int(cot(d*x+c)^4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{i A}{2 a d \tan \left(d x +c \right)^{2}}-\frac{B}{2 a d \tan \left(d x +c \right)^{2}}-\frac{A}{3 a d \tan \left(d x +c \right)^{3}}+\frac{2 i A \ln \left(\tan \left(d x +c \right)\right)}{a d}-\frac{2 B \ln \left(\tan \left(d x +c \right)\right)}{a d}+\frac{i B}{a d \tan \left(d x +c \right)}+\frac{2 A}{a d \tan \left(d x +c \right)}+\frac{A}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{i B}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{9 i \ln \left(\tan \left(d x +c \right)-i\right) A}{4 d a}+\frac{7 \ln \left(\tan \left(d x +c \right)-i\right) B}{4 d a}"," ",0,"1/4/d/a*B*ln(tan(d*x+c)+I)+1/4*I/d/a*A*ln(tan(d*x+c)+I)+1/2*I/a/d/tan(d*x+c)^2*A-1/2/a/d/tan(d*x+c)^2*B-1/3/a/d*A/tan(d*x+c)^3+2*I/a/d*A*ln(tan(d*x+c))-2/a/d*B*ln(tan(d*x+c))+I/a/d/tan(d*x+c)*B+2/a/d*A/tan(d*x+c)+1/2/d/a/(tan(d*x+c)-I)*A+1/2*I/d/a/(tan(d*x+c)-I)*B-9/4*I/a/d*ln(tan(d*x+c)-I)*A+7/4/d/a*ln(tan(d*x+c)-I)*B","A"
44,1,177,127,0.186000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","-\frac{B \tan \left(d x +c \right)}{d \,a^{2}}-\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{5 i A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{7 B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{7 \ln \left(\tan \left(d x +c \right)-i\right) A}{8 d \,a^{2}}-\frac{17 i \ln \left(\tan \left(d x +c \right)-i\right) B}{8 d \,a^{2}}"," ",0,"-1/d/a^2*B*tan(d*x+c)-1/8/d/a^2*A*ln(tan(d*x+c)+I)+1/8*I/d/a^2*B*ln(tan(d*x+c)+I)-1/4/d/a^2/(tan(d*x+c)-I)^2*A-1/4*I/d/a^2/(tan(d*x+c)-I)^2*B+5/4*I/d/a^2/(tan(d*x+c)-I)*A-7/4/d/a^2/(tan(d*x+c)-I)*B-7/8/d/a^2*ln(tan(d*x+c)-I)*A-17/8*I/d/a^2*ln(tan(d*x+c)-I)*B","A"
45,1,162,92,0.210000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","-\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{i A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{5 i B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}+\frac{3 A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right) A}{8 d \,a^{2}}-\frac{7 \ln \left(\tan \left(d x +c \right)-i\right) B}{8 d \,a^{2}}"," ",0,"-1/8/d/a^2*B*ln(tan(d*x+c)+I)-1/8*I/d/a^2*A*ln(tan(d*x+c)+I)+1/4*I/d/a^2/(tan(d*x+c)-I)^2*A-1/4/d/a^2/(tan(d*x+c)-I)^2*B+5/4*I/d/a^2/(tan(d*x+c)-I)*B+3/4/d/a^2/(tan(d*x+c)-I)*A+1/8*I/d/a^2*ln(tan(d*x+c)-I)*A-7/8/d/a^2*ln(tan(d*x+c)-I)*B","A"
46,1,162,67,0.202000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{i B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}+\frac{3 B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{\ln \left(\tan \left(d x +c \right)-i\right) A}{8 d \,a^{2}}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right) B}{8 d \,a^{2}}"," ",0,"1/8/d/a^2*A*ln(tan(d*x+c)+I)-1/8*I/d/a^2*B*ln(tan(d*x+c)+I)+1/4/d/a^2/(tan(d*x+c)-I)^2*A+1/4*I/d/a^2/(tan(d*x+c)-I)^2*B-1/4*I/d/a^2/(tan(d*x+c)-I)*A+3/4/d/a^2/(tan(d*x+c)-I)*B-1/8/d/a^2*ln(tan(d*x+c)-I)*A+1/8*I/d/a^2*ln(tan(d*x+c)-I)*B","B"
47,1,162,69,0.207000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{i A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{i B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) A}{8 d \,a^{2}}-\frac{\ln \left(\tan \left(d x +c \right)-i\right) B}{8 d \,a^{2}}"," ",0,"1/8/d/a^2*B*ln(tan(d*x+c)+I)+1/8*I/d/a^2*A*ln(tan(d*x+c)+I)-1/4*I/d/a^2/(tan(d*x+c)-I)^2*A+1/4/d/a^2/(tan(d*x+c)-I)^2*B+1/4/d/a^2/(tan(d*x+c)-I)*A-1/4*I/d/a^2/(tan(d*x+c)-I)*B-1/8*I/d/a^2*ln(tan(d*x+c)-I)*A-1/8/d/a^2*ln(tan(d*x+c)-I)*B","B"
48,1,177,84,0.641000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","-\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{A \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}+\frac{B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{3 i A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7 \ln \left(\tan \left(d x +c \right)-i\right) A}{8 d \,a^{2}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) B}{8 d \,a^{2}}"," ",0,"-1/8/d/a^2*A*ln(tan(d*x+c)+I)+1/8*I/d/a^2*B*ln(tan(d*x+c)+I)+1/a^2/d*A*ln(tan(d*x+c))+1/4/d/a^2/(tan(d*x+c)-I)*B-3/4*I/a^2/d/(tan(d*x+c)-I)*A-1/4/d/a^2/(tan(d*x+c)-I)^2*A-1/4*I/d/a^2/(tan(d*x+c)-I)^2*B-7/8/d/a^2*ln(tan(d*x+c)-I)*A-1/8*I/a^2/d*ln(tan(d*x+c)-I)*B","B"
49,1,211,126,0.563000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","-\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{A}{a^{2} d \tan \left(d x +c \right)}-\frac{2 i A \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}+\frac{B \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}-\frac{5 A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{3 i B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}+\frac{i A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7 \ln \left(\tan \left(d x +c \right)-i\right) B}{8 d \,a^{2}}+\frac{17 i \ln \left(\tan \left(d x +c \right)-i\right) A}{8 d \,a^{2}}"," ",0,"-1/8/d/a^2*B*ln(tan(d*x+c)+I)-1/8*I/d/a^2*A*ln(tan(d*x+c)+I)-1/a^2/d*A/tan(d*x+c)-2*I/a^2/d*A*ln(tan(d*x+c))+1/a^2/d*B*ln(tan(d*x+c))-5/4/d/a^2/(tan(d*x+c)-I)*A-3/4*I/a^2/d/(tan(d*x+c)-I)*B+1/4*I/d/a^2/(tan(d*x+c)-I)^2*A-1/4/d/a^2/(tan(d*x+c)-I)^2*B-7/8/d/a^2*ln(tan(d*x+c)-I)*B+17/8*I/a^2/d*ln(tan(d*x+c)-I)*A","A"
50,1,247,154,0.674000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{A}{2 a^{2} d \tan \left(d x +c \right)^{2}}-\frac{2 i B \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}-\frac{4 A \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}+\frac{2 i A}{a^{2} d \tan \left(d x +c \right)}-\frac{B}{a^{2} d \tan \left(d x +c \right)}+\frac{A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{i B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{5 B}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}+\frac{7 i A}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}+\frac{31 \ln \left(\tan \left(d x +c \right)-i\right) A}{8 d \,a^{2}}+\frac{17 i \ln \left(\tan \left(d x +c \right)-i\right) B}{8 d \,a^{2}}"," ",0,"1/8/d/a^2*A*ln(tan(d*x+c)+I)-1/8*I/d/a^2*B*ln(tan(d*x+c)+I)-1/2/a^2/d*A/tan(d*x+c)^2-2*I/a^2/d*B*ln(tan(d*x+c))-4/a^2/d*A*ln(tan(d*x+c))+2*I/a^2/d/tan(d*x+c)*A-1/a^2/d/tan(d*x+c)*B+1/4/d/a^2/(tan(d*x+c)-I)^2*A+1/4*I/d/a^2/(tan(d*x+c)-I)^2*B-5/4/d/a^2/(tan(d*x+c)-I)*B+7/4*I/a^2/d/(tan(d*x+c)-I)*A+31/8/d/a^2*ln(tan(d*x+c)-I)*A+17/8*I/a^2/d*ln(tan(d*x+c)-I)*B","A"
51,1,219,172,0.194000," ","int(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\frac{i B \tan \left(d x +c \right)}{d \,a^{3}}+\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{A}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i B}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{49 \ln \left(\tan \left(d x +c \right)-i\right) B}{16 d \,a^{3}}+\frac{15 i \ln \left(\tan \left(d x +c \right)-i\right) A}{16 d \,a^{3}}+\frac{17 A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}+\frac{31 i B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}+\frac{7 i A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{9 B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}"," ",0,"I/d/a^3*B*tan(d*x+c)+1/16/d/a^3*B*ln(tan(d*x+c)+I)+1/16*I/d/a^3*A*ln(tan(d*x+c)+I)-1/6/d/a^3/(tan(d*x+c)-I)^3*A-1/6*I/d/a^3/(tan(d*x+c)-I)^3*B-49/16/d/a^3*ln(tan(d*x+c)-I)*B+15/16*I/d/a^3*ln(tan(d*x+c)-I)*A+17/8/d/a^3/(tan(d*x+c)-I)*A+31/8*I/d/a^3/(tan(d*x+c)-I)*B+7/8*I/d/a^3/(tan(d*x+c)-I)^2*A-9/8/d/a^3/(tan(d*x+c)-I)^2*B","A"
52,1,203,132,0.222000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","-\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{\ln \left(\tan \left(d x +c \right)-i\right) A}{16 d \,a^{3}}+\frac{15 i \ln \left(\tan \left(d x +c \right)-i\right) B}{16 d \,a^{3}}+\frac{17 B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{7 i A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}+\frac{5 A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{7 i B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{i A}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{B}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}"," ",0,"-1/16/d/a^3*A*ln(tan(d*x+c)+I)+1/16*I/d/a^3*B*ln(tan(d*x+c)+I)+1/16/d/a^3*ln(tan(d*x+c)-I)*A+15/16*I/d/a^3*ln(tan(d*x+c)-I)*B+17/8/d/a^3/(tan(d*x+c)-I)*B-7/8*I/d/a^3/(tan(d*x+c)-I)*A+5/8/d/a^3/(tan(d*x+c)-I)^2*A+7/8*I/d/a^3/(tan(d*x+c)-I)^2*B+1/6*I/d/a^3/(tan(d*x+c)-I)^3*A-1/6/d/a^3/(tan(d*x+c)-I)^3*B","A"
53,1,203,109,0.235000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","-\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{A}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i B}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{7 i B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right) A}{16 d \,a^{3}}+\frac{\ln \left(\tan \left(d x +c \right)-i\right) B}{16 d \,a^{3}}-\frac{3 i A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{5 B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}"," ",0,"-1/16/d/a^3*B*ln(tan(d*x+c)+I)-1/16*I/d/a^3*A*ln(tan(d*x+c)+I)+1/6/d/a^3/(tan(d*x+c)-I)^3*A+1/6*I/d/a^3/(tan(d*x+c)-I)^3*B-1/8/d/a^3/(tan(d*x+c)-I)*A-7/8*I/d/a^3/(tan(d*x+c)-I)*B+1/16*I/d/a^3*ln(tan(d*x+c)-I)*A+1/16/d/a^3*ln(tan(d*x+c)-I)*B-3/8*I/d/a^3/(tan(d*x+c)-I)^2*A+5/8/d/a^3/(tan(d*x+c)-I)^2*B","A"
54,1,203,97,0.220000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{3 i B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i A}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{B}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{\ln \left(\tan \left(d x +c \right)-i\right) A}{16 d \,a^{3}}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right) B}{16 d \,a^{3}}"," ",0,"1/16/d/a^3*A*ln(tan(d*x+c)+I)-1/16*I/d/a^3*B*ln(tan(d*x+c)+I)-1/8/d/a^3/(tan(d*x+c)-I)^2*A-3/8*I/d/a^3/(tan(d*x+c)-I)^2*B-1/6*I/d/a^3/(tan(d*x+c)-I)^3*A+1/6/d/a^3/(tan(d*x+c)-I)^3*B-1/8*I/d/a^3/(tan(d*x+c)-I)*A-1/8/d/a^3/(tan(d*x+c)-I)*B-1/16/d/a^3*ln(tan(d*x+c)-I)*A+1/16*I/d/a^3*ln(tan(d*x+c)-I)*B","B"
55,1,203,97,0.203000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{i A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{i B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{A}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i B}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) A}{16 d \,a^{3}}-\frac{\ln \left(\tan \left(d x +c \right)-i\right) B}{16 d \,a^{3}}"," ",0,"1/16/d/a^3*B*ln(tan(d*x+c)+I)+1/16*I/d/a^3*A*ln(tan(d*x+c)+I)-1/8*I/d/a^3/(tan(d*x+c)-I)^2*A-1/8/d/a^3/(tan(d*x+c)-I)^2*B+1/8/d/a^3/(tan(d*x+c)-I)*A-1/8*I/d/a^3/(tan(d*x+c)-I)*B-1/6/d/a^3/(tan(d*x+c)-I)^3*A-1/6*I/d/a^3/(tan(d*x+c)-I)^3*B-1/16*I/d/a^3*ln(tan(d*x+c)-I)*A-1/16/d/a^3*ln(tan(d*x+c)-I)*B","B"
56,1,218,116,0.755000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","-\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{A \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}-\frac{3 A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{i A}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{B}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{7 i A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{15 \ln \left(\tan \left(d x +c \right)-i\right) A}{16 d \,a^{3}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) B}{16 d \,a^{3}}"," ",0,"-1/16/d/a^3*A*ln(tan(d*x+c)+I)+1/16*I/d/a^3*B*ln(tan(d*x+c)+I)+1/a^3/d*A*ln(tan(d*x+c))-3/8/d/a^3/(tan(d*x+c)-I)^2*A-1/8*I/a^3/d/(tan(d*x+c)-I)^2*B+1/6*I/d/a^3/(tan(d*x+c)-I)^3*A-1/6/d/a^3/(tan(d*x+c)-I)^3*B+1/8/d/a^3/(tan(d*x+c)-I)*B-7/8*I/d/a^3/(tan(d*x+c)-I)*A-15/16/d/a^3*ln(tan(d*x+c)-I)*A-1/16*I/a^3/d*ln(tan(d*x+c)-I)*B","A"
57,1,252,164,0.689000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","-\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{3 i A \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}+\frac{B \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}-\frac{A}{a^{3} d \tan \left(d x +c \right)}+\frac{5 i A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{3 B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{17 A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{7 i B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}+\frac{49 i \ln \left(\tan \left(d x +c \right)-i\right) A}{16 d \,a^{3}}-\frac{15 \ln \left(\tan \left(d x +c \right)-i\right) B}{16 d \,a^{3}}+\frac{A}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i B}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}"," ",0,"-1/16/d/a^3*B*ln(tan(d*x+c)+I)-1/16*I/d/a^3*A*ln(tan(d*x+c)+I)-3*I/a^3/d*A*ln(tan(d*x+c))+1/a^3/d*B*ln(tan(d*x+c))-1/a^3/d*A/tan(d*x+c)+5/8*I/a^3/d/(tan(d*x+c)-I)^2*A-3/8/d/a^3/(tan(d*x+c)-I)^2*B-17/8/d/a^3/(tan(d*x+c)-I)*A-7/8*I/d/a^3/(tan(d*x+c)-I)*B+49/16*I/a^3/d*ln(tan(d*x+c)-I)*A-15/16/d/a^3*ln(tan(d*x+c)-I)*B+1/6/d/a^3/(tan(d*x+c)-I)^3*A+1/6*I/d/a^3/(tan(d*x+c)-I)^3*B","A"
58,1,288,194,0.722000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{A}{2 a^{3} d \tan \left(d x +c \right)^{2}}-\frac{3 i B \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}-\frac{7 A \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}+\frac{3 i A}{a^{3} d \tan \left(d x +c \right)}-\frac{B}{a^{3} d \tan \left(d x +c \right)}+\frac{7 A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{5 i B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i A}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{B}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{31 i A}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{17 B}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}+\frac{49 i \ln \left(\tan \left(d x +c \right)-i\right) B}{16 d \,a^{3}}+\frac{111 \ln \left(\tan \left(d x +c \right)-i\right) A}{16 d \,a^{3}}"," ",0,"1/16/d/a^3*A*ln(tan(d*x+c)+I)-1/16*I/d/a^3*B*ln(tan(d*x+c)+I)-1/2/a^3/d*A/tan(d*x+c)^2-3*I/a^3/d*B*ln(tan(d*x+c))-7/a^3/d*A*ln(tan(d*x+c))+3*I/a^3/d/tan(d*x+c)*A-1/a^3/d/tan(d*x+c)*B+7/8/d/a^3/(tan(d*x+c)-I)^2*A+5/8*I/a^3/d/(tan(d*x+c)-I)^2*B-1/6*I/d/a^3/(tan(d*x+c)-I)^3*A+1/6/d/a^3/(tan(d*x+c)-I)^3*B+31/8*I/a^3/d/(tan(d*x+c)-I)*A-17/8/d/a^3/(tan(d*x+c)-I)*B+49/16*I/a^3/d*ln(tan(d*x+c)-I)*B+111/16/d/a^3*ln(tan(d*x+c)-I)*A","A"
59,1,244,166,0.231000," ","int(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i A}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{B}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{49 i B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{15 A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}+\frac{31 B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{17 i A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{3 i B}{4 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{7 A}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) A}{32 d \,a^{4}}+\frac{31 \ln \left(\tan \left(d x +c \right)-i\right) B}{32 d \,a^{4}}"," ",0,"1/32/d/a^4*B*ln(tan(d*x+c)+I)+1/32*I/d/a^4*A*ln(tan(d*x+c)+I)+1/8*I/d/a^4/(tan(d*x+c)-I)^4*A-1/8/d/a^4/(tan(d*x+c)-I)^4*B-49/16*I/d/a^4/(tan(d*x+c)-I)*B-15/16/d/a^4/(tan(d*x+c)-I)*A+31/16/d/a^4/(tan(d*x+c)-I)^2*B-17/16*I/d/a^4/(tan(d*x+c)-I)^2*A+3/4*I/d/a^4/(tan(d*x+c)-I)^3*B+7/12/d/a^4/(tan(d*x+c)-I)^3*A-1/32*I/d/a^4*ln(tan(d*x+c)-I)*A+31/32/d/a^4*ln(tan(d*x+c)-I)*B","A"
60,1,244,142,0.235000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","-\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{5 i A}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{7 B}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{15 B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{7 A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{17 i B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{A}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{i B}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{\ln \left(\tan \left(d x +c \right)-i\right) A}{32 d \,a^{4}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) B}{32 d \,a^{4}}"," ",0,"-1/32/d/a^4*A*ln(tan(d*x+c)+I)+1/32*I/d/a^4*B*ln(tan(d*x+c)+I)-5/12*I/d/a^4/(tan(d*x+c)-I)^3*A+7/12/d/a^4/(tan(d*x+c)-I)^3*B+1/16*I/d/a^4/(tan(d*x+c)-I)*A-15/16/d/a^4/(tan(d*x+c)-I)*B-7/16/d/a^4/(tan(d*x+c)-I)^2*A-17/16*I/d/a^4/(tan(d*x+c)-I)^2*B+1/8/d/a^4/(tan(d*x+c)-I)^4*A+1/8*I/d/a^4/(tan(d*x+c)-I)^4*B+1/32/d/a^4*ln(tan(d*x+c)-I)*A-1/32*I/d/a^4*ln(tan(d*x+c)-I)*B","A"
61,1,244,129,0.231000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","-\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7 B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i A}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{B}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}+\frac{i B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right) A}{32 d \,a^{4}}+\frac{\ln \left(\tan \left(d x +c \right)-i\right) B}{32 d \,a^{4}}-\frac{A}{4 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{5 i B}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}"," ",0,"-1/32/d/a^4*B*ln(tan(d*x+c)+I)-1/32*I/d/a^4*A*ln(tan(d*x+c)+I)+1/16*I/d/a^4/(tan(d*x+c)-I)^2*A-7/16/d/a^4/(tan(d*x+c)-I)^2*B-1/8*I/d/a^4/(tan(d*x+c)-I)^4*A+1/8/d/a^4/(tan(d*x+c)-I)^4*B-1/16/d/a^4/(tan(d*x+c)-I)*A+1/16*I/d/a^4/(tan(d*x+c)-I)*B+1/32*I/d/a^4*ln(tan(d*x+c)-I)*A+1/32/d/a^4*ln(tan(d*x+c)-I)*B-1/4/d/a^4/(tan(d*x+c)-I)^3*A-5/12*I/d/a^4/(tan(d*x+c)-I)^3*B","A"
62,1,244,126,0.226000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{A}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{i B}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{i A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{i B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{B}{4 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i A}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{\ln \left(\tan \left(d x +c \right)-i\right) A}{32 d \,a^{4}}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right) B}{32 d \,a^{4}}"," ",0,"1/32/d/a^4*A*ln(tan(d*x+c)+I)-1/32*I/d/a^4*B*ln(tan(d*x+c)+I)-1/8/d/a^4/(tan(d*x+c)-I)^4*A-1/8*I/d/a^4/(tan(d*x+c)-I)^4*B-1/16*I/d/a^4/(tan(d*x+c)-I)*A-1/16/d/a^4/(tan(d*x+c)-I)*B-1/16/d/a^4/(tan(d*x+c)-I)^2*A+1/16*I/d/a^4/(tan(d*x+c)-I)^2*B-1/4/d/a^4/(tan(d*x+c)-I)^3*B+1/12*I/d/a^4/(tan(d*x+c)-I)^3*A-1/32/d/a^4*ln(tan(d*x+c)-I)*A+1/32*I/d/a^4*ln(tan(d*x+c)-I)*B","A"
63,1,244,126,0.224000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{A}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i B}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{i A}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{B}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{i B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) A}{32 d \,a^{4}}-\frac{\ln \left(\tan \left(d x +c \right)-i\right) B}{32 d \,a^{4}}"," ",0,"1/32/d/a^4*B*ln(tan(d*x+c)+I)+1/32*I/d/a^4*A*ln(tan(d*x+c)+I)-1/12/d/a^4/(tan(d*x+c)-I)^3*A+1/12*I/d/a^4/(tan(d*x+c)-I)^3*B-1/16*I/d/a^4/(tan(d*x+c)-I)^2*A-1/16/d/a^4/(tan(d*x+c)-I)^2*B+1/8*I/d/a^4/(tan(d*x+c)-I)^4*A-1/8/d/a^4/(tan(d*x+c)-I)^4*B+1/16/d/a^4/(tan(d*x+c)-I)*A-1/16*I/d/a^4/(tan(d*x+c)-I)*B-1/32*I/d/a^4*ln(tan(d*x+c)-I)*A-1/32/d/a^4*ln(tan(d*x+c)-I)*B","A"
64,1,259,143,0.795000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","-\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{A \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}+\frac{B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{15 i A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{B}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i A}{4 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{7 A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{A}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{i B}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right) B}{32 d \,a^{4}}-\frac{31 \ln \left(\tan \left(d x +c \right)-i\right) A}{32 d \,a^{4}}"," ",0,"-1/32/d/a^4*A*ln(tan(d*x+c)+I)+1/32*I/d/a^4*B*ln(tan(d*x+c)+I)+1/a^4/d*A*ln(tan(d*x+c))+1/16/d/a^4/(tan(d*x+c)-I)*B-15/16*I/a^4/d/(tan(d*x+c)-I)*A-1/12/d/a^4/(tan(d*x+c)-I)^3*B+1/4*I/a^4/d/(tan(d*x+c)-I)^3*A-7/16/d/a^4/(tan(d*x+c)-I)^2*A-1/16*I/a^4/d/(tan(d*x+c)-I)^2*B+1/8/d/a^4/(tan(d*x+c)-I)^4*A+1/8*I/d/a^4/(tan(d*x+c)-I)^4*B-1/32*I/d/a^4*ln(tan(d*x+c)-I)*B-31/32/d/a^4*ln(tan(d*x+c)-I)*A","A"
65,1,293,197,0.712000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","-\frac{B \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{i A \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{A}{a^{4} d \tan \left(d x +c \right)}-\frac{4 i A \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}+\frac{B \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}-\frac{i A}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{B}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{49 A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{15 i B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}+\frac{5 A}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i B}{4 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{31 \ln \left(\tan \left(d x +c \right)-i\right) B}{32 d \,a^{4}}+\frac{129 i \ln \left(\tan \left(d x +c \right)-i\right) A}{32 d \,a^{4}}-\frac{7 B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{17 i A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}"," ",0,"-1/32/d/a^4*B*ln(tan(d*x+c)+I)-1/32*I/d/a^4*A*ln(tan(d*x+c)+I)-1/a^4/d*A/tan(d*x+c)-4*I/a^4/d*A*ln(tan(d*x+c))+1/a^4/d*B*ln(tan(d*x+c))-1/8*I/d/a^4/(tan(d*x+c)-I)^4*A+1/8/d/a^4/(tan(d*x+c)-I)^4*B-49/16/d/a^4/(tan(d*x+c)-I)*A-15/16*I/a^4/d/(tan(d*x+c)-I)*B+5/12/d/a^4/(tan(d*x+c)-I)^3*A+1/4*I/a^4/d/(tan(d*x+c)-I)^3*B-31/32/d/a^4*ln(tan(d*x+c)-I)*B+129/32*I/a^4/d*ln(tan(d*x+c)-I)*A-7/16/d/a^4/(tan(d*x+c)-I)^2*B+17/16*I/a^4/d/(tan(d*x+c)-I)^2*A","A"
66,1,329,229,0.792000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","\frac{A \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{i B}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{A}{2 a^{4} d \tan \left(d x +c \right)^{2}}-\frac{7 i A}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{11 A \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}+\frac{129 i \ln \left(\tan \left(d x +c \right)-i\right) B}{32 d \,a^{4}}-\frac{B}{a^{4} d \tan \left(d x +c \right)}-\frac{A}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{i B \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{49 B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}+\frac{4 i A}{a^{4} d \tan \left(d x +c \right)}+\frac{31 A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{111 i A}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}+\frac{5 B}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{17 i B}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{351 \ln \left(\tan \left(d x +c \right)-i\right) A}{32 d \,a^{4}}-\frac{4 i B \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}"," ",0,"1/32/d/a^4*A*ln(tan(d*x+c)+I)-1/8*I/d/a^4/(tan(d*x+c)-I)^4*B-1/2/a^4/d*A/tan(d*x+c)^2-7/12*I/a^4/d/(tan(d*x+c)-I)^3*A-11/a^4/d*A*ln(tan(d*x+c))+129/32*I/a^4/d*ln(tan(d*x+c)-I)*B-1/a^4/d/tan(d*x+c)*B-1/8/d/a^4/(tan(d*x+c)-I)^4*A-1/32*I/d/a^4*B*ln(tan(d*x+c)+I)-49/16/d/a^4/(tan(d*x+c)-I)*B+4*I/a^4/d/tan(d*x+c)*A+31/16/d/a^4/(tan(d*x+c)-I)^2*A+111/16*I/a^4/d/(tan(d*x+c)-I)*A+5/12/d/a^4/(tan(d*x+c)-I)^3*B+17/16*I/a^4/d/(tan(d*x+c)-I)^2*B+351/32/d/a^4*ln(tan(d*x+c)-I)*A-4*I/a^4/d*B*ln(tan(d*x+c))","A"
67,1,162,160,0.345000," ","int((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^3*(A+B*tan(d*x+c)),x)","-\frac{2 \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7}+\frac{2 i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5}+\frac{A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5}-\frac{2 i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3}-\frac{A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3}+A \,a^{3} \sqrt{a +i a \tan \left(d x +c \right)}-\frac{a^{\frac{7}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{2}\right)}{d \,a^{3}}"," ",0,"-2/d/a^3*(-1/7*I*B*(a+I*a*tan(d*x+c))^(7/2)+2/5*I*B*(a+I*a*tan(d*x+c))^(5/2)*a+1/5*A*(a+I*a*tan(d*x+c))^(5/2)*a-2/3*I*B*(a+I*a*tan(d*x+c))^(3/2)*a^2-1/3*A*(a+I*a*tan(d*x+c))^(3/2)*a^2+A*a^3*(a+I*a*tan(d*x+c))^(1/2)-1/2*a^(7/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
68,1,124,116,0.350000," ","int((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^2*(A+B*tan(d*x+c)),x)","-\frac{2 i \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}+\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}+\frac{A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}-i a^{2} B \sqrt{a +i a \tan \left(d x +c \right)}-\frac{a^{\frac{5}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{2}\right)}{d \,a^{2}}"," ",0,"-2*I/d/a^2*(-1/5*I*B*(a+I*a*tan(d*x+c))^(5/2)+1/3*I*B*(a+I*a*tan(d*x+c))^(3/2)*a+1/3*A*(a+I*a*tan(d*x+c))^(3/2)*a-I*a^2*B*(a+I*a*tan(d*x+c))^(1/2)-1/2*a^(5/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
69,1,82,85,0.262000," ","int((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)*(A+B*tan(d*x+c)),x)","\frac{-\frac{2 i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3}+2 A \sqrt{a +i a \tan \left(d x +c \right)}\, a -a^{\frac{3}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{d a}"," ",0,"2/d/a*(-1/3*I*B*(a+I*a*tan(d*x+c))^(3/2)+A*(a+I*a*tan(d*x+c))^(1/2)*a-1/2*a^(3/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
70,1,63,61,0.229000," ","int((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\frac{2 i \left(-i B \sqrt{a +i a \tan \left(d x +c \right)}-\frac{\sqrt{a}\, \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{2}\right)}{d}"," ",0,"2*I/d*(-I*B*(a+I*a*tan(d*x+c))^(1/2)-1/2*a^(1/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
71,1,312,68,3.764000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(i A \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+i B \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+i A \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-A \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+B \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)\right) \sin \left(d x +c \right)}{d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right)}"," ",0,"-1/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(I*A*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+I*B*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+I*A*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-A*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+B*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)))*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)","B"
72,1,1181,101,4.125000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-2 i A \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+2 i A \left(\cos^{2}\left(d x +c \right)\right)+2 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-i A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-i A \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-2 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-2 i A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 i B \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 A \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-2 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+2 i B \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-2 B \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+2 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-A \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 B \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-2 A \cos \left(d x +c \right) \sin \left(d x +c \right)+2 i A \cos \left(d x +c \right)\right)}{2 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(1+\cos \left(d x +c \right)\right)}"," ",0,"-1/2/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*I*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+2*I*A*cos(d*x+c)^2+2*I*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-I*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-I*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-2*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+2*I*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2*I*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-2*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-2*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+2*I*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-2*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+2*I*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-2*A*cos(d*x+c)*sin(d*x+c)+2*I*A*cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/(1+cos(d*x+c))","B"
73,1,2240,137,3.602000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/8/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+4*I*A*cos(d*x+c)^2-2*I*A*cos(d*x+c)+6*I*A*cos(d*x+c)^3-7*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3+4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3-7*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2+4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+8*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+7*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)-8*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)+8*I*B*cos(d*x+c)^2*sin(d*x+c)-7*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-4*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+8*I*B*cos(d*x+c)*sin(d*x+c)-2*A*cos(d*x+c)*sin(d*x+c)+7*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-8*B*cos(d*x+c)-6*A*cos(d*x+c)^2*sin(d*x+c)+8*B*cos(d*x+c)^3-8*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)+8*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+7*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3+4*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3+7*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+4*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2+8*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^3-8*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2-8*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-7*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)-8*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-4*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)-8*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^3+8*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+8*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)-8*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)-8*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+8*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^3+8*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^3+8*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2)/(I*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)/(1+cos(d*x+c))","B"
74,1,1783,172,3.379000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(42 A \cos \left(d x +c \right)+36 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-12 B \cos \left(d x +c \right) \sin \left(d x +c \right)+27 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+42 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-48 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-46 A \left(\cos^{2}\left(d x +c \right)\right)-42 i A \cos \left(d x +c \right) \sin \left(d x +c \right)-42 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+27 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{4}\left(d x +c \right)\right)+42 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right)-54 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-84 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)+62 i A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 i A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+48 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+48 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+27 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+62 A \left(\cos^{4}\left(d x +c \right)\right)-24 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+12 i B \left(\cos^{3}\left(d x +c \right)\right)-36 i B \left(\cos^{4}\left(d x +c \right)\right)+36 i B \left(\cos^{2}\left(d x +c \right)\right)-58 A \left(\cos^{3}\left(d x +c \right)\right)-12 i B \cos \left(d x +c \right)+48 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+27 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right)-42 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{4}\left(d x +c \right)\right)-54 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)+84 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)+48 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-96 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+48 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-96 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-48 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+96 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+48 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-96 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\right)}{48 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \sin \left(d x +c \right)^{3}}"," ",0,"-1/48/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(42*A*cos(d*x+c)-24*B*sin(d*x+c)*cos(d*x+c)^2+36*B*cos(d*x+c)^3*sin(d*x+c)-46*A*cos(d*x+c)^2+62*A*cos(d*x+c)^4-12*B*cos(d*x+c)*sin(d*x+c)+27*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+42*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-36*I*B*cos(d*x+c)^4+12*I*B*cos(d*x+c)^3+36*I*B*cos(d*x+c)^2-12*I*B*cos(d*x+c)-58*A*cos(d*x+c)^3+48*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^4*2^(1/2)-48*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^4*2^(1/2)-96*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*2^(1/2)+96*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)+27*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^4+42*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^4-54*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-84*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2+48*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+48*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+62*I*A*cos(d*x+c)^3*sin(d*x+c)-4*I*A*cos(d*x+c)^2*sin(d*x+c)+27*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-42*I*A*cos(d*x+c)*sin(d*x+c)-42*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+48*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^4*2^(1/2)+48*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^4*2^(1/2)-96*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)-96*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*2^(1/2)+27*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^4-42*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^4-54*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2+84*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+48*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-48*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2))/(I*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)^3","B"
75,1,164,162,0.286000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","-\frac{2 i \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7}+\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5}+\frac{A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5}-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3}-i a^{3} B \sqrt{a +i a \tan \left(d x +c \right)}+A \,a^{3} \sqrt{a +i a \tan \left(d x +c \right)}-a^{\frac{7}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{d \,a^{2}}"," ",0,"-2*I/d/a^2*(-1/7*I*B*(a+I*a*tan(d*x+c))^(7/2)+1/5*I*B*(a+I*a*tan(d*x+c))^(5/2)*a+1/5*A*(a+I*a*tan(d*x+c))^(5/2)*a-1/3*I*a^2*B*(a+I*a*tan(d*x+c))^(3/2)-I*a^3*B*(a+I*a*tan(d*x+c))^(1/2)+A*a^3*(a+I*a*tan(d*x+c))^(1/2)-a^(7/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
76,1,123,111,0.233000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\frac{-\frac{2 i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}+\frac{2 A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}-2 i a^{2} B \sqrt{a +i a \tan \left(d x +c \right)}+2 a^{2} A \sqrt{a +i a \tan \left(d x +c \right)}-2 a^{\frac{5}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{d a}"," ",0,"2/d/a*(-1/5*I*B*(a+I*a*tan(d*x+c))^(5/2)+1/3*A*(a+I*a*tan(d*x+c))^(3/2)*a-I*a^2*B*(a+I*a*tan(d*x+c))^(1/2)+a^2*A*(a+I*a*tan(d*x+c))^(1/2)-a^(5/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
77,1,99,87,0.188000," ","int((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\frac{2 i \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3}-i B a \sqrt{a +i a \tan \left(d x +c \right)}+A \sqrt{a +i a \tan \left(d x +c \right)}\, a -a^{\frac{3}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{d}"," ",0,"2*I/d*(-1/3*I*B*(a+I*a*tan(d*x+c))^(3/2)-I*B*a*(a+I*a*tan(d*x+c))^(1/2)+A*(a+I*a*tan(d*x+c))^(1/2)*a-a^(3/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
78,1,467,91,3.465000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(2 i A \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)+2 i B \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)-2 A \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)+i A \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 B \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)-A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 i B \cos \left(d x +c \right)+2 B \sin \left(d x +c \right)+2 i B \right) a}{d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right)}"," ",0,"-1/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(2*I*A*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)+2*I*B*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)-2*A*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)+I*A*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*B*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)-A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*I*B*cos(d*x+c)+2*B*sin(d*x+c)+2*I*B)/(I*sin(d*x+c)+cos(d*x+c)-1)*a","B"
79,1,1117,103,3.575000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(4 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+3 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)+4 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+4 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+4 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+2 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)+2 i A \cos \left(d x +c \right) \sin \left(d x +c \right)+2 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)-4 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-4 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-3 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-4 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-2 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-3 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 A \left(\cos^{2}\left(d x +c \right)\right)-2 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-2 A \cos \left(d x +c \right)\right) a}{2 d \left(1+\cos \left(d x +c \right)\right) \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"1/2/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)*(4*I*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2+4*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)-4*I*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2+4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*2^(1/2)-4*I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+2*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+3*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+2*I*A*cos(d*x+c)*sin(d*x+c)+2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2-4*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+4*I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2-3*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-2*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-3*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*A*cos(d*x+c)^2-2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-2*A*cos(d*x+c))/(1+cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/(-1+cos(d*x+c))*a","B"
80,1,1290,139,3.517000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-10 A \cos \left(d x +c \right)+11 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-16 B \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)+16 A \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)-11 i A \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-16 i A \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)-16 i B \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)+16 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+16 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-12 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-8 B \cos \left(d x +c \right) \sin \left(d x +c \right)-12 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-4 A \left(\cos^{2}\left(d x +c \right)\right)-10 i A \cos \left(d x +c \right) \sin \left(d x +c \right)+14 i A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-8 i B \left(\cos^{3}\left(d x +c \right)\right)+14 A \left(\cos^{3}\left(d x +c \right)\right)+8 i B \cos \left(d x +c \right)+16 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-16 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+11 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+12 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-11 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+12 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)\right) a}{8 d \left(-1+\cos \left(d x +c \right)\right) \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(1+\cos \left(d x +c \right)\right)}"," ",0,"1/8/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-16*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-10*A*cos(d*x+c)+8*B*sin(d*x+c)*cos(d*x+c)^2-4*A*cos(d*x+c)^2+11*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+16*A*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)-16*B*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)-8*B*cos(d*x+c)*sin(d*x+c)-8*I*B*cos(d*x+c)^3+8*I*B*cos(d*x+c)+14*A*cos(d*x+c)^3+16*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+16*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+14*I*A*cos(d*x+c)^2*sin(d*x+c)-10*I*A*cos(d*x+c)*sin(d*x+c)-12*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+16*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+11*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+12*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-16*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-16*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-11*I*A*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-12*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-11*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+12*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)))/(-1+cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/(1+cos(d*x+c))*a","B"
81,1,1804,175,2.151000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(54 A \cos \left(d x +c \right)+84 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-60 B \cos \left(d x +c \right) \sin \left(d x +c \right)+69 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+66 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-96 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-82 A \left(\cos^{2}\left(d x +c \right)\right)-54 i A \cos \left(d x +c \right) \sin \left(d x +c \right)-66 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+69 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{4}\left(d x +c \right)\right)+66 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right)-138 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-132 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)+98 i A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-28 i A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+96 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+96 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+69 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+98 A \left(\cos^{4}\left(d x +c \right)\right)-24 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+60 i B \left(\cos^{3}\left(d x +c \right)\right)-84 i B \left(\cos^{4}\left(d x +c \right)\right)+84 i B \left(\cos^{2}\left(d x +c \right)\right)-70 A \left(\cos^{3}\left(d x +c \right)\right)-60 i B \cos \left(d x +c \right)+96 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+69 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right)-66 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{4}\left(d x +c \right)\right)-138 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)+132 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)+96 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-192 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+96 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-192 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-96 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+192 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+96 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-192 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\right) a}{48 d \left(-1+\cos \left(d x +c \right)\right) \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \sin \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)}"," ",0,"1/48/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(96*I*A*2^(1/2)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+54*A*cos(d*x+c)-24*B*sin(d*x+c)*cos(d*x+c)^2+84*B*cos(d*x+c)^3*sin(d*x+c)-82*A*cos(d*x+c)^2+98*A*cos(d*x+c)^4+98*I*A*cos(d*x+c)^3*sin(d*x+c)-28*I*A*sin(d*x+c)*cos(d*x+c)^2-54*I*A*cos(d*x+c)*sin(d*x+c)+69*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-66*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-60*B*cos(d*x+c)*sin(d*x+c)+69*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+66*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-70*A*cos(d*x+c)^3-96*I*B*2^(1/2)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+69*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^4+66*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^4-138*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-132*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2+96*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+96*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+96*I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-96*I*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-138*I*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+132*I*B*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+69*I*A*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-66*I*B*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+84*I*B*cos(d*x+c)^2-60*I*B*cos(d*x+c)-84*I*B*cos(d*x+c)^4+60*I*B*cos(d*x+c)^3-192*I*A*2^(1/2)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+192*I*B*2^(1/2)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+96*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^4*2^(1/2)+96*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^4*2^(1/2)-192*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)-192*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*2^(1/2))/(-1+cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)/(1+cos(d*x+c))*a","B"
82,1,206,205,0.271000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","-\frac{2 i \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{9}{2}}}{9}+\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}} a}{7}+\frac{A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}} a}{7}-\frac{i a^{2} B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{3}}{3}+\frac{A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{3}}{3}-2 i B \,a^{4} \sqrt{a +i a \tan \left(d x +c \right)}+2 A \,a^{4} \sqrt{a +i a \tan \left(d x +c \right)}-2 a^{\frac{9}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{d \,a^{2}}"," ",0,"-2*I/d/a^2*(-1/9*I*B*(a+I*a*tan(d*x+c))^(9/2)+1/7*I*B*(a+I*a*tan(d*x+c))^(7/2)*a+1/7*A*(a+I*a*tan(d*x+c))^(7/2)*a-1/5*I*a^2*B*(a+I*a*tan(d*x+c))^(5/2)-1/3*I*B*(a+I*a*tan(d*x+c))^(3/2)*a^3+1/3*A*(a+I*a*tan(d*x+c))^(3/2)*a^3-2*I*B*a^4*(a+I*a*tan(d*x+c))^(1/2)+2*A*a^4*(a+I*a*tan(d*x+c))^(1/2)-2*a^(9/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
83,1,165,139,0.227000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\frac{-\frac{2 i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7}+\frac{2 A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5}-\frac{2 i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3}+\frac{2 A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3}-4 i B \,a^{3} \sqrt{a +i a \tan \left(d x +c \right)}+4 A \,a^{3} \sqrt{a +i a \tan \left(d x +c \right)}-4 a^{\frac{7}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{d a}"," ",0,"2/d/a*(-1/7*I*B*(a+I*a*tan(d*x+c))^(7/2)+1/5*A*(a+I*a*tan(d*x+c))^(5/2)*a-1/3*I*a^2*B*(a+I*a*tan(d*x+c))^(3/2)+1/3*A*(a+I*a*tan(d*x+c))^(3/2)*a^2-2*I*B*a^3*(a+I*a*tan(d*x+c))^(1/2)+2*A*a^3*(a+I*a*tan(d*x+c))^(1/2)-2*a^(7/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
84,1,141,115,0.188000," ","int((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\frac{2 i \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}+\frac{A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}-2 i a^{2} B \sqrt{a +i a \tan \left(d x +c \right)}+2 a^{2} A \sqrt{a +i a \tan \left(d x +c \right)}-2 a^{\frac{5}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{d}"," ",0,"2*I/d*(-1/5*I*B*(a+I*a*tan(d*x+c))^(5/2)-1/3*I*B*(a+I*a*tan(d*x+c))^(3/2)*a+1/3*A*(a+I*a*tan(d*x+c))^(3/2)*a-2*I*B*a^2*(a+I*a*tan(d*x+c))^(1/2)+2*a^2*A*(a+I*a*tan(d*x+c))^(1/2)-2*a^(5/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
85,1,965,119,3.431000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(28 i B \cos \left(d x +c \right)-12 i A \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+12 A \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+12 i A \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i A \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-12 B \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-12 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+12 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-12 i B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-12 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+3 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-3 i A \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-12 i A \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+12 A \left(\cos^{2}\left(d x +c \right)\right)+32 B \cos \left(d x +c \right) \sin \left(d x +c \right)-32 i B \left(\cos^{2}\left(d x +c \right)\right)-12 A \cos \left(d x +c \right)-4 B \sin \left(d x +c \right)+4 i B \right) a^{2}}{6 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)}"," ",0,"-1/6/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(28*I*B*cos(d*x+c)-12*I*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+12*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-12*I*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+12*I*A*cos(d*x+c)*sin(d*x+c)-12*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-3*I*A*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+3*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+12*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-12*I*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-12*B*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+3*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-3*I*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-12*I*A*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+12*A*cos(d*x+c)^2+32*B*cos(d*x+c)*sin(d*x+c)-32*I*B*cos(d*x+c)^2-12*A*cos(d*x+c)-4*B*sin(d*x+c)+4*I*B)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)*a^2","B"
86,1,1141,132,3.541000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(8 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-8 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+8 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-8 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+8 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+2 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+5 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)+2 i A \cos \left(d x +c \right) \sin \left(d x +c \right)+2 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)-5 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+8 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-8 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+5 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)-2 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-8 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-4 i B \left(\cos^{2}\left(d x +c \right)\right)+2 A \left(\cos^{2}\left(d x +c \right)\right)-5 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+4 B \cos \left(d x +c \right) \sin \left(d x +c \right)-2 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-2 A \cos \left(d x +c \right)-4 B \sin \left(d x +c \right)+4 i B \right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{2 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \sin \left(d x +c \right)}"," ",0,"-1/2/d*(8*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-8*I*B*cos(d*x+c)^2*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+8*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)+2*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+8*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*2^(1/2)+8*I*A*cos(d*x+c)^2*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+5*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+2*I*A*cos(d*x+c)*sin(d*x+c)+2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2-5*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+5*I*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-8*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-8*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-2*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-8*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-4*I*B*cos(d*x+c)^2+2*A*cos(d*x+c)^2-5*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+4*B*cos(d*x+c)*sin(d*x+c)-2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-2*A*cos(d*x+c)-4*B*sin(d*x+c)+4*I*B)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)*a^2","B"
87,1,1292,141,3.392000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\frac{\left(-18 A \cos \left(d x +c \right)+23 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+23 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-32 B \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)+32 A \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)-23 i A \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-32 i A \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)-32 i B \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right)+32 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-8 B \cos \left(d x +c \right) \sin \left(d x +c \right)+32 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)-20 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-4 A \left(\cos^{2}\left(d x +c \right)\right)-18 i A \cos \left(d x +c \right) \sin \left(d x +c \right)+22 i A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-8 i B \left(\cos^{3}\left(d x +c \right)\right)+22 A \left(\cos^{3}\left(d x +c \right)\right)+8 i B \cos \left(d x +c \right)+32 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-32 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+20 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-23 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+20 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-20 i B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{8 d \left(-1+\cos \left(d x +c \right)\right) \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(1+\cos \left(d x +c \right)\right)}"," ",0,"1/8/d*(-32*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-18*A*cos(d*x+c)+8*B*sin(d*x+c)*cos(d*x+c)^2-4*A*cos(d*x+c)^2+23*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+32*A*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)-32*B*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)+32*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-8*B*cos(d*x+c)*sin(d*x+c)-8*I*B*cos(d*x+c)^3+8*I*B*cos(d*x+c)+22*A*cos(d*x+c)^3-20*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+32*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+20*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-32*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+32*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2+22*I*A*cos(d*x+c)^2*sin(d*x+c)-18*I*A*cos(d*x+c)*sin(d*x+c)-32*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+23*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-23*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+20*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-23*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-20*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/(1+cos(d*x+c))*a^2","B"
88,1,2506,179,3.461000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/48/d*(192*A*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+132*B*cos(d*x+c)^2+192*I*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-182*I*A*cos(d*x+c)^4-130*I*A*cos(d*x+c)^3+166*I*A*cos(d*x+c)^2+114*I*A*cos(d*x+c)+182*A*cos(d*x+c)^3*sin(d*x+c)-114*A*cos(d*x+c)*sin(d*x+c)-192*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-132*B*cos(d*x+c)^4+108*B*cos(d*x+c)+52*A*cos(d*x+c)^2*sin(d*x+c)-108*B*cos(d*x+c)^3-135*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-138*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-132*I*B*cos(d*x+c)^3*sin(d*x+c)-24*I*B*sin(d*x+c)*cos(d*x+c)^2+108*I*B*cos(d*x+c)*sin(d*x+c)+192*I*A*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-192*I*B*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+192*I*A*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-135*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-192*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-138*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-192*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-135*I*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+138*I*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-192*I*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-192*I*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+192*I*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-192*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+135*I*A*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-138*I*B*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+135*I*A*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-138*I*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-192*I*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+192*B*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+192*A*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+192*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-135*I*A*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+138*I*B*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+135*A*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+138*B*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+135*A*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+138*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/(1+cos(d*x+c))^2*a^2","B"
89,1,3444,217,1.946000," ","int(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"1/384/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(1536*I*A*2^(1/2)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-416*B*cos(d*x+c)^2-1166*A*cos(d*x+c)^3*sin(d*x+c)+1080*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-1089*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)+1536*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+894*I*A*cos(d*x+c)+1690*I*A*cos(d*x+c)^5+524*I*A*cos(d*x+c)^4-2488*I*A*cos(d*x+c)^3-428*I*A*cos(d*x+c)^2-1690*A*cos(d*x+c)^4*sin(d*x+c)+1536*I*B*2^(1/2)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+894*A*cos(d*x+c)*sin(d*x+c)+416*B*cos(d*x+c)^4-1089*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+912*B*cos(d*x+c)+1322*A*cos(d*x+c)^2*sin(d*x+c)-2368*B*cos(d*x+c)^3+1456*B*cos(d*x+c)^5+2178*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3-2160*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3+2178*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2-2160*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-1536*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+1080*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)+1040*I*B*sin(d*x+c)*cos(d*x+c)^3-1328*I*B*sin(d*x+c)*cos(d*x+c)^2-912*I*B*cos(d*x+c)*sin(d*x+c)-1089*A*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+1080*B*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-1089*A*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+1080*B*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+1089*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+1080*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+1456*I*B*cos(d*x+c)^4*sin(d*x+c)+1536*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)-2160*I*B*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-2178*I*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2160*I*B*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-1536*A*2^(1/2)*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+1536*B*2^(1/2)*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-1536*A*2^(1/2)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+1536*B*2^(1/2)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+1536*I*A*2^(1/2)*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+1536*I*B*2^(1/2)*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+1536*I*A*2^(1/2)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+1536*I*B*2^(1/2)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-3072*I*A*2^(1/2)*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-3072*I*B*2^(1/2)*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-3072*I*A*2^(1/2)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-3072*I*B*2^(1/2)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+3072*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^3+1536*I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+1536*I*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+1089*I*A*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+1080*I*B*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+1089*I*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+1080*I*B*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-3072*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2-1536*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)-3072*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^3+3072*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+1089*I*A*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+1080*I*B*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-2178*I*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)))/(-1+cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)/(1+cos(d*x+c))^2*a^2","B"
90,1,168,173,0.267000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}+\frac{2 i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}+\frac{A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}-2 i a^{2} B \sqrt{a +i a \tan \left(d x +c \right)}-a^{2} A \sqrt{a +i a \tan \left(d x +c \right)}-\frac{a^{\frac{5}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{4}-\frac{a^{3} \left(i B +A \right)}{2 \sqrt{a +i a \tan \left(d x +c \right)}}\right)}{d \,a^{3}}"," ",0,"-2/d/a^3*(-1/5*I*B*(a+I*a*tan(d*x+c))^(5/2)+2/3*I*B*(a+I*a*tan(d*x+c))^(3/2)*a+1/3*A*(a+I*a*tan(d*x+c))^(3/2)*a-2*I*B*a^2*(a+I*a*tan(d*x+c))^(1/2)-a^2*A*(a+I*a*tan(d*x+c))^(1/2)-1/4*a^(5/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-1/2*a^3*(A+I*B)/(a+I*a*tan(d*x+c))^(1/2))","A"
91,1,127,135,0.265000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 i \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3}+i B a \sqrt{a +i a \tan \left(d x +c \right)}+A \sqrt{a +i a \tan \left(d x +c \right)}\, a -\frac{a^{\frac{3}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{4}+\frac{a^{2} \left(i B +A \right)}{2 \sqrt{a +i a \tan \left(d x +c \right)}}\right)}{d \,a^{2}}"," ",0,"-2*I/d/a^2*(-1/3*I*B*(a+I*a*tan(d*x+c))^(3/2)+I*B*a*(a+I*a*tan(d*x+c))^(1/2)+A*(a+I*a*tan(d*x+c))^(1/2)*a-1/4*a^(3/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))+1/2*a^2*(A+I*B)/(a+I*a*tan(d*x+c))^(1/2))","A"
92,1,88,91,0.248000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{-2 i B \sqrt{a +i a \tan \left(d x +c \right)}-\frac{\sqrt{a}\, \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{2}-\frac{a \left(i B +A \right)}{\sqrt{a +i a \tan \left(d x +c \right)}}}{d a}"," ",0,"2/d/a*(-I*B*(a+I*a*tan(d*x+c))^(1/2)-1/4*a^(1/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-1/2*a*(A+I*B)/(a+I*a*tan(d*x+c))^(1/2))","A"
93,1,71,67,0.221000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 i \left(-\frac{\left(-\frac{i B}{2}+\frac{A}{2}\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{2 \sqrt{a}}-\frac{-\frac{A}{2}-\frac{i B}{2}}{\sqrt{a +i a \tan \left(d x +c \right)}}\right)}{d}"," ",0,"2*I/d*(-1/2*(-1/2*I*B+1/2*A)*2^(1/2)/a^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-(-1/2*A-1/2*I*B)/(a+I*a*tan(d*x+c))^(1/2))","A"
94,1,948,93,3.718000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(i A \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-i B \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 i A \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+A \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 i A \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-i B \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+B \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 A \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+A \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-4 i B \cos \left(d x +c \right)-4 A \cos \left(d x +c \right)\right)}{4 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right) a}"," ",0,"-1/4/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(I*A*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-I*B*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+2*I*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+A*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+2*I*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-I*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+B*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+2*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-2*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-4*I*B*cos(d*x+c)-4*A*cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c))/a","B"
95,1,2727,141,3.929000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"1/4/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)+I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)+2*I*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-4*B*cos(d*x+c)+4*A*cos(d*x+c)^2*sin(d*x+c)+4*B*cos(d*x+c)^3+I*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)-I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^3-I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2-I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2-2*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)*cos(d*x+c)^2-A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3-2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3-A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2-2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)+B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-I*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-8*I*A*cos(d*x+c)^3+8*I*A*cos(d*x+c)-2*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3-2*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2-I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)+2*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)+I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3-B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^3+I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2+I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)-A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-A*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)))/(-1+cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c))/(1+cos(d*x+c))/a","B"
96,1,2751,182,4.091000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"1/16/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(4*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+28*A*cos(d*x+c)+16*B*sin(d*x+c)*cos(d*x+c)^2+11*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*I*B*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+4*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+4*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+11*I*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+4*I*B*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+4*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+4*I*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+11*I*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+4*I*B*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-11*I*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-11*I*A*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-11*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-20*A*cos(d*x+c)^3-4*I*B*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-4*B*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+11*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2-4*I*A*sin(d*x+c)*cos(d*x+c)^2-4*B*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+4*B*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-11*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-4*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+11*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-4*I*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-4*I*B*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+4*I*B*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-4*I*A*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+11*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+32*I*B*cos(d*x+c)-32*I*B*cos(d*x+c)^3-11*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-4*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+4*I*A*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-4*A*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-11*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)))/(-1+cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c))/(1+cos(d*x+c))/a","B"
97,1,153,174,0.236000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3}+2 i B a \sqrt{a +i a \tan \left(d x +c \right)}+A \sqrt{a +i a \tan \left(d x +c \right)}\, a -\frac{a^{\frac{3}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8}+\frac{a^{2} \left(7 i B +5 A \right)}{4 \sqrt{a +i a \tan \left(d x +c \right)}}-\frac{a^{3} \left(i B +A \right)}{6 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\right)}{d \,a^{3}}"," ",0,"-2/d/a^3*(-1/3*I*B*(a+I*a*tan(d*x+c))^(3/2)+2*I*B*a*(a+I*a*tan(d*x+c))^(1/2)+A*(a+I*a*tan(d*x+c))^(1/2)*a-1/8*a^(3/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))+1/4*a^2*(5*A+7*I*B)/(a+I*a*tan(d*x+c))^(1/2)-1/6*a^3*(A+I*B)/(a+I*a*tan(d*x+c))^(3/2))","A"
98,1,116,136,0.228000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 i \left(-i B \sqrt{a +i a \tan \left(d x +c \right)}-\frac{\sqrt{a}\, \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8}-\frac{a \left(5 i B +3 A \right)}{4 \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{a^{2} \left(i B +A \right)}{6 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\right)}{d \,a^{2}}"," ",0,"-2*I/d/a^2*(-I*B*(a+I*a*tan(d*x+c))^(1/2)-1/8*a^(1/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-1/4*a*(3*A+5*I*B)/(a+I*a*tan(d*x+c))^(1/2)+1/6*a^2*(A+I*B)/(a+I*a*tan(d*x+c))^(3/2))","A"
99,1,96,96,0.200000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{-\frac{\left(-\frac{i B}{4}+\frac{A}{4}\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{\sqrt{a}}-\frac{2 \left(-\frac{3 i B}{4}-\frac{A}{4}\right)}{\sqrt{a +i a \tan \left(d x +c \right)}}-\frac{a \left(i B +A \right)}{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}}{d a}"," ",0,"2/d/a*(-1/2*(-1/4*I*B+1/4*A)*2^(1/2)/a^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-(-3/4*I*B-1/4*A)/(a+I*a*tan(d*x+c))^(1/2)-1/6*a*(A+I*B)/(a+I*a*tan(d*x+c))^(3/2))","A"
100,1,96,96,0.167000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 i \left(-\frac{\left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 a^{\frac{3}{2}}}-\frac{-\frac{A}{2}-\frac{i B}{2}}{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{i B -A}{4 a \sqrt{a +i a \tan \left(d x +c \right)}}\right)}{d}"," ",0,"2*I/d*(-1/8*(A-I*B)/a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-1/3*(-1/2*A-1/2*I*B)/(a+I*a*tan(d*x+c))^(3/2)-1/4/a*(-A+I*B)/(a+I*a*tan(d*x+c))^(1/2))","A"
101,1,1026,124,3.403000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(12 i A \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 i B \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-12 i A \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-36 i A \cos \left(d x +c \right) \sin \left(d x +c \right)-12 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-16 i A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-3 A \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+16 A \left(\cos^{4}\left(d x +c \right)\right)+3 i A \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3 B \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+16 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 i B \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+16 i B \left(\cos^{4}\left(d x +c \right)\right)-12 A \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-12 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 A \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+4 i B \left(\cos^{2}\left(d x +c \right)\right)-12 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+28 A \left(\cos^{2}\left(d x +c \right)\right)+12 B \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{24 d \,a^{2}}"," ",0,"1/24/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(12*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+3*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-12*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)-36*I*A*cos(d*x+c)*sin(d*x+c)-12*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-16*I*A*cos(d*x+c)^3*sin(d*x+c)-3*A*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+16*A*cos(d*x+c)^4+3*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)+3*B*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+16*B*cos(d*x+c)^3*sin(d*x+c)+3*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+16*I*B*cos(d*x+c)^4-12*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-12*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+4*I*B*cos(d*x+c)^2-12*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+28*A*cos(d*x+c)^2+12*B*cos(d*x+c)*sin(d*x+c))/a^2","B"
102,1,2818,178,3.546000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-1/24/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+28*B*cos(d*x+c)^2+44*A*cos(d*x+c)^3*sin(d*x+c)-12*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-18*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)-84*A*cos(d*x+c)*sin(d*x+c)-12*B*cos(d*x+c)^4-18*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+18*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-12*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+3*I*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+3*I*A*2^(1/2)*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-3*I*A*2^(1/2)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-18*I*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)+18*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3+12*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3+18*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2+12*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-12*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)-3*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-36*I*B*cos(d*x+c)*sin(d*x+c)+16*I*B*cos(d*x+c)^5*sin(d*x+c)+20*I*B*cos(d*x+c)^3*sin(d*x+c)+18*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-12*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+18*I*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-12*I*B*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-18*I*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+12*I*B*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-3*I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+18*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)+12*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-18*I*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+12*I*B*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+16*A*cos(d*x+c)^5*sin(d*x+c)+16*I*A*cos(d*x+c)^6+36*I*A*cos(d*x+c)^4-52*I*A*cos(d*x+c)^2-3*I*B*2^(1/2)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+3*I*A*2^(1/2)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-12*I*B*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+3*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^3+3*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2-3*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)-3*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-16*B*cos(d*x+c)^6-18*A*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+12*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)))/(cos(d*x+c)^2-1)/a^2","B"
103,1,2818,221,3.500000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"1/48/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-6*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+176*A*cos(d*x+c)^2-69*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+32*I*A*cos(d*x+c)^5*sin(d*x+c)+136*I*A*cos(d*x+c)^3*sin(d*x+c)-252*I*A*cos(d*x+c)*sin(d*x+c)-69*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-36*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-120*A*cos(d*x+c)^4-88*B*cos(d*x+c)^3*sin(d*x+c)+6*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+6*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+168*B*cos(d*x+c)*sin(d*x+c)-69*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+36*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-32*B*cos(d*x+c)^5*sin(d*x+c)-32*I*B*cos(d*x+c)^6-72*I*B*cos(d*x+c)^4+104*I*B*cos(d*x+c)^2+6*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-69*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+36*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+6*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-6*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-36*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+69*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+36*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-69*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-36*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+69*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+6*B*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+69*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-36*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2-36*B*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+36*B*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+69*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+36*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+69*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-6*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-69*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-6*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-6*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-36*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+6*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-6*A*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+69*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+36*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-32*A*cos(d*x+c)^6)/(cos(d*x+c)^2-1)/a^2","B"
104,1,181,212,0.245000," ","int(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 i \left(-\frac{i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3}+3 i B a \sqrt{a +i a \tan \left(d x +c \right)}+A \sqrt{a +i a \tan \left(d x +c \right)}\, a -\frac{a^{\frac{3}{2}} \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16}+\frac{a^{2} \left(31 i B +17 A \right)}{8 \sqrt{a +i a \tan \left(d x +c \right)}}-\frac{a^{3} \left(9 i B +7 A \right)}{12 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{a^{4} \left(i B +A \right)}{10 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}\right)}{d \,a^{4}}"," ",0,"2*I/d/a^4*(-1/3*I*B*(a+I*a*tan(d*x+c))^(3/2)+3*I*B*a*(a+I*a*tan(d*x+c))^(1/2)+A*(a+I*a*tan(d*x+c))^(1/2)*a-1/16*a^(3/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))+1/8*a^2*(31*I*B+17*A)/(a+I*a*tan(d*x+c))^(1/2)-1/12*a^3*(9*I*B+7*A)/(a+I*a*tan(d*x+c))^(3/2)+1/10*a^4*(A+I*B)/(a+I*a*tan(d*x+c))^(5/2))","A"
105,1,142,174,0.240000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 \left(-i B \sqrt{a +i a \tan \left(d x +c \right)}-\frac{\sqrt{a}\, \left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16}-\frac{a \left(17 i B +7 A \right)}{8 \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{a^{2} \left(7 i B +5 A \right)}{12 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{a^{3} \left(i B +A \right)}{10 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}\right)}{d \,a^{3}}"," ",0,"-2/d/a^3*(-I*B*(a+I*a*tan(d*x+c))^(1/2)-1/16*a^(1/2)*(A-I*B)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-1/8*a*(7*A+17*I*B)/(a+I*a*tan(d*x+c))^(1/2)+1/12*a^2*(5*A+7*I*B)/(a+I*a*tan(d*x+c))^(3/2)-1/10*a^3*(A+I*B)/(a+I*a*tan(d*x+c))^(5/2))","A"
106,1,124,136,0.241000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 i \left(-\frac{\left(\frac{A}{8}-\frac{i B}{8}\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{2 \sqrt{a}}-\frac{-\frac{7 i B}{8}-\frac{A}{8}}{\sqrt{a +i a \tan \left(d x +c \right)}}-\frac{a \left(5 i B +3 A \right)}{12 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{a^{2} \left(i B +A \right)}{10 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}\right)}{d \,a^{2}}"," ",0,"-2*I/d/a^2*(-1/2*(1/8*A-1/8*I*B)*2^(1/2)/a^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-(-7/8*I*B-1/8*A)/(a+I*a*tan(d*x+c))^(1/2)-1/12*a*(3*A+5*I*B)/(a+I*a*tan(d*x+c))^(3/2)+1/10*a^2*(A+I*B)/(a+I*a*tan(d*x+c))^(5/2))","A"
107,1,121,124,0.217000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{-\frac{\left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 a^{\frac{3}{2}}}-\frac{2 \left(-\frac{3 i B}{4}-\frac{A}{4}\right)}{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{a \left(i B +A \right)}{5 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{i B -A}{4 a \sqrt{a +i a \tan \left(d x +c \right)}}}{d a}"," ",0,"2/d/a*(-1/16*(A-I*B)/a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-1/3*(-3/4*I*B-1/4*A)/(a+I*a*tan(d*x+c))^(3/2)-1/10*a*(A+I*B)/(a+I*a*tan(d*x+c))^(5/2)-1/8/a*(-A+I*B)/(a+I*a*tan(d*x+c))^(1/2))","A"
108,1,123,124,0.180000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 i \left(-\frac{\left(-i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16 a^{\frac{5}{2}}}-\frac{-\frac{A}{2}-\frac{i B}{2}}{5 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{i B -A}{12 a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{i B -A}{8 a^{2} \sqrt{a +i a \tan \left(d x +c \right)}}\right)}{d}"," ",0,"2*I/d*(-1/16*(A-I*B)/a^(5/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-1/5*(-1/2*A-1/2*I*B)/(a+I*a*tan(d*x+c))^(5/2)-1/12/a*(-A+I*B)/(a+I*a*tan(d*x+c))^(3/2)-1/8/a^2*(-A+I*B)/(a+I*a*tan(d*x+c))^(1/2))","A"
109,1,1084,154,3.605000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(120 i A \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+192 i B \left(\cos^{6}\left(d x +c \right)\right)+192 A \left(\cos^{6}\left(d x +c \right)\right)+192 B \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i B \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-120 i A \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-420 i A \cos \left(d x +c \right) \sin \left(d x +c \right)-120 i A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-15 A \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-192 i A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i A \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+96 A \left(\cos^{4}\left(d x +c \right)\right)+15 B \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-192 i A \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+32 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-15 A \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-120 A \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-120 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+15 i B \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-64 i B \left(\cos^{4}\left(d x +c \right)\right)+20 i B \left(\cos^{2}\left(d x +c \right)\right)-120 A \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+300 A \left(\cos^{2}\left(d x +c \right)\right)+60 B \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{240 d \,a^{3}}"," ",0,"1/240/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(120*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+192*I*B*cos(d*x+c)^6+192*A*cos(d*x+c)^6+192*B*cos(d*x+c)^5*sin(d*x+c)+15*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-120*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)-420*I*A*cos(d*x+c)*sin(d*x+c)-120*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-15*A*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-192*I*A*cos(d*x+c)^3*sin(d*x+c)+15*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)+96*A*cos(d*x+c)^4+15*B*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-192*I*A*cos(d*x+c)^5*sin(d*x+c)+32*B*cos(d*x+c)^3*sin(d*x+c)-15*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-120*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-120*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+15*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)-64*I*B*cos(d*x+c)^4+20*I*B*cos(d*x+c)^2-120*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+300*A*cos(d*x+c)^2+60*B*cos(d*x+c)*sin(d*x+c))/a^3","B"
110,1,2858,214,3.651000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-1/240/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(15*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+300*B*cos(d*x+c)^2+668*A*cos(d*x+c)^3*sin(d*x+c)-120*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-300*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)-1260*A*cos(d*x+c)*sin(d*x+c)-204*B*cos(d*x+c)^4-300*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-15*I*B*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+300*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-120*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+300*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3+120*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3+300*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2+120*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-120*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)-15*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+192*I*B*sin(d*x+c)*cos(d*x+c)^7+228*I*B*sin(d*x+c)*cos(d*x+c)^3-420*I*B*sin(d*x+c)*cos(d*x+c)+300*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-120*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+160*A*cos(d*x+c)^5*sin(d*x+c)+192*I*A*cos(d*x+c)^8+64*I*A*cos(d*x+c)^6+564*I*A*cos(d*x+c)^4-820*I*A*cos(d*x+c)^2+192*A*sin(d*x+c)*cos(d*x+c)^7-300*I*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+120*I*B*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+120*I*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-15*I*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+300*I*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-120*I*B*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+300*I*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-300*I*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+120*I*B*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+15*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^3+15*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2-15*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)-15*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+96*B*cos(d*x+c)^6-300*A*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+120*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-192*B*cos(d*x+c)^8+15*I*B*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-300*I*A*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-120*I*B*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+15*I*A*2^(1/2)*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+15*I*A*2^(1/2)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-15*I*A*2^(1/2)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))/(cos(d*x+c)^2-1)/a^3","B"
111,1,2876,259,3.550000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-1/240/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(15*B*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-1700*A*cos(d*x+c)^2+645*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+15*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+1164*A*cos(d*x+c)^4+668*B*cos(d*x+c)^3*sin(d*x+c)-15*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-15*A*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-1260*B*cos(d*x+c)*sin(d*x+c)+645*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-300*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+160*B*cos(d*x+c)^5*sin(d*x+c)+300*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+645*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+300*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-192*I*A*cos(d*x+c)^7*sin(d*x+c)-320*I*A*cos(d*x+c)^5*sin(d*x+c)-1348*I*A*cos(d*x+c)^3*sin(d*x+c)+2520*I*A*cos(d*x+c)*sin(d*x+c)-15*B*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+192*I*B*cos(d*x+c)^8+64*I*B*cos(d*x+c)^6+564*I*B*cos(d*x+c)^4-820*I*B*cos(d*x+c)^2+192*B*cos(d*x+c)^7*sin(d*x+c)-645*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+300*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2+300*B*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-300*B*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-645*A*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+645*A*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+15*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-645*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-300*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3-645*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+15*A*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-300*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-645*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+645*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+300*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+300*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)-645*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-300*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-15*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+224*A*cos(d*x+c)^6+192*A*cos(d*x+c)^8+15*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+645*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-300*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+15*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-15*I*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-15*I*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2))/(cos(d*x+c)^2-1)/a^3","B"
112,1,537,105,0.095000," ","int(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{i a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{2 i a A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{2 a B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{i a A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{2 a A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{2 i a B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}-\frac{2 a B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{i a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{i a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{2 i a A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{2 i a B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{i a B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{i a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}"," ",0,"1/2*I/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+2/5*I/d*a*A*tan(d*x+c)^(5/2)+2/5/d*a*B*tan(d*x+c)^(5/2)+1/4*I/d*a*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2/3/d*a*A*tan(d*x+c)^(3/2)+2/7*I*a*B*tan(d*x+c)^(7/2)/d-2/d*a*B*tan(d*x+c)^(1/2)+1/2*I/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2*I/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a*A*tan(d*x+c)^(1/2)+1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/3*I/d*a*B*tan(d*x+c)^(3/2)+1/4*I/d*a*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2*I/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
113,1,506,85,0.097000," ","int(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-\frac{i a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{i a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{2 a B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{2 i a A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{2 a A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{i a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{i a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{i a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{2 i a B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{2 i a B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{i a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}"," ",0,"-1/2*I/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4*I/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2/3/d*a*B*tan(d*x+c)^(3/2)+2/3*I/d*a*A*tan(d*x+c)^(3/2)+2/d*a*A*tan(d*x+c)^(1/2)+1/2*I/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/4*I/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2*I/d*a*B*tan(d*x+c)^(1/2)+2/5*I*a*B*tan(d*x+c)^(5/2)/d+1/2*I/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))","B"
114,1,475,65,0.099000," ","int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{2 i a B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{2 i a A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{2 a B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{i a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{i a A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{i a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{i a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{i a B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{i a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}"," ",0,"2/3*I*a*B*tan(d*x+c)^(3/2)/d+2*I/d*a*A*tan(d*x+c)^(1/2)+2/d*a*B*tan(d*x+c)^(1/2)-1/2*I/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4*I/d*a*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2*I/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4*I/d*a*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2*I/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","B"
115,1,444,45,0.095000," ","int((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\frac{2 i a B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{i a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{i a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{i a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{i a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{i a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{i a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}"," ",0,"2*I*a*B*tan(d*x+c)^(1/2)/d-1/2*I/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4*I/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*a*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2*I/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2*I/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4*I/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*a*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))","B"
116,1,443,44,0.104000," ","int((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","-\frac{2 a A}{d \sqrt{\tan \left(d x +c \right)}}+\frac{i a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{i a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{i a A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{i a B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{i a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{i a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}"," ",0,"-2*a*A/d/tan(d*x+c)^(1/2)+1/2*I/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2*I/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4*I/d*a*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/4*I/d*a*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2*I/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2*I/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
117,1,474,64,0.102000," ","int((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","-\frac{2 a A}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 i a A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 a B}{d \sqrt{\tan \left(d x +c \right)}}+\frac{i a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{i a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{i a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{i a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{i a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{i a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}"," ",0,"-2/3*a*A/d/tan(d*x+c)^(3/2)-2*I/d*a/tan(d*x+c)^(1/2)*A-2/d*a/tan(d*x+c)^(1/2)*B+1/2*I/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2*I/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4*I/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/4*I/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2*I/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
118,1,505,84,0.107000," ","int((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","-\frac{2 a A}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{i a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{2 a A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{i a B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{2 a B}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{i a A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{i a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{i a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{2 i a B}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 i a A}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{i a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}"," ",0,"-2/5*a*A/d/tan(d*x+c)^(5/2)-1/2*I/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+2*a*A/d/tan(d*x+c)^(1/2)-1/4*I/d*a*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/3/d*a/tan(d*x+c)^(3/2)*B-1/4*I/d*a*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2*I/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a/tan(d*x+c)^(1/2)*B-2/3*I/d*a/tan(d*x+c)^(3/2)*A-1/2*I/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))","B"
119,1,607,152,0.099000," ","int(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{2 a^{2} B \left(\tan^{\frac{9}{2}}\left(d x +c \right)\right)}{9 d}+\frac{i a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{2 a^{2} A \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}-\frac{4 i a^{2} B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{4 a^{2} B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{i a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{4 a^{2} A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{4 i a^{2} B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}-\frac{4 a^{2} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{i a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{4 i a^{2} A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{i a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{4 i a^{2} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{i a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/9/d*a^2*B*tan(d*x+c)^(9/2)+1/2*I/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/7/d*a^2*A*tan(d*x+c)^(7/2)-4/3*I/d*a^2*B*tan(d*x+c)^(3/2)+4/5/d*a^2*B*tan(d*x+c)^(5/2)+1/2*I/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+4/3/d*a^2*A*tan(d*x+c)^(3/2)+4/7*I/d*a^2*B*tan(d*x+c)^(7/2)-4/d*a^2*B*tan(d*x+c)^(1/2)+I/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+4/5*I/d*a^2*A*tan(d*x+c)^(5/2)+I/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-4*I/d*a^2*A*tan(d*x+c)^(1/2)+I/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+I/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","B"
120,1,574,130,0.101000," ","int(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{2 a^{2} B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}-\frac{4 i a^{2} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{i a^{2} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{4 a^{2} B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}-\frac{i a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{4 a^{2} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{4 i a^{2} B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{4 i a^{2} A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{i a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/7/d*a^2*B*tan(d*x+c)^(7/2)-4*I/d*a^2*B*tan(d*x+c)^(1/2)-2/5/d*a^2*A*tan(d*x+c)^(5/2)+1/2*I/d*a^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+4/3/d*a^2*B*tan(d*x+c)^(3/2)-I/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+4/d*a^2*A*tan(d*x+c)^(1/2)+4/5*I/d*a^2*B*tan(d*x+c)^(5/2)+4/3*I/d*a^2*A*tan(d*x+c)^(3/2)+I/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+I/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","B"
121,1,537,108,0.105000," ","int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{2 a^{2} B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{4 i a^{2} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}-\frac{i a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{4 a^{2} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{i a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{i a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{4 i a^{2} B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/5/d*a^2*B*tan(d*x+c)^(5/2)+4*I/d*a^2*A*tan(d*x+c)^(1/2)-2/3/d*a^2*A*tan(d*x+c)^(3/2)-1/2*I/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+4/d*a^2*B*tan(d*x+c)^(1/2)-I/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-I/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+4/3*I/d*a^2*B*tan(d*x+c)^(3/2)+1/2/d*a^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
122,1,500,86,0.102000," ","int((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","-\frac{2 a^{2} B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{2} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{4 i a^{2} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{i a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{i a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{2} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{i a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/3/d*a^2*B*tan(d*x+c)^(3/2)-2/d*a^2*A*tan(d*x+c)^(1/2)+4*I/d*a^2*B*tan(d*x+c)^(1/2)-I/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-I/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2*I/d*a^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+I/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+I/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","B"
123,1,484,85,0.104000," ","int((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","-\frac{2 a^{2} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} A}{d \sqrt{\tan \left(d x +c \right)}}+\frac{i a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{i a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{i a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/d*a^2*B*tan(d*x+c)^(1/2)-2*a^2*A/d/tan(d*x+c)^(1/2)+1/2*I/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+I/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+I/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2*I/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+I/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+I/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
124,1,504,85,0.108000," ","int((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","-\frac{2 a^{2} A}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{4 i a^{2} A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 a^{2} B}{d \sqrt{\tan \left(d x +c \right)}}+\frac{i a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{2} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{i a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}"," ",0,"-2/3*a^2*A/d/tan(d*x+c)^(3/2)-4*I/d*a^2/tan(d*x+c)^(1/2)*A-2/d*a^2/tan(d*x+c)^(1/2)*B+I/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+I/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2*I/d*a^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-I/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))","B"
125,1,537,107,0.109000," ","int((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","-\frac{2 a^{2} A}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{i a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{4 a^{2} A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{4 i a^{2} A}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 a^{2} B}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{i a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{i a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}-\frac{4 i a^{2} B}{d \sqrt{\tan \left(d x +c \right)}}+\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/5*a^2*A/d/tan(d*x+c)^(5/2)-1/2*I/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+4*a^2*A/d/tan(d*x+c)^(1/2)-4/3*I/d*a^2/tan(d*x+c)^(3/2)*A-2/3/d*a^2/tan(d*x+c)^(3/2)*B-I/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-I/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2*I/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-4*I/d*a^2/tan(d*x+c)^(1/2)*B+1/2/d*a^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
126,1,570,129,0.113000," ","int((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x)","-\frac{2 a^{2} A}{7 d \tan \left(d x +c \right)^{\frac{7}{2}}}+\frac{4 a^{2} A}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{4 i a^{2} B}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{i a^{2} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{4 a^{2} B}{d \sqrt{\tan \left(d x +c \right)}}+\frac{i a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{2} B}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}+\frac{4 i a^{2} A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{i a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{i a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{4 i a^{2} A}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}+\frac{i a^{2} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{2 d}"," ",0,"-2/7/d*a^2*A/tan(d*x+c)^(7/2)+4/3*a^2*A/d/tan(d*x+c)^(3/2)-4/3*I/d*a^2/tan(d*x+c)^(3/2)*B-1/2*I/d*a^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+4/d*a^2/tan(d*x+c)^(1/2)*B+I/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2/5/d*a^2/tan(d*x+c)^(5/2)*B+4*I/d*a^2/tan(d*x+c)^(1/2)*A-I/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+I/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-4/5*I/d*a^2/tan(d*x+c)^(5/2)*A+1/2*I/d*a^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))","B"
127,1,610,166,0.112000," ","int(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\frac{8 i a^{3} B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}-\frac{i a^{3} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{6 a^{3} B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}+\frac{8 i a^{3} A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}-\frac{6 a^{3} A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{i a^{3} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{8 a^{3} B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}-\frac{8 i a^{3} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{8 a^{3} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 i a^{3} A \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}-\frac{2 a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{3} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 i a^{3} B \left(\tan^{\frac{9}{2}}\left(d x +c \right)\right)}{9 d}-\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{3} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"8/5*I/d*a^3*B*tan(d*x+c)^(5/2)-I/d*a^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-6/7/d*a^3*B*tan(d*x+c)^(7/2)+8/3*I/d*a^3*A*tan(d*x+c)^(3/2)-6/5/d*a^3*A*tan(d*x+c)^(5/2)+I/d*a^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+8/3/d*a^3*B*tan(d*x+c)^(3/2)-8*I/d*a^3*B*tan(d*x+c)^(1/2)+8*a^3*A*tan(d*x+c)^(1/2)/d-2*I/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+2*I/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-2/7*I/d*a^3*A*tan(d*x+c)^(7/2)-2/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/9*I/d*a^3*B*tan(d*x+c)^(9/2)-2*I/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+2*I/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
128,1,574,144,0.102000," ","int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{2 i a^{3} A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}-\frac{i a^{3} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{6 a^{3} B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{8 i a^{3} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 a^{3} A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{d}+\frac{8 i a^{3} B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{8 a^{3} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 i a^{3} B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}-\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{3} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{3} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{3} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{2 a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/5*I/d*a^3*A*tan(d*x+c)^(5/2)-I/d*a^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-6/5/d*a^3*B*tan(d*x+c)^(5/2)+8*I/d*a^3*A*tan(d*x+c)^(1/2)-2/d*a^3*A*tan(d*x+c)^(3/2)+8/3*I/d*a^3*B*tan(d*x+c)^(3/2)+8*a^3*B*tan(d*x+c)^(1/2)/d-2/7*I/d*a^3*B*tan(d*x+c)^(7/2)-2*I/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2*I/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+2/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
129,1,538,122,0.103000," ","int((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\frac{i a^{3} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 i a^{3} B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}-\frac{2 a^{3} B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{d}+\frac{8 i a^{3} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{6 a^{3} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 i a^{3} A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{3} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{i a^{3} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{3} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{2 a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"I/d*a^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/5*I/d*a^3*B*tan(d*x+c)^(5/2)-2/d*a^3*B*tan(d*x+c)^(3/2)+8*I/d*a^3*B*tan(d*x+c)^(1/2)-6*a^3*A*tan(d*x+c)^(1/2)/d-2/3*I/d*a^3*A*tan(d*x+c)^(3/2)+2*I/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+2/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+2/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-I/d*a^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2*I/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+2/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
130,1,521,114,0.107000," ","int((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\frac{i a^{3} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 i a^{3} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{6 a^{3} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 a^{3} A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 i a^{3} B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{3} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{i a^{3} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{3} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}"," ",0,"I/d*a^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2*I/d*a^3*A*tan(d*x+c)^(1/2)-6*a^3*B*tan(d*x+c)^(1/2)/d-2/d*a^3*A/tan(d*x+c)^(1/2)-2/3*I/d*a^3*B*tan(d*x+c)^(3/2)+2*I/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+2*I/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+2/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+2/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+I/d*a^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2*I/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+2*I/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))","B"
131,1,522,114,0.116000," ","int((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","-\frac{2 i a^{3} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 a^{3} A}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{3} B}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{6 i a^{3} A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{i a^{3} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{3} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{i a^{3} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{3} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}"," ",0,"-2*I/d*a^3*B*tan(d*x+c)^(1/2)-2/3/d*a^3*A/tan(d*x+c)^(3/2)+2*I/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-2/d*a^3/tan(d*x+c)^(1/2)*B-2*I/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-6*I/d*a^3/tan(d*x+c)^(1/2)*A-I/d*a^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+I/d*a^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2*I/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+2*I/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-2/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))","B"
132,1,538,121,0.110000," ","int((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","-\frac{2 a^{3} A}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{i a^{3} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 a^{3} B}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 i a^{3} A}{d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{8 a^{3} A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{6 i a^{3} B}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a^{3} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{3} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}-\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{3} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{2 a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/5/d*a^3*A/tan(d*x+c)^(5/2)-I/d*a^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/3/d*a^3/tan(d*x+c)^(3/2)*B-2*I/d*a^3/tan(d*x+c)^(3/2)*A+8/d*a^3*A/tan(d*x+c)^(1/2)-6*I/d*a^3/tan(d*x+c)^(1/2)*B-2*I/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-2*I/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+2/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
133,1,572,143,0.110000," ","int((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x)","-\frac{2 a^{3} A}{7 d \tan \left(d x +c \right)^{\frac{7}{2}}}+\frac{i a^{3} A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{8 a^{3} B}{d \sqrt{\tan \left(d x +c \right)}}-\frac{6 i a^{3} A}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{2 a^{3} B}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{2 i a^{3} B}{d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{8 a^{3} A}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{8 i a^{3} A}{d \sqrt{\tan \left(d x +c \right)}}+\frac{2 a^{3} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{3} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{2 a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{i a^{3} B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{2 i a^{3} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{2 i a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a^{3} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{d}+\frac{2 a^{3} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{2 a^{3} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/7/d*a^3*A/tan(d*x+c)^(7/2)+I/d*a^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+8/d*a^3/tan(d*x+c)^(1/2)*B-6/5*I/d*a^3/tan(d*x+c)^(5/2)*A-2/5/d*a^3/tan(d*x+c)^(5/2)*B-2*I/d*a^3/tan(d*x+c)^(3/2)*B+8/3/d*a^3*A/tan(d*x+c)^(3/2)+2*I/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+8*I/d*a^3/tan(d*x+c)^(1/2)*A+2/d*a^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-I/d*a^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2*I/d*a^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-2*I/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+2/d*a^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+2/d*a^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","B"
134,1,290,251,0.437000," ","int(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","-\frac{2 i B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d a}+\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d a}-\frac{2 i A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d a}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{d a \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{d a \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{i \left(\sqrt{\tan}\left(d x +c \right)\right) B}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) A}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{4 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{d a \left(\sqrt{2}-i \sqrt{2}\right)}+\frac{6 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{d a \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-2/3*I/d/a*B*tan(d*x+c)^(3/2)+2/d/a*B*tan(d*x+c)^(1/2)-2*I/d/a*A*tan(d*x+c)^(1/2)-1/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+I/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-1/2*I/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*B-1/2/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*A+4/d/a/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A+6*I/d/a/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B","A"
135,1,255,225,0.438000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","-\frac{2 i B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d a}-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{d a \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{d a \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{i \left(\sqrt{\tan}\left(d x +c \right)\right) A}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) B}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{4 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{d a \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{2 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{d a \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-2*I/d/a*B*tan(d*x+c)^(1/2)-I/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A-1/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B+1/2*I/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*A-1/2/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*B+4/d/a/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B-2*I/d/a/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
136,1,192,189,0.463000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{d a \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{d a \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{i \left(\sqrt{\tan}\left(d x +c \right)\right) B}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) A}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{2 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{d a \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-I/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B+1/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+1/2*I/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*B+1/2/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*A-2*I/d/a*B/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))","A"
137,1,192,191,0.405000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x)","\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{d a \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{d a \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) B}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{i \left(\sqrt{\tan}\left(d x +c \right)\right) A}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{2 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{d a \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"I/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+1/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B+1/2/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*B-1/2*I/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*A-2*I/d/a/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
138,1,254,221,0.355000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x)","-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{d a \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{d a \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{2 A}{a d \sqrt{\tan \left(d x +c \right)}}-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) A}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{i \left(\sqrt{\tan}\left(d x +c \right)\right) B}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{2 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{d a \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{4 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{d a \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-1/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+I/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-2*A/a/d/tan(d*x+c)^(1/2)-1/2/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*A-1/2*I/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*B-2*I/d/a*B/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))-4/d/a/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
139,1,289,245,0.362000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c)),x)","-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{d a \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{d a \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{2 A}{3 a d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 i A}{d a \sqrt{\tan \left(d x +c \right)}}-\frac{2 B}{a d \sqrt{\tan \left(d x +c \right)}}+\frac{i \left(\sqrt{\tan}\left(d x +c \right)\right) A}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) B}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{4 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{d a \left(\sqrt{2}-i \sqrt{2}\right)}+\frac{6 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{d a \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-I/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A-1/d/a/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-2/3*A/a/d/tan(d*x+c)^(3/2)+2*I/d/a/tan(d*x+c)^(1/2)*A-2*B/a/d/tan(d*x+c)^(1/2)+1/2*I/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*A-1/2/d/a*tan(d*x+c)^(1/2)/(tan(d*x+c)-I)*B-4/d/a/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B+6*I/d/a/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
140,1,311,262,0.448000," ","int(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,a^{2}}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{7 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{11 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{5 i \left(\sqrt{\tan}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{9 \left(\sqrt{\tan}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{23 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-2/d/a^2*B*tan(d*x+c)^(1/2)-1/2/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+1/2*I/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B+7/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*A+11/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*B-5/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*A+9/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*B-7/4/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A-23/4*I/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B","A"
141,1,294,232,0.470000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{7 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{3 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{5 i \left(\sqrt{\tan}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-1/2/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-1/2*I/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+7/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*B-3/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*A-5/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*B-1/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*A-7/4/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B-1/4*I/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
142,1,294,234,0.490000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{\left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{3 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{3 i \left(\sqrt{\tan}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"1/2/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A-1/2*I/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B+1/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*A-3/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*B-3/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*A-1/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*B-1/4/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A-1/4*I/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B","A"
143,1,294,236,0.391000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{5 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{\left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7 \left(\sqrt{\tan}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{3 i \left(\sqrt{\tan}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"1/2/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B+1/2*I/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A-5/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*A+1/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*B-7/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*A-3/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*B-7/4*I/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A-1/4/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B","A"
144,1,311,262,0.362000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{2 A}{d \,a^{2} \sqrt{\tan \left(d x +c \right)}}-\frac{9 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{5 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{11 i \left(\sqrt{\tan}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7 \left(\sqrt{\tan}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{23 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-1/2/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+1/2*I/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-2/d/a^2*A/tan(d*x+c)^(1/2)-9/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*A-5/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*B+11/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*A-7/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*B-7/4*I/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B-23/4/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
145,1,346,286,0.362000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{2 d \,a^{2} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{2 A}{3 d \,a^{2} \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{4 i A}{d \,a^{2} \sqrt{\tan \left(d x +c \right)}}-\frac{2 B}{d \,a^{2} \sqrt{\tan \left(d x +c \right)}}+\frac{13 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{9 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{15 \left(\sqrt{\tan}\left(d x +c \right)\right) A}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{11 i \left(\sqrt{\tan}\left(d x +c \right)\right) B}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{23 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}+\frac{47 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{2} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-1/2/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-1/2*I/d/a^2/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A-2/3/d/a^2*A/tan(d*x+c)^(3/2)+4*I/d/a^2/tan(d*x+c)^(1/2)*A-2/d/a^2/tan(d*x+c)^(1/2)*B+13/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*A-9/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(3/2)*B+15/8/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*A+11/8*I/d/a^2/(tan(d*x+c)-I)^2*tan(d*x+c)^(1/2)*B-23/4/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B+47/4*I/d/a^2/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
146,1,404,326,0.446000," ","int(tan(d*x+c)^(9/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\frac{2 i B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d \,a^{3}}-\frac{6 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,a^{3}}+\frac{2 i A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,a^{3}}+\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{35 i B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{5 A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{2 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{91 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{49 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{7 A \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{27 i B \left(\sqrt{\tan}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{29 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{19 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"2/3*I/d/a^3*B*tan(d*x+c)^(3/2)-6/d/a^3*B*tan(d*x+c)^(1/2)+2*I/d/a^3*A*tan(d*x+c)^(1/2)+1/4/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A-1/4*I/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B+35/8*I/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(5/2)+5/2/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(5/2)+91/12/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(3/2)-49/12*I/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*A-7/4/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(1/2)-27/8*I/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(1/2)-29/4/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A-19*I/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B","A"
147,1,369,302,0.444000," ","int(tan(d*x+c)^(7/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\frac{2 i B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,a^{3}}+\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{9 i A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{5 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{2 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{19 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{49 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{7 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{5 i A \left(\sqrt{\tan}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{29 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}+\frac{3 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{2 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"2*I/d/a^3*B*tan(d*x+c)^(1/2)+1/4*I/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+1/4/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-9/8*I/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(5/2)+5/2/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(5/2)-19/12/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*A-49/12*I/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*B-7/4/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(1/2)+5/8*I/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(1/2)-29/4/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B+3/2*I/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
148,1,323,257,0.442000," ","int(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{9 i B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{4 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{19 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{5 i B \left(\sqrt{\tan}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}+\frac{3 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{2 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-1/4/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+1/4*I/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-9/8*I/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(5/2)-1/4/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(5/2)-19/12/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(3/2)+1/12*I/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*A+5/8*I/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(1/2)-1/4/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A+3/2*I/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B","A"
149,1,278,258,0.434000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{4 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{5 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i A \left(\sqrt{\tan}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-1/4*I/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A-1/4/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-1/4/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(5/2)-1/8*I/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(5/2)-5/12/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*A+1/12*I/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*B+1/8*I/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(1/2)-1/4/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B","A"
150,1,278,261,0.469000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{i B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{5 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{i B \left(\sqrt{\tan}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{A \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"1/4/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A-1/4*I/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-1/8*I/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(5/2)-5/12/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(3/2)-1/12*I/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*A+1/8*I/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(1/2)-1/4/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(1/2)-1/4/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
151,1,323,261,0.461000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x)","\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{5 i A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{19 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{9 i A \left(\sqrt{\tan}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{B \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{3 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{2 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"1/4*I/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+1/4/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-5/8*I/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(5/2)-19/12/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*A-1/12*I/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*B+9/8*I/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(1/2)-1/4/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(1/2)-3/2*I/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A-1/4/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B","A"
152,1,368,302,0.431000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^3,x)","-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}+\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{2 A}{d \,a^{3} \sqrt{\tan \left(d x +c \right)}}-\frac{7 A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{4 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{5 i B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{49 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{19 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{9 i B \left(\sqrt{\tan}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{5 A \left(\sqrt{\tan}\left(d x +c \right)\right)}{2 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{3 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{2 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}-\frac{29 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-1/4/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A+1/4*I/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-2/d/a^3*A/tan(d*x+c)^(1/2)-7/4/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(5/2)-5/8*I/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(5/2)+49/12*I/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*A-19/12/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(3/2)+9/8*I/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(1/2)+5/2/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(1/2)-3/2*I/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B-29/4/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
153,1,403,326,0.467000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^3,x)","-\frac{i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) A}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{\arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}+i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}+i \sqrt{2}\right)}-\frac{2 A}{3 d \,a^{3} \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{6 i A}{d \,a^{3} \sqrt{\tan \left(d x +c \right)}}-\frac{2 B}{d \,a^{3} \sqrt{\tan \left(d x +c \right)}}+\frac{27 i A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{7 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{4 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{91 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{49 i \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{5 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{2 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{35 i A \left(\sqrt{\tan}\left(d x +c \right)\right)}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{29 \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) B}{4 d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}+\frac{19 i \arctan \left(\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{\sqrt{2}-i \sqrt{2}}\right) A}{d \,a^{3} \left(\sqrt{2}-i \sqrt{2}\right)}"," ",0,"-1/4*I/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*A-1/4/d/a^3/(2^(1/2)+I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)+I*2^(1/2)))*B-2/3/d/a^3*A/tan(d*x+c)^(3/2)+6*I/d/a^3/tan(d*x+c)^(1/2)*A-2/d/a^3/tan(d*x+c)^(1/2)*B+27/8*I/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(5/2)-7/4/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(5/2)+91/12/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*A+49/12*I/d/a^3/(tan(d*x+c)-I)^3*tan(d*x+c)^(3/2)*B+5/2/d/a^3/(tan(d*x+c)-I)^3*B*tan(d*x+c)^(1/2)-35/8*I/d/a^3/(tan(d*x+c)-I)^3*A*tan(d*x+c)^(1/2)-29/4/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*B+19*I/d/a^3/(2^(1/2)-I*2^(1/2))*arctan(2*tan(d*x+c)^(1/2)/(2^(1/2)-I*2^(1/2)))*A","A"
154,1,838,159,0.389000," ","int((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2)*(A+B*tan(d*x+c)),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(\sqrt{\tan}\left(d x +c \right)\right) \left(4 i A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -4 i B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -6 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-7 i B \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \tan \left(d x +c \right) a +4 B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +4 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)-8 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-4 i A \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) a +4 A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +8 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+4 A \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \tan \left(d x +c \right) a -2 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-7 B \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) a \right)}{8 d \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)}"," ",0,"-1/8/d*(a*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^(1/2)*(4*I*A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-4*I*B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-6*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-7*I*B*(-I*a)^(1/2)*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*tan(d*x+c)*a+4*B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+4*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-8*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-4*I*A*(-I*a)^(1/2)*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a+4*A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+8*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+4*A*(-I*a)^(1/2)*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*tan(d*x+c)*a-2*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-7*B*(-I*a)^(1/2)*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)","B"
155,1,713,123,0.388000," ","int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(i B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +2 i A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a +i A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -2 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +2 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a +B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +2 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a \right)}{2 d \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)}"," ",0,"-1/2/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*(I*B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+2*I*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a+I*A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-2*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+2*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a+B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+2*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)","B"
156,1,502,89,0.349000," ","int((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(\sqrt{\tan}\left(d x +c \right)\right) a \left(i A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right)-2 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right)-i B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right)+B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right)+A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right)-2 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\right)}{2 d \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)}"," ",0,"1/2/d*(a*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^(1/2)*a*(I*A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)-2*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)-I*B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))+B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)+A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))-2*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)","B"
157,1,434,75,0.313000," ","int((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -4 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+4 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)}"," ",0,"1/2/d*(a*(1+I*tan(d*x+c)))^(1/2)*(I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-4*I*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+4*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c))/tan(d*x+c)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)","B"
158,1,553,110,0.319000," ","int((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(3 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -12 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)-3 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +3 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -8 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-4 i A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+3 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +12 i B \tan \left(d x +c \right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}+4 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{6 d \tan \left(d x +c \right)^{\frac{3}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)}"," ",0,"-1/6/d*(a*(1+I*tan(d*x+c)))^(1/2)/tan(d*x+c)^(3/2)*(3*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-12*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-3*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+3*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-8*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)-4*I*A*tan(d*x+c)^2*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+3*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+12*I*B*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)+4*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)","B"
159,1,630,145,0.322000," ","int((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(15 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +15 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -15 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -20 i B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+15 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -56 i A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+52 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)+20 i B \tan \left(d x +c \right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-40 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)+12 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-16 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)\right)}{30 d \tan \left(d x +c \right)^{\frac{5}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)}"," ",0,"-1/30/d*(a*(1+I*tan(d*x+c)))^(1/2)*(15*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+15*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-15*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-20*I*B*tan(d*x+c)^3*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+15*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-56*I*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)+52*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+20*I*B*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-40*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+12*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-16*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c))/tan(d*x+c)^(5/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)","B"
160,1,707,180,0.332000," ","int((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-172 i A \left(\tan^{4}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-364 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right)-84 i B \tan \left(d x +c \right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}+105 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a -296 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)-105 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +105 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +112 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)+392 i B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+72 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-60 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+105 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +136 i A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{210 d \tan \left(d x +c \right)^{\frac{7}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)}"," ",0,"1/210/d*(a*(1+I*tan(d*x+c)))^(1/2)/tan(d*x+c)^(7/2)*(-172*I*A*tan(d*x+c)^4*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-364*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^4-84*I*B*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)+105*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a-296*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3-105*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+105*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+112*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+392*I*B*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)+72*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)-60*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)+105*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+136*I*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)","B"
161,1,650,198,0.385000," ","int(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(16 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+24 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+27 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -54 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+28 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-24 i \sqrt{i a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -30 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +60 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+24 \sqrt{i a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -48 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -48 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a \right)}{48 d \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/48/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*a*(16*I*B*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+24*I*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)+27*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a-54*I*B*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+28*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-24*I*(I*a)^(1/2)*2^(1/2)*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-30*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+60*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+24*(I*a)^(1/2)*2^(1/2)*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-48*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a-48*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
162,1,565,162,0.407000," ","int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(-4 i B \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+4 i A \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) a -8 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-4 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +5 B \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) a -10 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+8 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -4 \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a \sqrt{i a}-8 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a \right)}{8 d \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}}"," ",0,"-1/8/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*a*(-4*I*B*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)+4*I*A*(-I*a)^(1/2)*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a-8*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-4*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+5*B*(-I*a)^(1/2)*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a-10*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+8*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a*(-I*a)^(1/2)-4*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a*(I*a)^(1/2)-8*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a)/(I*a)^(1/2)/(-I*a)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)","B"
163,1,486,126,0.347000," ","int((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(\sqrt{\tan}\left(d x +c \right)\right) a \left(2 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +2 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +2 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +2 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -\sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a \sqrt{i a}\right)}{2 d \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/2/d*(a*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^(1/2)*a*(2*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+2*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+2*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+2*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a*(-I*a)^(1/2)-2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a*(I*a)^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
164,1,521,118,0.309000," ","int((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(4 i A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a -i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +2 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a +2 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a -\sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -4 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-2 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a \right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}}"," ",0,"1/2/d*(a*(1+I*tan(d*x+c)))^(1/2)*a*(4*I*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a-I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+2*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a+2*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a-(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-4*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-2*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a)/tan(d*x+c)^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)","B"
165,1,618,112,0.360000," ","int((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(-12 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +3 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +16 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+12 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +6 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a -3 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +12 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+6 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +4 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{6 d \tan \left(d x +c \right)^{\frac{3}{2}} \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}}"," ",0,"-1/6/d*(a*(1+I*tan(d*x+c)))^(1/2)*a/tan(d*x+c)^(3/2)*(-12*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a+3*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+16*I*A*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+12*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a+6*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a-3*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+12*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+6*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a+4*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(I*a)^(1/2)/(-I*a)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)","B"
166,1,707,148,0.337000," ","int((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(-72 A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+60 i A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a -15 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +80 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+60 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a +30 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a -15 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +24 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-30 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a +20 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+12 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{30 d \tan \left(d x +c \right)^{\frac{5}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"-1/30/d*(a*(1+I*tan(d*x+c)))^(1/2)*a/tan(d*x+c)^(5/2)*(-72*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+60*I*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a-15*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+80*I*B*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+60*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a+30*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a-15*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+24*I*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)-30*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a+20*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+12*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
167,1,796,184,0.323000," ","int((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(504 B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+105 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +536 i A \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+152 A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-96 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+420 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right) a -420 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right) a -105 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +210 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right) a +210 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right) a -168 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-84 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-60 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{210 d \tan \left(d x +c \right)^{\frac{7}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/210/d*(a*(1+I*tan(d*x+c)))^(1/2)*a/tan(d*x+c)^(7/2)*(504*B*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+105*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+536*I*A*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+152*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-96*I*A*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+420*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^4*a-420*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^4*a-105*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+210*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^4*a+210*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^4*a-168*I*B*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-84*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-60*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
168,1,885,220,0.325000," ","int((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(-1544 A \left(\tan^{4}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+630 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{5}\left(d x +c \right)\right) a +488 i A \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+456 B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+1608 i B \left(\tan^{4}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+1260 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{5}\left(d x +c \right)\right) a +1260 i A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{5}\left(d x +c \right)\right) a -315 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +264 A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-200 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-630 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{5}\left(d x +c \right)\right) a -288 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-315 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a -180 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-140 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{630 d \tan \left(d x +c \right)^{\frac{9}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/630/d*(a*(1+I*tan(d*x+c)))^(1/2)*a/tan(d*x+c)^(9/2)*(-1544*A*tan(d*x+c)^4*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+630*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^5*a+488*I*A*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+456*B*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+1608*I*B*tan(d*x+c)^4*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+1260*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^5*a+1260*I*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^5*a-315*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+264*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-200*I*A*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-630*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^5*a-288*I*B*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-315*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a-180*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-140*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
169,1,742,240,0.400000," ","int(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(-96 B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-128 A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+272 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+416 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+447 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -894 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+428 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-384 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -456 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +912 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-768 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +384 \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a \sqrt{i a}-768 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a \right)}{384 d \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/384/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*a^2*(-96*B*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-128*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+272*I*B*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+416*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+447*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a-894*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+428*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-384*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-456*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+912*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-768*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+384*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a*(I*a)^(1/2)-768*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
170,1,653,202,0.413000," ","int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(16 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)-52 i B \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+54 i A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -108 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+24 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-48 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +57 B \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) a -114 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+96 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -48 \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a \sqrt{i a}-96 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a \right)}{48 d \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}}"," ",0,"-1/48/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*a^2*(16*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-52*I*B*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)+54*I*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a-108*I*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+24*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-48*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+57*B*(-I*a)^(1/2)*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a-114*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+96*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a-48*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a*(I*a)^(1/2)-96*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a)/(I*a)^(1/2)/(-I*a)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)","B"
171,1,566,164,0.368000," ","int((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(\sqrt{\tan}\left(d x +c \right)\right) a^{2} \left(-9 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +18 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-4 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+8 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +12 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -8 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+16 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -8 \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a \sqrt{i a}+16 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a \right)}{8 d \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/8/d*(a*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^(1/2)*a^2*(-9*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+18*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-4*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+8*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+12*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a-8*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+16*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a*(-I*a)^(1/2)-8*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a*(I*a)^(1/2)+16*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
172,1,565,161,0.336000," ","int((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(6 i A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a -2 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +3 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a -2 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+4 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a -2 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -4 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-4 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a \right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/2/d*(a*(1+I*tan(d*x+c)))^(1/2)*a^2*(6*I*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a-2*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+3*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a-2*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+4*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a-2*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-4*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-4*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a)/tan(d*x+c)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
173,1,620,154,0.331000," ","int((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(-9 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +3 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +14 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+12 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +6 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a -3 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +6 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+6 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +2 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{3 d \tan \left(d x +c \right)^{\frac{3}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"-1/3/d*(a*(1+I*tan(d*x+c)))^(1/2)*a^2/tan(d*x+c)^(3/2)*(-9*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a+3*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+14*I*A*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+12*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a+6*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a-3*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+6*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+6*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a+2*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
174,1,709,152,0.330000," ","int((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(-76 A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+60 i A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a -15 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +70 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+60 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a +30 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a -15 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +22 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-30 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a +10 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+6 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{15 d \tan \left(d x +c \right)^{\frac{5}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"-1/15/d*(a*(1+I*tan(d*x+c)))^(1/2)*a^2/tan(d*x+c)^(5/2)*(-76*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+60*I*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a-15*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+70*I*B*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+60*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a+30*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a-15*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+22*I*A*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-30*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a+10*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+6*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
175,1,798,190,0.331000," ","int((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(532 B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-154 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+210 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right) a +160 A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-420 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right) a +420 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right) a -90 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-105 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +520 i A \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+210 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right) a +105 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -42 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-30 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{105 d \tan \left(d x +c \right)^{\frac{7}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/105/d*(a*(1+I*tan(d*x+c)))^(1/2)*a^2/tan(d*x+c)^(7/2)*(532*B*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-154*I*B*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+210*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^4*a+160*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-420*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^4*a+420*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^4*a-90*I*A*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-105*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+520*I*A*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+210*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^4*a+105*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-42*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-30*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
176,1,887,228,0.331000," ","int((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(-1576 A \left(\tan^{4}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-270 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+1260 i A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{5}\left(d x +c \right)\right) a +480 B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-190 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+1260 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{5}\left(d x +c \right)\right) a +630 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{5}\left(d x +c \right)\right) a -315 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +276 A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+472 i A \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-630 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{5}\left(d x +c \right)\right) a -315 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +1560 i B \left(\tan^{4}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-90 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-70 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{315 d \tan \left(d x +c \right)^{\frac{9}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/315/d*(a*(1+I*tan(d*x+c)))^(1/2)*a^2/tan(d*x+c)^(9/2)*(-1576*A*tan(d*x+c)^4*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-270*I*B*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+1260*I*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^5*a+480*B*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-190*I*A*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+1260*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^5*a+630*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^5*a-315*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+276*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+472*I*A*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-630*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^5*a-315*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+1560*I*B*tan(d*x+c)^4*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-90*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-70*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
177,1,976,266,0.344000," ","int((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(13/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(17336 B \left(\tan^{5}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-3000 i A \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+2090 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+5240 A \left(\tan^{4}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+17240 i A \left(\tan^{5}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+13860 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{6}\left(d x +c \right)\right) a -5192 i B \left(\tan^{4}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-3465 \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{6}\left(d x +c \right)\right) a -3036 B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+3465 i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{6}\left(d x +c \right)\right) a +6930 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{6}\left(d x +c \right)\right) a -2120 A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+6930 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{6}\left(d x +c \right)\right) a -13860 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{6}\left(d x +c \right)\right) a +1610 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+770 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+630 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{3465 d \tan \left(d x +c \right)^{\frac{11}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"-1/3465/d*(a*(1+I*tan(d*x+c)))^(1/2)*a^2/tan(d*x+c)^(11/2)*(17336*B*tan(d*x+c)^5*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-3000*I*A*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+2090*I*B*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+5240*A*tan(d*x+c)^4*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+17240*I*A*tan(d*x+c)^5*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+13860*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^6*a-5192*I*B*tan(d*x+c)^4*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-3465*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^6*a-3036*B*tan(d*x+c)^3*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+3465*I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^6*a+6930*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^6*a-2120*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+6930*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^6*a-13860*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^6*a+1610*I*A*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+770*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+630*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
178,1,551,156,0.401000," ","int((a+I*a*tan(d*x+c))^(5/2)*(3/2*b*B/a+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","\frac{B a \left(-i \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -2 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a^{2}+2 i \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a -14 i \tan \left(d x +c \right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, b +\sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -2 \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a -4 a \tan \left(d x +c \right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-2 b \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}}{2 d \tan \left(d x +c \right)^{\frac{3}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/2/d*B*a*(-I*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-2*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a^2+2*I*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a-14*I*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*b+(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-2*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a-4*a*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-2*b*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2))*(a*(1+I*tan(d*x+c)))^(1/2)/tan(d*x+c)^(3/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
179,1,1141,165,0.442000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(8 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-2 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a -4 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, a +B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \left(\tan^{2}\left(d x +c \right)\right) a -2 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \tan \left(d x +c \right) a +2 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +2 A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +4 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a -8 i A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a +4 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +4 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a -12 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-4 A \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +4 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{4 d a \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{2}}"," ",0,"1/4/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*(8*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*(I*a)^(1/2)-2*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a-4*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*(I*a)^(1/2)*tan(d*x+c)^2-I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*a+B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*tan(d*x+c)^2*a-2*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*tan(d*x+c)*a+2*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a+I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*tan(d*x+c)^2*a+2*A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+4*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a-8*I*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a+4*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*(I*a)^(1/2)*tan(d*x+c)-B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+4*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a-12*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-4*A*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+4*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/a/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^2","B"
180,1,900,123,0.423000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(i B \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \sqrt{2}\, \left(\tan^{2}\left(d x +c \right)\right) a +2 i A \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \sqrt{2}\, \tan \left(d x +c \right) a -A \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \sqrt{2}\, \left(\tan^{2}\left(d x +c \right)\right) a -8 i B \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \tan \left(d x +c \right) a -i B \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \sqrt{2}\, a +4 i B \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+4 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +2 B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -4 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +4 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-4 B \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) a +4 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\right)}{4 d a \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{2}}"," ",0,"1/4/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)/a*(I*B*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*2^(1/2)*tan(d*x+c)^2*a+2*I*A*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*2^(1/2)*tan(d*x+c)*a-A*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*2^(1/2)*tan(d*x+c)^2*a-8*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a-I*B*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*2^(1/2)*a+4*I*B*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)+4*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a+2*B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-4*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+4*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-4*B*(-I*a)^(1/2)*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a+4*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^2","B"
181,1,639,79,0.366000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -2 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +4 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)+2 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +4 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -4 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)+4 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{4 d a \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{2}}"," ",0,"-1/4/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*(I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-2*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+4*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+2*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+4*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-4*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+4*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/a/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^2","B"
182,1,701,117,0.371000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +2 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +4 i B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+2 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -20 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)+A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +12 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+4 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)-8 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{4 d a \sqrt{\tan \left(d x +c \right)}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{2}}"," ",0,"-1/4/d*(a*(1+I*tan(d*x+c)))^(1/2)*(I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+2*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+4*I*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2+2*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-20*I*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)+A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+12*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2+4*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-8*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/a/tan(d*x+c)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^2","B"
183,1,746,155,0.355000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-3 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -36 B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{3}\left(d x +c \right)\right)-6 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +3 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +36 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+28 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)+60 i B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+6 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +3 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -3 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +24 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)+8 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{12 d a \tan \left(d x +c \right)^{\frac{3}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{2}}"," ",0,"1/12/d*(a*(1+I*tan(d*x+c)))^(1/2)/a/tan(d*x+c)^(3/2)*(-3*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-36*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3-6*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+3*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+36*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2+28*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+60*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+6*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+3*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-3*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+24*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+8*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^2","B"
184,1,821,193,0.369000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(15 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +30 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -15 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a -15 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +140 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right)+30 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -396 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)+15 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +244 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right)+180 B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{3}\left(d x +c \right)\right)+16 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)-144 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+40 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)+24 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{60 d a \tan \left(d x +c \right)^{\frac{5}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{2}}"," ",0,"1/60/d*(a*(1+I*tan(d*x+c)))^(1/2)*(15*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+30*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-15*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a-15*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+140*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^4+30*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-396*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+15*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+244*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^4+180*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3+16*I*A*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-144*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2+40*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+24*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/a/tan(d*x+c)^(5/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^2","B"
185,1,1223,160,0.389000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{i \left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-36 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+20 A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-3 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, a -3 A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +24 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, a +44 i B \left(\tan^{2}\left(d x +c \right)\right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-9 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \tan \left(d x +c \right) a +9 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +24 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a -72 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +9 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \left(\tan^{2}\left(d x +c \right)\right) a +9 A \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +3 i B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -32 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-3 B \sqrt{i a}\, \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -72 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a +80 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)-12 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\right)}{24 d \,a^{2} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(-\tan \left(d x +c \right)+i\right)^{3} \sqrt{i a}\, \sqrt{-i a}}"," ",0,"1/24*I/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)/a^2*(-36*I*B*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+20*A*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-3*I*A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-3*A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+24*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*a+44*I*B*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2-9*I*B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+9*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*tan(d*x+c)^2*a+24*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a-72*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a+9*I*A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+9*A*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+3*I*B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-32*I*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)-3*B*(I*a)^(1/2)*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-72*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a+80*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-12*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-tan(d*x+c)+I)^3/(I*a)^(1/2)/(-I*a)^(1/2)","B"
186,1,868,120,0.375000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-3 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +4 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)-9 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -3 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -20 i B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+9 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +9 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -16 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)+3 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +9 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +12 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-3 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -32 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)-12 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{24 d \,a^{2} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{3}}"," ",0,"-1/24/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)/a^2*(-3*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+4*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2-9*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-3*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-20*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+9*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+9*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-16*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+3*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+9*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+12*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-3*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-32*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-12*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^3","B"
187,1,868,118,0.351000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(3 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -9 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +3 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -9 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +28 i A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+9 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +3 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +16 i B \tan \left(d x +c \right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-9 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -4 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)-36 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-3 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +64 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+12 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{24 d \,a^{2} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{3}}"," ",0,"1/24/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*(3*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-9*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+3*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-9*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+28*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+9*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+3*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+16*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-9*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-4*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-36*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-3*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+64*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)+12*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/a^2/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^3","B"
188,1,931,156,0.304000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(3 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +9 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -3 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -9 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +28 i B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+9 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -3 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -256 i A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+9 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +100 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)-36 i B \tan \left(d x +c \right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-3 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +64 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)+48 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-204 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)\right)}{24 d \,a^{2} \sqrt{\tan \left(d x +c \right)}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{3}}"," ",0,"1/24/d*(a*(1+I*tan(d*x+c)))^(1/2)*(3*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+9*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-3*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-9*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+28*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+9*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-3*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-256*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+9*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+100*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3-36*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-3*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+64*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+48*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-204*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c))/a^2/tan(d*x+c)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^3","B"
189,1,1012,194,0.337000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-48 i B \tan \left(d x +c \right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-100 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right)+3 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +3 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +384 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)+156 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{4}\left(d x +c \right)\right)+256 i B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+9 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +204 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)-9 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -276 i A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-9 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -32 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-9 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -3 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -16 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+3 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a \right)}{24 d \,a^{2} \tan \left(d x +c \right)^{\frac{3}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{3}}"," ",0,"-1/24/d*(a*(1+I*tan(d*x+c)))^(1/2)/a^2/tan(d*x+c)^(3/2)*(-48*I*B*(-I*a)^(1/2)*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-100*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^4+3*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+3*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+384*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+156*I*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^4+256*I*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3+9*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+204*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-9*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-276*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-9*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-32*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)-9*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-3*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-16*I*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+3*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^3","B"
190,1,1532,198,0.381000," ","int(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-60 i A \sqrt{i a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -15 A \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \sqrt{2}\, a +240 B \sqrt{-i a}\, \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) a +15 i B \sqrt{i a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -960 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right) a +960 i B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \tan \left(d x +c \right) a +15 i B \sqrt{i a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +240 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right) a -1440 B \ln \left(\frac{2 i a \tan \left(d x +c \right)+2 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}+a}{2 \sqrt{i a}}\right) \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right) a -420 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+60 i A \sqrt{i a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -1380 i B \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)-308 i A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+588 i B \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{3}\left(d x +c \right)\right)-90 i B \sqrt{i a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +60 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+148 A \sqrt{i a}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{3}\left(d x +c \right)\right)-220 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \tan \left(d x +c \right)+1548 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)-15 A \sqrt{i a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +60 B \sqrt{i a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +90 A \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \sqrt{2}\, \left(\tan^{2}\left(d x +c \right)\right) a -60 B \ln \left(\frac{2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-i a +3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \sqrt{i a}\, \sqrt{2}\, \tan \left(d x +c \right) a \right)}{240 d \,a^{3} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{4}}"," ",0,"-1/240/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)/a^3*(-60*I*A*(I*a)^(1/2)*2^(1/2)*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-15*A*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*2^(1/2)*a+240*B*(-I*a)^(1/2)*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*a+15*I*B*(I*a)^(1/2)*2^(1/2)*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-960*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^3*a+960*I*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)*a+15*I*B*(I*a)^(1/2)*2^(1/2)*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+240*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^4*a-1440*B*ln(1/2*(2*I*a*tan(d*x+c)+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)+a)/(I*a)^(1/2))*(-I*a)^(1/2)*tan(d*x+c)^2*a-420*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+60*I*A*(I*a)^(1/2)*2^(1/2)*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-1380*I*B*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)-308*I*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2+588*I*B*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3-90*I*B*(I*a)^(1/2)*2^(1/2)*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+60*I*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+148*A*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3-220*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+1548*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-15*A*(I*a)^(1/2)*2^(1/2)*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+60*B*(I*a)^(1/2)*2^(1/2)*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+90*A*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*2^(1/2)*tan(d*x+c)^2*a-60*B*ln((2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-I*a+3*a*tan(d*x+c))/(tan(d*x+c)+I))*(I*a)^(1/2)*2^(1/2)*tan(d*x+c)*a)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^4","B"
191,1,1096,156,0.378000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-52 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)-148 B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{3}\left(d x +c \right)\right)-60 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}+15 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -212 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+15 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +60 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +60 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -90 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +220 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)-90 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +15 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -60 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -60 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +308 i B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+15 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +220 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)+60 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{240 d \,a^{3} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{4}}"," ",0,"1/240/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)/a^3*(-52*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3-148*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3-60*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)+15*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-212*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2+15*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+60*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+60*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-90*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+220*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-90*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+15*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-60*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-60*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+308*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+15*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+220*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+60*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^4","B"
192,1,1096,158,0.351000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-60 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -12 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)+220 i B \tan \left(d x +c \right) \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-15 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -212 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{2}\left(d x +c \right)\right)+15 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -52 i B \left(\tan^{3}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+60 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +60 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +12 i A \left(\tan^{2}\left(d x +c \right)\right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+90 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +15 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +60 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-60 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -90 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -15 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a -60 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \tan \left(d x +c \right)+60 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{240 d \,a^{3} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(-\tan \left(d x +c \right)+i\right)^{4} \sqrt{-i a}}"," ",0,"1/240/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)/a^3*(-60*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-12*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+220*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-15*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-212*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+15*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-52*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+60*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+60*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+12*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+90*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+15*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+60*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-60*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-90*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-15*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a-60*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)+60*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-tan(d*x+c)+I)^4/(-I*a)^(1/2)","B"
193,1,1096,156,0.352000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(268 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)-60 i B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}+15 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +15 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +60 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +60 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -90 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -1060 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)-90 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +12 B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{3}\left(d x +c \right)\right)+15 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -60 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -60 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a +908 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)-12 i B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+15 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) a +60 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)-420 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{240 d \,a^{3} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(-\tan \left(d x +c \right)+i\right)^{4} \sqrt{-i a}}"," ",0,"-1/240/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*(268*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3-60*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)+15*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+15*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+60*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+60*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-90*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-1060*I*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-90*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+12*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3+15*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-60*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a-60*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a+908*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2-12*I*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+15*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*a+60*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-420*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/a^3/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-tan(d*x+c)+I)^4/(-I*a)^(1/2)","B"
194,1,1158,194,0.289000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-4468 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)+1268 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right)+15 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -15 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +908 B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{3}\left(d x +c \right)\right)+15 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a -60 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +60 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -5660 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)+2940 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)+60 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +90 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +268 i B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{4}\left(d x +c \right)\right)-90 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a -60 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a -1060 i B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)-15 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \tan \left(d x +c \right) a -420 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)+480 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{240 d \,a^{3} \sqrt{\tan \left(d x +c \right)}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(-\tan \left(d x +c \right)+i\right)^{4}}"," ",0,"-1/240/d*(a*(1+I*tan(d*x+c)))^(1/2)/a^3*(-4468*I*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3+1268*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^4+15*I*B*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*2^(1/2)*tan(d*x+c)*a-15*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+908*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3+15*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a-60*I*A*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*2^(1/2)*tan(d*x+c)^2*a+60*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-5660*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2+2940*I*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)+60*I*A*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*2^(1/2)*tan(d*x+c)^4*a+90*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+268*I*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^4-90*I*B*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*2^(1/2)*tan(d*x+c)^3*a-60*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a-1060*I*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2-15*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)*a-420*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+480*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/tan(d*x+c)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^4","B"
195,1,1239,232,0.293000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, \left(-12260 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{3}\left(d x +c \right)\right)+15 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{6}\left(d x +c \right)\right) a +15 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{6}\left(d x +c \right)\right) a -60 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +2828 i A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{5}\left(d x +c \right)\right)+60 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{5}\left(d x +c \right)\right) a +15 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +640 i A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)-90 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a -1268 B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{5}\left(d x +c \right)\right)-90 i A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{4}\left(d x +c \right)\right) a +4468 i B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{4}\left(d x +c \right)\right)-60 A \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +9868 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \left(\tan^{4}\left(d x +c \right)\right)+60 i B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{3}\left(d x +c \right)\right) a +15 B \sqrt{2}\, \ln \left(-\frac{-2 \sqrt{2}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+i a -3 a \tan \left(d x +c \right)}{\tan \left(d x +c \right)+i}\right) \left(\tan^{2}\left(d x +c \right)\right) a +5660 B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{3}\left(d x +c \right)\right)-2940 i B \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)-6020 A \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(\tan^{2}\left(d x +c \right)\right)-480 B \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\, \tan \left(d x +c \right)-160 A \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right)}{240 d \,a^{3} \tan \left(d x +c \right)^{\frac{3}{2}} \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \left(-\tan \left(d x +c \right)+i\right)^{4} \sqrt{-i a}}"," ",0,"1/240/d*(a*(1+I*tan(d*x+c)))^(1/2)*(-12260*I*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3+15*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^6*a+15*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^6*a-60*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+2828*I*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^5+60*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^5*a+15*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+640*I*A*(-I*a)^(1/2)*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-90*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a-1268*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^5-90*I*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^4*a+4468*I*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^4-60*A*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+9868*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^4+60*I*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^3*a+15*B*2^(1/2)*ln(-(-2*2^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+I*a-3*a*tan(d*x+c))/(tan(d*x+c)+I))*tan(d*x+c)^2*a+5660*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3-2940*I*B*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2-6020*A*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2-480*B*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-160*A*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/a^3/tan(d*x+c)^(3/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(-tan(d*x+c)+I)^4/(-I*a)^(1/2)","B"
196,1,297,153,0.175000," ","int((a+I*a*tan(d*x+c))^(1/3)*(A+B*tan(d*x+c)),x)","\frac{3 B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{d}+\frac{a^{\frac{1}{3}} 2^{\frac{1}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) B}{2 d}+\frac{i a^{\frac{1}{3}} 2^{\frac{1}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) A}{2 d}-\frac{a^{\frac{1}{3}} 2^{\frac{1}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) B}{4 d}-\frac{i a^{\frac{1}{3}} 2^{\frac{1}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) A}{4 d}-\frac{a^{\frac{1}{3}} 2^{\frac{1}{3}} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) B}{2 d}-\frac{i a^{\frac{1}{3}} 2^{\frac{1}{3}} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) A}{2 d}"," ",0,"3*B*(a+I*a*tan(d*x+c))^(1/3)/d+1/2/d*a^(1/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*B+1/2*I/d*a^(1/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*A-1/4/d*a^(1/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*B-1/4*I/d*a^(1/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*A-1/2/d*a^(1/3)*2^(1/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*B-1/2*I/d*a^(1/3)*2^(1/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*A","A"
197,1,367,209,0.250000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x)","-\frac{3 B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{8}{3}}}{8 d \,a^{2}}+\frac{3 B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{3}}}{5 d a}-\frac{3 i A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{3}}}{5 d a}-\frac{3 B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{2 d}-\frac{a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) B}{2 d}-\frac{i a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) A}{2 d}+\frac{a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) B}{4 d}+\frac{i a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) A}{4 d}-\frac{a^{\frac{2}{3}} \sqrt{3}\, 2^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) B}{2 d}-\frac{i a^{\frac{2}{3}} \sqrt{3}\, 2^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) A}{2 d}"," ",0,"-3/8/d/a^2*B*(a+I*a*tan(d*x+c))^(8/3)+3/5/d/a*B*(a+I*a*tan(d*x+c))^(5/3)-3/5*I/d/a*A*(a+I*a*tan(d*x+c))^(5/3)-3/2*B*(a+I*a*tan(d*x+c))^(2/3)/d-1/2/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*B-1/2*I/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*A+1/4/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*B+1/4*I/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*A-1/2/d*a^(2/3)*3^(1/2)*2^(2/3)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*B-1/2*I/d*a^(2/3)*3^(1/2)*2^(2/3)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*A","A"
198,1,321,177,0.208000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x)","-\frac{3 i B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{3}}}{5 d a}+\frac{3 A \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{2 d}-\frac{i a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) B}{2 d}+\frac{a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) A}{2 d}+\frac{i a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) B}{4 d}-\frac{a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) A}{4 d}-\frac{i a^{\frac{2}{3}} \sqrt{3}\, 2^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) B}{2 d}+\frac{a^{\frac{2}{3}} \sqrt{3}\, 2^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) A}{2 d}"," ",0,"-3/5*I*B*(a+I*a*tan(d*x+c))^(5/3)/d/a+3/2*A*(a+I*a*tan(d*x+c))^(2/3)/d-1/2*I/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*B+1/2/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*A+1/4*I/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*B-1/4/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*A-1/2*I/d*a^(2/3)*3^(1/2)*2^(2/3)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*B+1/2/d*a^(2/3)*3^(1/2)*2^(2/3)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*A","A"
199,1,297,153,0.168000," ","int((a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x)","\frac{3 B \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{2 d}+\frac{a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) B}{2 d}+\frac{i a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) A}{2 d}-\frac{a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) B}{4 d}-\frac{i a^{\frac{2}{3}} 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) A}{4 d}+\frac{a^{\frac{2}{3}} \sqrt{3}\, 2^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) B}{2 d}+\frac{i a^{\frac{2}{3}} \sqrt{3}\, 2^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) A}{2 d}"," ",0,"3/2*B*(a+I*a*tan(d*x+c))^(2/3)/d+1/2/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*B+1/2*I/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*A-1/4/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*B-1/4*I/d*a^(2/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*A+1/2/d*a^(2/3)*3^(1/2)*2^(2/3)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*B+1/2*I/d*a^(2/3)*3^(1/2)*2^(2/3)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*A","A"
200,0,0,219,1.266000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x)","\int \cot \left(d x +c \right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x)","F"
201,0,0,267,1.145000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x)","F"
202,1,318,160,0.168000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/3),x)","\frac{2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) B}{4 d \,a^{\frac{1}{3}}}+\frac{i 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) A}{4 d \,a^{\frac{1}{3}}}-\frac{2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) B}{8 d \,a^{\frac{1}{3}}}-\frac{i 2^{\frac{2}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) A}{8 d \,a^{\frac{1}{3}}}+\frac{\sqrt{3}\, 2^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) B}{4 d \,a^{\frac{1}{3}}}+\frac{i \sqrt{3}\, 2^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) A}{4 d \,a^{\frac{1}{3}}}-\frac{3 B}{2 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}+\frac{3 i A}{2 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}"," ",0,"1/4/d*2^(2/3)/a^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*B+1/4*I/d*2^(2/3)/a^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*A-1/8/d*2^(2/3)/a^(1/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*B-1/8*I/d*2^(2/3)/a^(1/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*A+1/4/d*3^(1/2)*2^(2/3)/a^(1/3)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*B+1/4*I/d*3^(1/2)*2^(2/3)/a^(1/3)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*A-3/2/d/(a+I*a*tan(d*x+c))^(1/3)*B+3/2*I/d/(a+I*a*tan(d*x+c))^(1/3)*A","A"
203,1,318,160,0.161000," ","int((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(2/3),x)","\frac{3 i A}{4 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}-\frac{3 B}{4 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}+\frac{2^{\frac{1}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) B}{4 d \,a^{\frac{2}{3}}}+\frac{i 2^{\frac{1}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}-2^{\frac{1}{3}} a^{\frac{1}{3}}\right) A}{4 d \,a^{\frac{2}{3}}}-\frac{2^{\frac{1}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) B}{8 d \,a^{\frac{2}{3}}}-\frac{i 2^{\frac{1}{3}} \ln \left(\left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}+2^{\frac{1}{3}} a^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}+2^{\frac{2}{3}} a^{\frac{2}{3}}\right) A}{8 d \,a^{\frac{2}{3}}}-\frac{2^{\frac{1}{3}} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) B}{4 d \,a^{\frac{2}{3}}}-\frac{i 2^{\frac{1}{3}} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{a^{\frac{1}{3}}}+1\right)}{3}\right) A}{4 d \,a^{\frac{2}{3}}}"," ",0,"3/4*I/d/(a+I*a*tan(d*x+c))^(2/3)*A-3/4/d/(a+I*a*tan(d*x+c))^(2/3)*B+1/4/d*2^(1/3)/a^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*B+1/4*I/d*2^(1/3)/a^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))*A-1/8/d*2^(1/3)/a^(2/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*B-1/8*I/d*2^(1/3)/a^(2/3)*ln((a+I*a*tan(d*x+c))^(2/3)+2^(1/3)*a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+2^(2/3)*a^(2/3))*A-1/4/d*2^(1/3)/a^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*B-1/4*I/d*2^(1/3)/a^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2^(2/3)/a^(1/3)*(a+I*a*tan(d*x+c))^(1/3)+1))*A","A"
204,0,0,283,1.338000," ","int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{4} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","F"
205,0,0,200,1.277000," ","int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{3} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","F"
206,0,0,128,1.233000," ","int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{2} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","F"
207,0,0,69,1.982000," ","int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","F"
208,0,0,154,4.562000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{a +i a \tan \left(d x +c \right)}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","F"
209,0,0,208,4.654000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +i a \tan \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","F"
210,0,0,286,5.051000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +i a \tan \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","F"
211,0,0,360,4.727000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +i a \tan \left(d x +c \right)\right)^{4}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x)","F"
212,0,0,289,3.790000," ","int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","F"
213,0,0,204,3.766000," ","int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","F"
214,0,0,141,3.888000," ","int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \sqrt{a +i a \tan \left(d x +c \right)}\, \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","F"
215,0,0,189,3.930000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*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)\right)}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","F"
216,0,0,250,3.776000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","F"
217,0,0,322,3.788000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","F"
218,0,0,160,196.488000," ","int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
219,0,0,231,2.202000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{3}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
220,0,0,153,5.481000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{2}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
221,0,0,101,4.970000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \tan \left(d x +c \right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
222,0,0,70,4.518000," ","int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
223,0,0,90,4.416000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \cot \left(d x +c \right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
224,0,0,122,4.443000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
225,0,0,168,4.879000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
226,0,0,349,1.792000," ","int(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
227,0,0,261,1.868000," ","int(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
228,0,0,193,1.834000," ","int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\sqrt{\tan}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
229,0,0,139,1.950000," ","int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\sqrt{\tan \left(d x +c \right)}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","F"
230,0,0,172,1.625000," ","int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\tan \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","F"
231,0,0,215,1.642000," ","int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\tan \left(d x +c \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","F"
232,1,135,83,0.026000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{b B \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{A \left(\tan^{2}\left(d x +c \right)\right) b}{2 d}+\frac{a B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a A \tan \left(d x +c \right)}{d}-\frac{b B \tan \left(d x +c \right)}{d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A b}{2 d}-\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right) B}{2 d}-\frac{a A \arctan \left(\tan \left(d x +c \right)\right)}{d}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b}{d}"," ",0,"1/3*b*B*tan(d*x+c)^3/d+1/2/d*A*tan(d*x+c)^2*b+1/2/d*B*tan(d*x+c)^2*a+a*A*tan(d*x+c)/d-b*B*tan(d*x+c)/d-1/2/d*ln(1+tan(d*x+c)^2)*A*b-1/2/d*ln(1+tan(d*x+c)^2)*a*B-1/d*a*A*arctan(tan(d*x+c))+1/d*B*arctan(tan(d*x+c))*b","A"
233,1,105,63,0.026000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{b B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{A b \tan \left(d x +c \right)}{d}+\frac{a B \tan \left(d x +c \right)}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a A}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B b}{2 d}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) b}{d}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a}{d}"," ",0,"1/2*b*B*tan(d*x+c)^2/d+A*b*tan(d*x+c)/d+1/d*a*B*tan(d*x+c)+1/2/d*ln(1+tan(d*x+c)^2)*a*A-1/2/d*ln(1+tan(d*x+c)^2)*B*b-1/d*A*arctan(tan(d*x+c))*b-1/d*B*arctan(tan(d*x+c))*a","A"
234,1,77,42,0.024000," ","int((a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{b B \tan \left(d x +c \right)}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A b}{2 d}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right) B}{2 d}+\frac{a A \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) b}{d}"," ",0,"b*B*tan(d*x+c)/d+1/2/d*ln(1+tan(d*x+c)^2)*A*b+1/2/d*ln(1+tan(d*x+c)^2)*a*B+1/d*a*A*arctan(tan(d*x+c))-1/d*B*arctan(tan(d*x+c))*b","A"
235,1,51,37,0.441000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","A x b +a B x +\frac{a A \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{A b c}{d}-\frac{b B \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{B a c}{d}"," ",0,"A*x*b+a*B*x+a*A*ln(sin(d*x+c))/d+1/d*A*b*c-b*B*ln(cos(d*x+c))/d+1/d*B*a*c","A"
236,1,65,43,0.324000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-a A x +B x b -\frac{a A \cot \left(d x +c \right)}{d}+\frac{A b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{A a c}{d}+\frac{a B \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{B b c}{d}"," ",0,"-a*A*x+B*x*b-a*A*cot(d*x+c)/d+1/d*A*b*ln(sin(d*x+c))-1/d*A*a*c+1/d*a*B*ln(sin(d*x+c))+1/d*B*b*c","A"
237,1,96,64,0.451000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-\frac{a A \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a A \ln \left(\sin \left(d x +c \right)\right)}{d}-a B x -\frac{B \cot \left(d x +c \right) a}{d}-\frac{B a c}{d}-A x b -\frac{A \cot \left(d x +c \right) b}{d}-\frac{A b c}{d}+\frac{B b \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a*A*cot(d*x+c)^2/d-a*A*ln(sin(d*x+c))/d-a*B*x-1/d*B*cot(d*x+c)*a-1/d*B*a*c-A*x*b-1/d*A*cot(d*x+c)*b-1/d*A*b*c+1/d*B*b*ln(sin(d*x+c))","A"
238,1,124,83,0.381000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-\frac{a A \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a A \cot \left(d x +c \right)}{d}+a A x +\frac{A a c}{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 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}-B x b -\frac{B \cot \left(d x +c \right) b}{d}-\frac{B b c}{d}"," ",0,"-1/3*a*A*cot(d*x+c)^3/d+a*A*cot(d*x+c)/d+a*A*x+1/d*A*a*c-1/2/d*a*B*cot(d*x+c)^2-1/d*a*B*ln(sin(d*x+c))-1/2/d*A*b*cot(d*x+c)^2-1/d*A*b*ln(sin(d*x+c))-B*x*b-1/d*B*cot(d*x+c)*b-1/d*B*b*c","A"
239,1,150,102,0.409000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-\frac{a A \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a A \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a A \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{B \cot \left(d x +c \right) a}{d}+a B x +\frac{B a c}{d}-\frac{A b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{A \cot \left(d x +c \right) b}{d}+A x b +\frac{A b c}{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}"," ",0,"-1/4*a*A*cot(d*x+c)^4/d+1/2*a*A*cot(d*x+c)^2/d+a*A*ln(sin(d*x+c))/d-1/3/d*a*B*cot(d*x+c)^3+1/d*B*cot(d*x+c)*a+a*B*x+1/d*B*a*c-1/3/d*A*b*cot(d*x+c)^3+1/d*A*cot(d*x+c)*b+A*x*b+1/d*A*b*c-1/2/d*B*b*cot(d*x+c)^2-1/d*B*b*ln(sin(d*x+c))","A"
240,1,249,142,0.025000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\frac{b^{2} B \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{A \left(\tan^{3}\left(d x +c \right)\right) b^{2}}{3 d}+\frac{2 B \left(\tan^{3}\left(d x +c \right)\right) a b}{3 d}+\frac{A \left(\tan^{2}\left(d x +c \right)\right) a b}{d}+\frac{B \,a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{2} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} A \tan \left(d x +c \right)}{d}-\frac{A \tan \left(d x +c \right) b^{2}}{d}-\frac{2 B \tan \left(d x +c \right) a b}{d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A a b}{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{A \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}+\frac{2 B \arctan \left(\tan \left(d x +c \right)\right) a b}{d}"," ",0,"1/4/d*b^2*B*tan(d*x+c)^4+1/3/d*A*tan(d*x+c)^3*b^2+2/3/d*B*tan(d*x+c)^3*a*b+1/d*A*tan(d*x+c)^2*a*b+1/2/d*B*a^2*tan(d*x+c)^2-1/2/d*b^2*B*tan(d*x+c)^2+a^2*A*tan(d*x+c)/d-1/d*A*tan(d*x+c)*b^2-2/d*B*tan(d*x+c)*a*b-1/d*ln(1+tan(d*x+c)^2)*A*a*b-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*A*arctan(tan(d*x+c))*a^2+1/d*A*arctan(tan(d*x+c))*b^2+2/d*B*arctan(tan(d*x+c))*a*b","A"
241,1,199,108,0.024000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\frac{B \left(\tan^{3}\left(d x +c \right)\right) b^{2}}{3 d}+\frac{A \left(\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d}+\frac{B \left(\tan^{2}\left(d x +c \right)\right) a b}{d}+\frac{2 a A b \tan \left(d x +c \right)}{d}+\frac{a^{2} B \tan \left(d x +c \right)}{d}-\frac{b^{2} B \tan \left(d x +c \right)}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} A}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{2}}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B a b}{d}-\frac{2 A \arctan \left(\tan \left(d x +c \right)\right) a b}{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}"," ",0,"1/3/d*B*tan(d*x+c)^3*b^2+1/2/d*A*tan(d*x+c)^2*b^2+1/d*B*tan(d*x+c)^2*a*b+2*a*A*b*tan(d*x+c)/d+a^2*B*tan(d*x+c)/d-b^2*B*tan(d*x+c)/d+1/2/d*ln(1+tan(d*x+c)^2)*a^2*A-1/2/d*ln(1+tan(d*x+c)^2)*A*b^2-1/d*ln(1+tan(d*x+c)^2)*B*a*b-2/d*A*arctan(tan(d*x+c))*a*b-1/d*B*arctan(tan(d*x+c))*a^2+1/d*B*arctan(tan(d*x+c))*b^2","A"
242,1,151,85,0.023000," ","int((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\frac{b^{2} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{A \tan \left(d x +c \right) b^{2}}{d}+\frac{2 B \tan \left(d x +c \right) a b}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A a b}{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{A \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}-\frac{2 B \arctan \left(\tan \left(d x +c \right)\right) a b}{d}"," ",0,"1/2/d*b^2*B*tan(d*x+c)^2+1/d*A*tan(d*x+c)*b^2+2/d*B*tan(d*x+c)*a*b+1/d*ln(1+tan(d*x+c)^2)*A*a*b+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*A*arctan(tan(d*x+c))*a^2-1/d*A*arctan(tan(d*x+c))*b^2-2/d*B*arctan(tan(d*x+c))*a*b","A"
243,1,109,70,0.383000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","2 A x a b +a^{2} B x -B x \,b^{2}-\frac{A \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} A \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{2 A a b c}{d}+\frac{b^{2} B \tan \left(d x +c \right)}{d}-\frac{2 B a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{B \,a^{2} c}{d}-\frac{B \,b^{2} c}{d}"," ",0,"2*A*x*a*b+a^2*B*x-B*x*b^2-1/d*A*b^2*ln(cos(d*x+c))+a^2*A*ln(sin(d*x+c))/d+2/d*A*a*b*c+b^2*B*tan(d*x+c)/d-2/d*B*a*b*ln(cos(d*x+c))+1/d*B*a^2*c-1/d*B*b^2*c","A"
244,1,110,72,0.369000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-a^{2} A x +A x \,b^{2}+2 B x a b -\frac{a^{2} A \cot \left(d x +c \right)}{d}+\frac{2 A a b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{A \,a^{2} c}{d}+\frac{A \,b^{2} c}{d}+\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}"," ",0,"-a^2*A*x+A*x*b^2+2*B*x*a*b-a^2*A*cot(d*x+c)/d+2/d*A*a*b*ln(sin(d*x+c))-1/d*A*a^2*c+1/d*A*b^2*c+1/d*a^2*B*ln(sin(d*x+c))-b^2*B*ln(cos(d*x+c))/d+2/d*B*a*b*c","A"
245,1,141,86,0.466000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{a^{2} A \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} A \ln \left(\sin \left(d x +c \right)\right)}{d}-a^{2} B x -\frac{B \cot \left(d x +c \right) a^{2}}{d}-\frac{B \,a^{2} c}{d}-2 A x a b -\frac{2 A \cot \left(d x +c \right) a b}{d}-\frac{2 A a b c}{d}+\frac{2 B a b \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{A \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+B x \,b^{2}+\frac{B \,b^{2} c}{d}"," ",0,"-1/2*a^2*A*cot(d*x+c)^2/d-a^2*A*ln(sin(d*x+c))/d-a^2*B*x-1/d*B*cot(d*x+c)*a^2-1/d*B*a^2*c-2*A*x*a*b-2/d*A*cot(d*x+c)*a*b-2/d*A*a*b*c+2/d*B*a*b*ln(sin(d*x+c))+1/d*A*b^2*ln(sin(d*x+c))+B*x*b^2+1/d*B*b^2*c","A"
246,1,188,114,0.375000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{a^{2} A \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} A \cot \left(d x +c \right)}{d}+a^{2} A x +\frac{A \,a^{2} c}{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 a b \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{2 A a b \ln \left(\sin \left(d x +c \right)\right)}{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}-A x \,b^{2}-\frac{A \cot \left(d x +c \right) b^{2}}{d}-\frac{A \,b^{2} c}{d}+\frac{b^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/3*a^2*A*cot(d*x+c)^3/d+a^2*A*cot(d*x+c)/d+a^2*A*x+1/d*A*a^2*c-1/2/d*a^2*B*cot(d*x+c)^2-1/d*a^2*B*ln(sin(d*x+c))-1/d*A*a*b*cot(d*x+c)^2-2/d*A*a*b*ln(sin(d*x+c))-2*B*x*a*b-2/d*B*cot(d*x+c)*a*b-2/d*B*a*b*c-A*x*b^2-1/d*A*cot(d*x+c)*b^2-1/d*A*b^2*c+1/d*b^2*B*ln(sin(d*x+c))","A"
247,1,238,145,0.415000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{a^{2} A \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} A \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} A \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{B \cot \left(d x +c \right) a^{2}}{d}+a^{2} B x +\frac{B \,a^{2} c}{d}-\frac{2 A a b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 A \cot \left(d x +c \right) a b}{d}+2 A x a b +\frac{2 A a b c}{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}-\frac{A \,b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{A \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-B x \,b^{2}-\frac{B \cot \left(d x +c \right) b^{2}}{d}-\frac{B \,b^{2} c}{d}"," ",0,"-1/4*a^2*A*cot(d*x+c)^4/d+1/2*a^2*A*cot(d*x+c)^2/d+a^2*A*ln(sin(d*x+c))/d-1/3/d*a^2*B*cot(d*x+c)^3+1/d*B*cot(d*x+c)*a^2+a^2*B*x+1/d*B*a^2*c-2/3/d*A*a*b*cot(d*x+c)^3+2/d*A*cot(d*x+c)*a*b+2*A*x*a*b+2/d*A*a*b*c-1/d*B*a*b*cot(d*x+c)^2-2/d*B*a*b*ln(sin(d*x+c))-1/2/d*A*b^2*cot(d*x+c)^2-1/d*A*b^2*ln(sin(d*x+c))-B*x*b^2-1/d*B*cot(d*x+c)*b^2-1/d*B*b^2*c","A"
248,1,383,193,0.027000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\frac{B \left(\tan^{5}\left(d x +c \right)\right) b^{3}}{5 d}+\frac{A \left(\tan^{4}\left(d x +c \right)\right) b^{3}}{4 d}+\frac{3 B \left(\tan^{4}\left(d x +c \right)\right) a \,b^{2}}{4 d}+\frac{A \left(\tan^{3}\left(d x +c \right)\right) a \,b^{2}}{d}+\frac{B \left(\tan^{3}\left(d x +c \right)\right) a^{2} b}{d}-\frac{B \left(\tan^{3}\left(d x +c \right)\right) b^{3}}{3 d}+\frac{3 A \left(\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d}-\frac{A \left(\tan^{2}\left(d x +c \right)\right) b^{3}}{2 d}+\frac{a^{3} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 B \left(\tan^{2}\left(d x +c \right)\right) a \,b^{2}}{2 d}+\frac{A \,a^{3} \tan \left(d x +c \right)}{d}-\frac{3 A \tan \left(d x +c \right) a \,b^{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{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b}{2 d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{3}}{2 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{a^{3} A \arctan \left(\tan \left(d x +c \right)\right)}{d}+\frac{3 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{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}"," ",0,"1/5/d*B*tan(d*x+c)^5*b^3+1/4/d*A*tan(d*x+c)^4*b^3+3/4/d*B*tan(d*x+c)^4*a*b^2+1/d*A*tan(d*x+c)^3*a*b^2+1/d*B*tan(d*x+c)^3*a^2*b-1/3/d*B*tan(d*x+c)^3*b^3+3/2/d*A*tan(d*x+c)^2*a^2*b-1/2/d*A*tan(d*x+c)^2*b^3+1/2/d*B*tan(d*x+c)^2*a^3-3/2/d*B*tan(d*x+c)^2*a*b^2+1/d*A*a^3*tan(d*x+c)-3/d*A*tan(d*x+c)*a*b^2-3/d*B*tan(d*x+c)*a^2*b+1/d*B*tan(d*x+c)*b^3-3/2/d*ln(1+tan(d*x+c)^2)*A*a^2*b+1/2/d*ln(1+tan(d*x+c)^2)*A*b^3-1/2/d*ln(1+tan(d*x+c)^2)*a^3*B+3/2/d*ln(1+tan(d*x+c)^2)*B*a*b^2-1/d*a^3*A*arctan(tan(d*x+c))+3/d*A*arctan(tan(d*x+c))*a*b^2+3/d*B*arctan(tan(d*x+c))*a^2*b-1/d*B*arctan(tan(d*x+c))*b^3","A"
249,1,314,159,0.025000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\frac{b^{3} B \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{A \left(\tan^{3}\left(d x +c \right)\right) b^{3}}{3 d}+\frac{B \left(\tan^{3}\left(d x +c \right)\right) a \,b^{2}}{d}+\frac{3 A \left(\tan^{2}\left(d x +c \right)\right) a \,b^{2}}{2 d}+\frac{3 B \left(\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d}-\frac{b^{3} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 A \tan \left(d x +c \right) a^{2} b}{d}-\frac{A \tan \left(d x +c \right) b^{3}}{d}+\frac{a^{3} B \tan \left(d x +c \right)}{d}-\frac{3 B \tan \left(d x +c \right) a \,b^{2}}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3}}{2 d}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A a \,b^{2}}{2 d}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b B}{2 d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3} B}{2 d}-\frac{3 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d}+\frac{3 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d}"," ",0,"1/4/d*b^3*B*tan(d*x+c)^4+1/3/d*A*tan(d*x+c)^3*b^3+1/d*B*tan(d*x+c)^3*a*b^2+3/2/d*A*tan(d*x+c)^2*a*b^2+3/2/d*B*tan(d*x+c)^2*a^2*b-1/2/d*b^3*B*tan(d*x+c)^2+3/d*A*tan(d*x+c)*a^2*b-1/d*A*tan(d*x+c)*b^3+1/d*a^3*B*tan(d*x+c)-3/d*B*tan(d*x+c)*a*b^2+1/2/d*ln(1+tan(d*x+c)^2)*A*a^3-3/2/d*ln(1+tan(d*x+c)^2)*A*a*b^2-3/2/d*ln(1+tan(d*x+c)^2)*a^2*b*B+1/2/d*ln(1+tan(d*x+c)^2)*b^3*B-3/d*A*arctan(tan(d*x+c))*a^2*b+1/d*A*arctan(tan(d*x+c))*b^3-1/d*B*arctan(tan(d*x+c))*a^3+3/d*B*arctan(tan(d*x+c))*a*b^2","A"
250,1,247,136,0.023000," ","int((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\frac{B \left(\tan^{3}\left(d x +c \right)\right) b^{3}}{3 d}+\frac{A \left(\tan^{2}\left(d x +c \right)\right) b^{3}}{2 d}+\frac{3 B \left(\tan^{2}\left(d x +c \right)\right) a \,b^{2}}{2 d}+\frac{3 A \tan \left(d x +c \right) a \,b^{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{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{3}}{2 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{a^{3} A \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{3 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{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}"," ",0,"1/3/d*B*tan(d*x+c)^3*b^3+1/2/d*A*tan(d*x+c)^2*b^3+3/2/d*B*tan(d*x+c)^2*a*b^2+3/d*A*tan(d*x+c)*a*b^2+3/d*B*tan(d*x+c)*a^2*b-1/d*B*tan(d*x+c)*b^3+3/2/d*ln(1+tan(d*x+c)^2)*A*a^2*b-1/2/d*ln(1+tan(d*x+c)^2)*A*b^3+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+1/d*a^3*A*arctan(tan(d*x+c))-3/d*A*arctan(tan(d*x+c))*a*b^2-3/d*B*arctan(tan(d*x+c))*a^2*b+1/d*B*arctan(tan(d*x+c))*b^3","A"
251,1,183,115,0.415000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\frac{a^{3} A \ln \left(\sin \left(d x +c \right)\right)}{d}+a^{3} B x +\frac{a^{3} B c}{d}+3 A x \,a^{2} b +\frac{3 A \,a^{2} b c}{d}-\frac{3 a^{2} b B \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{3 A a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{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}-A x \,b^{3}+\frac{A \tan \left(d x +c \right) b^{3}}{d}-\frac{A \,b^{3} c}{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}"," ",0,"a^3*A*ln(sin(d*x+c))/d+a^3*B*x+1/d*a^3*B*c+3*A*x*a^2*b+3/d*A*a^2*b*c-3/d*a^2*b*B*ln(cos(d*x+c))-3/d*A*a*b^2*ln(cos(d*x+c))-3*B*x*a*b^2+3/d*B*tan(d*x+c)*a*b^2-3/d*B*a*b^2*c-A*x*b^3+1/d*A*tan(d*x+c)*b^3-1/d*A*b^3*c+1/2/d*b^3*B*tan(d*x+c)^2+b^3*B*ln(cos(d*x+c))/d","A"
252,1,168,119,0.360000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-A \,a^{3} x +3 A x a \,b^{2}+3 B x \,a^{2} b -B x \,b^{3}-\frac{A \cot \left(d x +c \right) a^{3}}{d}-\frac{A \,b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 A \,a^{2} b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{A \,a^{3} c}{d}+\frac{3 A a \,b^{2} c}{d}+\frac{B \tan \left(d x +c \right) b^{3}}{d}-\frac{3 B a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{3 B \,a^{2} b c}{d}-\frac{B \,b^{3} c}{d}"," ",0,"-A*a^3*x+3*A*x*a*b^2+3*B*x*a^2*b-B*x*b^3-1/d*A*cot(d*x+c)*a^3-1/d*A*b^3*ln(cos(d*x+c))+3/d*A*a^2*b*ln(sin(d*x+c))-1/d*A*a^3*c+3/d*A*a*b^2*c+1/d*B*tan(d*x+c)*b^3-3/d*B*a*b^2*ln(cos(d*x+c))+1/d*a^3*B*ln(sin(d*x+c))+3/d*B*a^2*b*c-1/d*B*b^3*c","A"
253,1,186,125,0.496000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{A \,a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} A \ln \left(\sin \left(d x +c \right)\right)}{d}-a^{3} B x -\frac{B \cot \left(d x +c \right) a^{3}}{d}-\frac{a^{3} B c}{d}-3 A x \,a^{2} b -\frac{3 A \cot \left(d x +c \right) a^{2} b}{d}-\frac{3 A \,a^{2} b c}{d}+\frac{3 a^{2} b B \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{3 A a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+3 B x a \,b^{2}+\frac{3 B a \,b^{2} c}{d}+A x \,b^{3}+\frac{A \,b^{3} c}{d}-\frac{b^{3} B \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*A*a^3*cot(d*x+c)^2-a^3*A*ln(sin(d*x+c))/d-a^3*B*x-1/d*B*cot(d*x+c)*a^3-1/d*a^3*B*c-3*A*x*a^2*b-3/d*A*cot(d*x+c)*a^2*b-3/d*A*a^2*b*c+3/d*a^2*b*B*ln(sin(d*x+c))+3/d*A*a*b^2*ln(sin(d*x+c))+3*B*x*a*b^2+3/d*B*a*b^2*c+A*x*b^3+1/d*A*b^3*c-b^3*B*ln(cos(d*x+c))/d","A"
254,1,233,148,0.400000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{A \,a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{A \cot \left(d x +c \right) a^{3}}{d}+A \,a^{3} x +\frac{A \,a^{3} c}{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{3 A \,a^{2} b \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 A \,a^{2} b \ln \left(\sin \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}-3 A x a \,b^{2}-\frac{3 A \cot \left(d x +c \right) a \,b^{2}}{d}-\frac{3 A a \,b^{2} c}{d}+\frac{3 B a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{A \,b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+B x \,b^{3}+\frac{B \,b^{3} c}{d}"," ",0,"-1/3/d*A*a^3*cot(d*x+c)^3+1/d*A*cot(d*x+c)*a^3+A*a^3*x+1/d*A*a^3*c-1/2/d*a^3*B*cot(d*x+c)^2-1/d*a^3*B*ln(sin(d*x+c))-3/2/d*A*a^2*b*cot(d*x+c)^2-3/d*A*a^2*b*ln(sin(d*x+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*A*x*a*b^2-3/d*A*cot(d*x+c)*a*b^2-3/d*A*a*b^2*c+3/d*B*a*b^2*ln(sin(d*x+c))+1/d*A*b^3*ln(sin(d*x+c))+B*x*b^3+1/d*B*b^3*c","A"
255,1,302,185,0.438000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{A \,a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{A \,a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} A \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{B \cot \left(d x +c \right) a^{3}}{d}+a^{3} B x +\frac{a^{3} B c}{d}-\frac{A \,a^{2} b \left(\cot^{3}\left(d x +c \right)\right)}{d}+3 A x \,a^{2} b +\frac{3 A \cot \left(d x +c \right) a^{2} b}{d}+\frac{3 A \,a^{2} b c}{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}-\frac{3 A a \,b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 A a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{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}-A x \,b^{3}-\frac{A \cot \left(d x +c \right) b^{3}}{d}-\frac{A \,b^{3} c}{d}+\frac{b^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/4/d*A*a^3*cot(d*x+c)^4+1/2/d*A*a^3*cot(d*x+c)^2+a^3*A*ln(sin(d*x+c))/d-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/d*A*a^2*b*cot(d*x+c)^3+3*A*x*a^2*b+3/d*A*cot(d*x+c)*a^2*b+3/d*A*a^2*b*c-3/2/d*a^2*b*B*cot(d*x+c)^2-3/d*a^2*b*B*ln(sin(d*x+c))-3/2/d*A*a*b^2*cot(d*x+c)^2-3/d*A*a*b^2*ln(sin(d*x+c))-3*B*x*a*b^2-3/d*B*cot(d*x+c)*a*b^2-3/d*B*a*b^2*c-A*x*b^3-1/d*A*cot(d*x+c)*b^3-1/d*A*b^3*c+1/d*b^3*B*ln(sin(d*x+c))","A"
256,1,376,225,0.436000," ","int(cot(d*x+c)^6*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{a^{2} b B \left(\cot^{3}\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{A \,b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{A \,a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{A \,a^{3} c}{d}-\frac{B \,b^{3} c}{d}+3 A x a \,b^{2}+3 B x \,a^{2} b -\frac{3 A \,a^{2} b \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{A a \,b^{2} \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{A \,b^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{A \,a^{3} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{3} B \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{B \cot \left(d x +c \right) b^{3}}{d}-\frac{3 B a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{A \cot \left(d x +c \right) a^{3}}{d}+\frac{a^{3} B \ln \left(\sin \left(d x +c \right)\right)}{d}-A \,a^{3} x -B x \,b^{3}+\frac{3 A \,a^{2} b \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 A \,a^{2} b \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{3 A a \,b^{2} c}{d}+\frac{3 B \,a^{2} b c}{d}+\frac{3 B \cot \left(d x +c \right) a^{2} b}{d}+\frac{3 A \cot \left(d x +c \right) a \,b^{2}}{d}"," ",0,"-1/d*a^2*b*B*cot(d*x+c)^3-3/4/d*A*a^2*b*cot(d*x+c)^4-1/d*A*a*b^2*cot(d*x+c)^3+3/2/d*A*a^2*b*cot(d*x+c)^2+1/3/d*A*a^3*cot(d*x+c)^3+1/2/d*a^3*B*cot(d*x+c)^2-1/d*A*b^3*ln(sin(d*x+c))-1/d*A*a^3*c-1/d*B*b^3*c+3*A*x*a*b^2+3*B*x*a^2*b-1/5/d*A*a^3*cot(d*x+c)^5-1/4/d*a^3*B*cot(d*x+c)^4-1/d*B*cot(d*x+c)*b^3-1/2/d*A*b^3*cot(d*x+c)^2-3/d*B*a*b^2*ln(sin(d*x+c))-1/d*A*cot(d*x+c)*a^3+1/d*a^3*B*ln(sin(d*x+c))-A*a^3*x-B*x*b^3+3/d*A*a^2*b*ln(sin(d*x+c))+3/d*A*a*b^2*c+3/d*B*a^2*b*c+3/d*B*cot(d*x+c)*a^2*b+3/d*A*cot(d*x+c)*a*b^2-3/2/d*B*a*b^2*cot(d*x+c)^2","A"
257,1,539,253,0.025000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","\frac{2 A \left(\tan^{3}\left(d x +c \right)\right) a^{2} b^{2}}{d}-\frac{2 A a \,b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3} b}{d}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a A \,b^{3}}{d}+\frac{A \left(\tan^{5}\left(d x +c \right)\right) b^{4}}{5 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4} B}{2 d}-\frac{A \left(\tan^{3}\left(d x +c \right)\right) b^{4}}{3 d}+\frac{B \,b^{4} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}-\frac{B \left(\tan^{4}\left(d x +c \right)\right) b^{4}}{4 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,b^{4}}{2 d}+\frac{B \,b^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{4} B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d}+\frac{A \tan \left(d x +c \right) b^{4}}{d}-\frac{6 A \tan \left(d x +c \right) a^{2} b^{2}}{d}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{2} B}{d}+\frac{4 B \left(\tan^{5}\left(d x +c \right)\right) a \,b^{3}}{5 d}+\frac{A \left(\tan^{4}\left(d x +c \right)\right) a \,b^{3}}{d}-\frac{3 B \,a^{2} b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 B \left(\tan^{3}\left(d x +c \right)\right) a^{3} b}{3 d}-\frac{4 B \left(\tan^{3}\left(d x +c \right)\right) a \,b^{3}}{3 d}+\frac{2 A \,a^{3} b \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{3 B \left(\tan^{4}\left(d x +c \right)\right) a^{2} b^{2}}{2 d}+\frac{A \,a^{4} \tan \left(d x +c \right)}{d}-\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d}-\frac{4 B \tan \left(d x +c \right) a^{3} b}{d}+\frac{4 B \tan \left(d x +c \right) a \,b^{3}}{d}+\frac{6 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d}+\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d}"," ",0,"-1/2/d*ln(1+tan(d*x+c)^2)*B*b^4-1/d*A*arctan(tan(d*x+c))*a^4-1/d*A*arctan(tan(d*x+c))*b^4+1/d*A*tan(d*x+c)*b^4+1/2/d*B*b^4*tan(d*x+c)^2+1/2/d*a^4*B*tan(d*x+c)^2-1/4/d*B*tan(d*x+c)^4*b^4-1/3/d*A*tan(d*x+c)^3*b^4+1/6/d*B*b^4*tan(d*x+c)^6+1/5/d*A*tan(d*x+c)^5*b^4-1/2/d*ln(1+tan(d*x+c)^2)*a^4*B-6/d*A*tan(d*x+c)*a^2*b^2+1/d*A*a^4*tan(d*x+c)+2/d*A*tan(d*x+c)^3*a^2*b^2-2/d*A*a*b^3*tan(d*x+c)^2-4/d*B*arctan(tan(d*x+c))*a*b^3-4/d*B*tan(d*x+c)*a^3*b+4/d*B*tan(d*x+c)*a*b^3-2/d*ln(1+tan(d*x+c)^2)*A*a^3*b+2/d*ln(1+tan(d*x+c)^2)*a*A*b^3+3/d*ln(1+tan(d*x+c)^2)*a^2*b^2*B+6/d*A*arctan(tan(d*x+c))*a^2*b^2+4/d*B*arctan(tan(d*x+c))*a^3*b+4/5/d*B*tan(d*x+c)^5*a*b^3+1/d*A*tan(d*x+c)^4*a*b^3-3/d*B*a^2*b^2*tan(d*x+c)^2+4/3/d*B*tan(d*x+c)^3*a^3*b-4/3/d*B*tan(d*x+c)^3*a*b^3+2/d*A*a^3*b*tan(d*x+c)^2+3/2/d*B*tan(d*x+c)^4*a^2*b^2","B"
258,1,449,218,0.025000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","\frac{2 B \left(\tan^{3}\left(d x +c \right)\right) a^{2} b^{2}}{d}-\frac{2 B \left(\tan^{2}\left(d x +c \right)\right) a \,b^{3}}{d}+\frac{3 A \left(\tan^{2}\left(d x +c \right)\right) a^{2} b^{2}}{d}+\frac{4 A \left(\tan^{3}\left(d x +c \right)\right) a \,b^{3}}{3 d}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b^{2}}{d}+\frac{B \left(\tan^{5}\left(d x +c \right)\right) b^{4}}{5 d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{4}}{2 d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{4}}{2 d}+\frac{A \left(\tan^{4}\left(d x +c \right)\right) b^{4}}{4 d}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d}+\frac{B \,b^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} B \tan \left(d x +c \right)}{d}-\frac{A \left(\tan^{2}\left(d x +c \right)\right) b^{4}}{2 d}-\frac{B \left(\tan^{3}\left(d x +c \right)\right) b^{4}}{3 d}+\frac{2 B \left(\tan^{2}\left(d x +c \right)\right) a^{3} b}{d}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,a^{3} b}{d}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B a \,b^{3}}{d}+\frac{6 B \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d}+\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d}-\frac{6 B \,a^{2} b^{2} \tan \left(d x +c \right)}{d}-\frac{4 A a \,b^{3} \tan \left(d x +c \right)}{d}+\frac{B \left(\tan^{4}\left(d x +c \right)\right) a \,b^{3}}{d}-\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d}+\frac{4 A \,a^{3} b \tan \left(d x +c \right)}{d}"," ",0,"1/d*B*tan(d*x+c)^4*a*b^3+1/5/d*B*tan(d*x+c)^5*b^4-1/d*B*arctan(tan(d*x+c))*a^4-1/d*B*arctan(tan(d*x+c))*b^4+1/d*B*b^4*tan(d*x+c)+1/2/d*ln(1+tan(d*x+c)^2)*A*a^4+1/2/d*ln(1+tan(d*x+c)^2)*A*b^4+1/d*a^4*B*tan(d*x+c)+1/4/d*A*tan(d*x+c)^4*b^4-1/2/d*A*tan(d*x+c)^2*b^4-1/3/d*B*tan(d*x+c)^3*b^4+6/d*B*arctan(tan(d*x+c))*a^2*b^2+3/d*A*tan(d*x+c)^2*a^2*b^2+4/d*A*arctan(tan(d*x+c))*a*b^3+4/3/d*A*tan(d*x+c)^3*a*b^3-3/d*ln(1+tan(d*x+c)^2)*A*a^2*b^2-6/d*B*a^2*b^2*tan(d*x+c)-4/d*A*a*b^3*tan(d*x+c)+2/d*B*tan(d*x+c)^3*a^2*b^2-4/d*A*arctan(tan(d*x+c))*a^3*b-2/d*B*tan(d*x+c)^2*a*b^3+4/d*A*a^3*b*tan(d*x+c)-2/d*ln(1+tan(d*x+c)^2)*B*a^3*b+2/d*ln(1+tan(d*x+c)^2)*B*a*b^3+2/d*B*tan(d*x+c)^2*a^3*b","B"
259,1,362,196,0.024000," ","int((a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","\frac{B \left(\tan^{4}\left(d x +c \right)\right) b^{4}}{4 d}+\frac{A \left(\tan^{3}\left(d x +c \right)\right) b^{4}}{3 d}+\frac{4 B \left(\tan^{3}\left(d x +c \right)\right) a \,b^{3}}{3 d}+\frac{2 A a \,b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{3 B \,a^{2} b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{B \,b^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{6 A \tan \left(d x +c \right) a^{2} b^{2}}{d}-\frac{A \tan \left(d x +c \right) b^{4}}{d}+\frac{4 B \tan \left(d x +c \right) a^{3} b}{d}-\frac{4 B \tan \left(d x +c \right) a \,b^{3}}{d}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3} b}{d}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a A \,b^{3}}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4} B}{2 d}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{2} B}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,b^{4}}{2 d}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d}-\frac{6 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d}-\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d}+\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d}"," ",0,"1/4/d*B*tan(d*x+c)^4*b^4+1/3/d*A*tan(d*x+c)^3*b^4+4/3/d*B*tan(d*x+c)^3*a*b^3+2/d*A*a*b^3*tan(d*x+c)^2+3/d*B*a^2*b^2*tan(d*x+c)^2-1/2/d*B*b^4*tan(d*x+c)^2+6/d*A*tan(d*x+c)*a^2*b^2-1/d*A*tan(d*x+c)*b^4+4/d*B*tan(d*x+c)*a^3*b-4/d*B*tan(d*x+c)*a*b^3+2/d*ln(1+tan(d*x+c)^2)*A*a^3*b-2/d*ln(1+tan(d*x+c)^2)*a*A*b^3+1/2/d*ln(1+tan(d*x+c)^2)*a^4*B-3/d*ln(1+tan(d*x+c)^2)*a^2*b^2*B+1/2/d*ln(1+tan(d*x+c)^2)*B*b^4+1/d*A*arctan(tan(d*x+c))*a^4-6/d*A*arctan(tan(d*x+c))*a^2*b^2+1/d*A*arctan(tan(d*x+c))*b^4-4/d*B*arctan(tan(d*x+c))*a^3*b+4/d*B*arctan(tan(d*x+c))*a*b^3","A"
260,1,277,168,0.448000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","\frac{a^{4} A \ln \left(\sin \left(d x +c \right)\right)}{d}+a^{4} B x +\frac{a^{4} B c}{d}+4 A \,a^{3} b x +\frac{4 A \,a^{3} b c}{d}-\frac{4 B \,a^{3} b \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{6 A \,a^{2} b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}-6 B \,a^{2} b^{2} x +\frac{6 B \,a^{2} b^{2} \tan \left(d x +c \right)}{d}-\frac{6 B \,a^{2} b^{2} c}{d}-4 A a \,b^{3} x +\frac{4 A a \,b^{3} \tan \left(d x +c \right)}{d}-\frac{4 A a \,b^{3} c}{d}+\frac{2 B \left(\tan^{2}\left(d x +c \right)\right) a \,b^{3}}{d}+\frac{4 B a \,b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{A \left(\tan^{2}\left(d x +c \right)\right) b^{4}}{2 d}+\frac{A \,b^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{B \left(\tan^{3}\left(d x +c \right)\right) b^{4}}{3 d}-\frac{B \,b^{4} \tan \left(d x +c \right)}{d}+B \,b^{4} x +\frac{B \,b^{4} c}{d}"," ",0,"a^4*A*ln(sin(d*x+c))/d+a^4*B*x+1/d*a^4*B*c+4*A*a^3*b*x+4/d*A*a^3*b*c-4/d*B*a^3*b*ln(cos(d*x+c))-6/d*A*a^2*b^2*ln(cos(d*x+c))-6*B*a^2*b^2*x+6/d*B*a^2*b^2*tan(d*x+c)-6/d*B*a^2*b^2*c-4*A*a*b^3*x+4/d*A*a*b^3*tan(d*x+c)-4/d*A*a*b^3*c+2/d*B*tan(d*x+c)^2*a*b^3+4/d*B*a*b^3*ln(cos(d*x+c))+1/2/d*A*tan(d*x+c)^2*b^4+1/d*A*b^4*ln(cos(d*x+c))+1/3/d*B*tan(d*x+c)^3*b^4-1/d*B*b^4*tan(d*x+c)+B*b^4*x+1/d*B*b^4*c","A"
261,1,242,173,0.399000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-A \,a^{4} x -\frac{A \cot \left(d x +c \right) a^{4}}{d}-\frac{A \,a^{4} c}{d}+\frac{a^{4} B \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 A \,a^{3} b \ln \left(\sin \left(d x +c \right)\right)}{d}+4 B x \,a^{3} b +\frac{4 B \,a^{3} b c}{d}+6 A x \,a^{2} b^{2}+\frac{6 A \,a^{2} b^{2} c}{d}-\frac{6 a^{2} b^{2} B \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{4 a A \,b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}-4 B x a \,b^{3}+\frac{4 B \tan \left(d x +c \right) a \,b^{3}}{d}-\frac{4 B a \,b^{3} c}{d}-A x \,b^{4}+\frac{A \tan \left(d x +c \right) b^{4}}{d}-\frac{A \,b^{4} c}{d}+\frac{B \,b^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{4} B \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-A*a^4*x-1/d*A*cot(d*x+c)*a^4-1/d*A*a^4*c+1/d*a^4*B*ln(sin(d*x+c))+4/d*A*a^3*b*ln(sin(d*x+c))+4*B*x*a^3*b+4/d*B*a^3*b*c+6*A*x*a^2*b^2+6/d*A*a^2*b^2*c-6/d*a^2*b^2*B*ln(cos(d*x+c))-4/d*a*A*b^3*ln(cos(d*x+c))-4*B*x*a*b^3+4/d*B*tan(d*x+c)*a*b^3-4/d*B*a*b^3*c-A*x*b^4+1/d*A*tan(d*x+c)*b^4-1/d*A*b^4*c+1/2/d*B*b^4*tan(d*x+c)^2+b^4*B*ln(cos(d*x+c))/d","A"
262,1,244,182,0.476000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{A \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{4} A \ln \left(\sin \left(d x +c \right)\right)}{d}-a^{4} B x -\frac{B \cot \left(d x +c \right) a^{4}}{d}-\frac{a^{4} B c}{d}-4 A \,a^{3} b x -\frac{4 A \cot \left(d x +c \right) a^{3} b}{d}-\frac{4 A \,a^{3} b c}{d}+\frac{4 B \,a^{3} b \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{6 A \,a^{2} b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+6 B \,a^{2} b^{2} x +\frac{6 B \,a^{2} b^{2} c}{d}+4 A a \,b^{3} x +\frac{4 A a \,b^{3} c}{d}-\frac{4 B a \,b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{A \,b^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}-B \,b^{4} x +\frac{B \,b^{4} \tan \left(d x +c \right)}{d}-\frac{B \,b^{4} c}{d}"," ",0,"-1/2/d*A*a^4*cot(d*x+c)^2-a^4*A*ln(sin(d*x+c))/d-a^4*B*x-1/d*B*cot(d*x+c)*a^4-1/d*a^4*B*c-4*A*a^3*b*x-4/d*A*cot(d*x+c)*a^3*b-4/d*A*a^3*b*c+4/d*B*a^3*b*ln(sin(d*x+c))+6/d*A*a^2*b^2*ln(sin(d*x+c))+6*B*a^2*b^2*x+6/d*B*a^2*b^2*c+4*A*a*b^3*x+4/d*A*a*b^3*c-4/d*B*a*b^3*ln(cos(d*x+c))-1/d*A*b^4*ln(cos(d*x+c))-B*b^4*x+1/d*B*b^4*tan(d*x+c)-1/d*B*b^4*c","A"
263,1,278,183,0.452000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{A \,a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{A \cot \left(d x +c \right) a^{4}}{d}+A \,a^{4} x +\frac{A \,a^{4} c}{d}-\frac{a^{4} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{4} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 A \,a^{3} b \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{4 A \,a^{3} b \ln \left(\sin \left(d x +c \right)\right)}{d}-4 B x \,a^{3} b -\frac{4 B \cot \left(d x +c \right) a^{3} b}{d}-\frac{4 B \,a^{3} b c}{d}-6 A x \,a^{2} b^{2}-\frac{6 A \cot \left(d x +c \right) a^{2} b^{2}}{d}-\frac{6 A \,a^{2} b^{2} c}{d}+\frac{6 a^{2} b^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 a A \,b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+4 B x a \,b^{3}+\frac{4 B a \,b^{3} c}{d}+A x \,b^{4}+\frac{A \,b^{4} c}{d}-\frac{b^{4} B \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*A*a^4*cot(d*x+c)^3+1/d*A*cot(d*x+c)*a^4+A*a^4*x+1/d*A*a^4*c-1/2/d*a^4*B*cot(d*x+c)^2-1/d*a^4*B*ln(sin(d*x+c))-2/d*A*a^3*b*cot(d*x+c)^2-4/d*A*a^3*b*ln(sin(d*x+c))-4*B*x*a^3*b-4/d*B*cot(d*x+c)*a^3*b-4/d*B*a^3*b*c-6*A*x*a^2*b^2-6/d*A*cot(d*x+c)*a^2*b^2-6/d*A*a^2*b^2*c+6/d*a^2*b^2*B*ln(sin(d*x+c))+4/d*a*A*b^3*ln(sin(d*x+c))+4*B*x*a*b^3+4/d*B*a*b^3*c+A*x*b^4+1/d*A*b^4*c-b^4*B*ln(cos(d*x+c))/d","A"
264,1,347,217,0.464000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{2 B \,a^{3} b \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{4 A \,a^{3} b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{3 A \,a^{2} b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}+a^{4} B x +\frac{B \cot \left(d x +c \right) a^{4}}{d}+\frac{A \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+B \,b^{4} x +\frac{A \,b^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{a^{4} B c}{d}+\frac{B \,b^{4} c}{d}+4 A \,a^{3} b x -6 B \,a^{2} b^{2} x -4 A a \,b^{3} x +\frac{4 A \,a^{3} b c}{d}-\frac{6 B \,a^{2} b^{2} c}{d}-\frac{4 A a \,b^{3} c}{d}-\frac{A \,a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{4} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{4 B \,a^{3} b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{6 A \,a^{2} b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 B a \,b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{6 B \cot \left(d x +c \right) a^{2} b^{2}}{d}-\frac{4 A \cot \left(d x +c \right) a \,b^{3}}{d}+\frac{4 A \cot \left(d x +c \right) a^{3} b}{d}+\frac{a^{4} A \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"a^4*B*x+1/2/d*A*a^4*cot(d*x+c)^2+1/d*B*cot(d*x+c)*a^4+B*b^4*x+1/d*A*b^4*ln(sin(d*x+c))-1/4/d*A*a^4*cot(d*x+c)^4-1/3/d*a^4*B*cot(d*x+c)^3+1/d*a^4*B*c+1/d*B*b^4*c+4*A*a^3*b*x-6*B*a^2*b^2*x-4*A*a*b^3*x-2/d*B*a^3*b*cot(d*x+c)^2+4/d*A*a^3*b*c-6/d*B*a^2*b^2*c-4/d*A*a*b^3*c-4/d*B*a^3*b*ln(sin(d*x+c))-6/d*A*a^2*b^2*ln(sin(d*x+c))+4/d*B*a*b^3*ln(sin(d*x+c))-4/3/d*A*a^3*b*cot(d*x+c)^3-3/d*A*a^2*b^2*cot(d*x+c)^2-6/d*B*cot(d*x+c)*a^2*b^2-4/d*A*cot(d*x+c)*a*b^3+4/d*A*cot(d*x+c)*a^3*b+a^4*A*ln(sin(d*x+c))/d","A"
265,1,440,265,0.479000," ","int(cot(d*x+c)^6*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{4 B \,a^{3} b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{4 B \cot \left(d x +c \right) a \,b^{3}}{d}-A \,a^{4} x -\frac{A \,a^{4} c}{d}-\frac{A \,b^{4} c}{d}-\frac{A \cot \left(d x +c \right) a^{4}}{d}+\frac{a^{4} B \ln \left(\sin \left(d x +c \right)\right)}{d}+4 B x \,a^{3} b +6 A x \,a^{2} b^{2}-4 B x a \,b^{3}+\frac{2 A \,a^{3} b \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{4 B \cot \left(d x +c \right) a^{3} b}{d}+\frac{6 A \cot \left(d x +c \right) a^{2} b^{2}}{d}-\frac{6 a^{2} b^{2} B \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 a A \,b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 B \,a^{3} b c}{d}+\frac{6 A \,a^{2} b^{2} c}{d}-\frac{4 B a \,b^{3} c}{d}+\frac{A \,a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b^{2} B \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{2 A \,a^{2} b^{2} \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{a^{4} B \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{A \,a^{4} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}-\frac{A \cot \left(d x +c \right) b^{4}}{d}+\frac{B \,b^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-A x \,b^{4}+\frac{4 A \,a^{3} b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{A \,a^{3} b \left(\cot^{4}\left(d x +c \right)\right)}{d}-\frac{2 a A \,b^{3} \left(\cot^{2}\left(d x +c \right)\right)}{d}"," ",0,"-4/3/d*B*a^3*b*cot(d*x+c)^3-3/d*a^2*b^2*B*cot(d*x+c)^2-2/d*A*a^2*b^2*cot(d*x+c)^3-1/d*A*a^3*b*cot(d*x+c)^4-2/d*a*A*b^3*cot(d*x+c)^2-4/d*B*cot(d*x+c)*a*b^3-A*a^4*x-1/d*A*a^4*c-1/d*A*b^4*c-1/d*A*cot(d*x+c)*a^4+1/d*a^4*B*ln(sin(d*x+c))+4*B*x*a^3*b+6*A*x*a^2*b^2-4*B*x*a*b^3+4/d*B*cot(d*x+c)*a^3*b+6/d*A*cot(d*x+c)*a^2*b^2-6/d*a^2*b^2*B*ln(sin(d*x+c))-4/d*a*A*b^3*ln(sin(d*x+c))+2/d*A*a^3*b*cot(d*x+c)^2+4/d*B*a^3*b*c+6/d*A*a^2*b^2*c-4/d*B*a*b^3*c+1/3/d*A*a^4*cot(d*x+c)^3+1/2/d*a^4*B*cot(d*x+c)^2-1/d*A*cot(d*x+c)*b^4+1/d*B*b^4*ln(sin(d*x+c))-1/4/d*a^4*B*cot(d*x+c)^4-1/5/d*A*a^4*cot(d*x+c)^5-A*x*b^4+4/d*A*a^3*b*ln(sin(d*x+c))","A"
266,1,532,313,0.514000," ","int(cot(d*x+c)^7*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","-\frac{B \cot \left(d x +c \right) b^{4}}{d}+\frac{2 B \,a^{3} b \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{4 A \,a^{3} b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{3 A \,a^{2} b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}-a^{4} B x -\frac{B \cot \left(d x +c \right) a^{4}}{d}-\frac{A \,a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-B \,b^{4} x -\frac{4 A \,a^{3} b \left(\cot^{5}\left(d x +c \right)\right)}{5 d}-\frac{4 a A \,b^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 B a \,b^{3} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{B \,a^{3} b \left(\cot^{4}\left(d x +c \right)\right)}{d}-\frac{3 A \,a^{2} b^{2} \left(\cot^{4}\left(d x +c \right)\right)}{2 d}-\frac{2 a^{2} b^{2} B \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{A \,a^{4} \left(\cot^{6}\left(d x +c \right)\right)}{6 d}-\frac{A \,b^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{4} B c}{d}-\frac{B \,b^{4} c}{d}-4 A \,a^{3} b x +6 B \,a^{2} b^{2} x +4 A a \,b^{3} x -\frac{4 A \,a^{3} b c}{d}+\frac{6 B \,a^{2} b^{2} c}{d}+\frac{4 A a \,b^{3} c}{d}-\frac{A \,b^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{4} B \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{A \,a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{4} B \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{4 B \,a^{3} b \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{6 A \,a^{2} b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 B a \,b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{6 B \cot \left(d x +c \right) a^{2} b^{2}}{d}+\frac{4 A \cot \left(d x +c \right) a \,b^{3}}{d}-\frac{4 A \cot \left(d x +c \right) a^{3} b}{d}-\frac{a^{4} A \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/6/d*A*a^4*cot(d*x+c)^6-1/2/d*A*b^4*cot(d*x+c)^2-1/d*B*cot(d*x+c)*b^4-1/5/d*a^4*B*cot(d*x+c)^5-a^4*B*x-1/2/d*A*a^4*cot(d*x+c)^2-1/d*B*cot(d*x+c)*a^4-B*b^4*x-1/d*A*b^4*ln(sin(d*x+c))+1/4/d*A*a^4*cot(d*x+c)^4+1/3/d*a^4*B*cot(d*x+c)^3-1/d*a^4*B*c-1/d*B*b^4*c-4*A*a^3*b*x+6*B*a^2*b^2*x+4*A*a*b^3*x+2/d*B*a^3*b*cot(d*x+c)^2-4/d*A*a^3*b*c+6/d*B*a^2*b^2*c+4/d*A*a*b^3*c-4/5/d*A*a^3*b*cot(d*x+c)^5-4/3/d*a*A*b^3*cot(d*x+c)^3-2/d*B*a*b^3*cot(d*x+c)^2-1/d*B*a^3*b*cot(d*x+c)^4-3/2/d*A*a^2*b^2*cot(d*x+c)^4-2/d*a^2*b^2*B*cot(d*x+c)^3+4/d*B*a^3*b*ln(sin(d*x+c))+6/d*A*a^2*b^2*ln(sin(d*x+c))-4/d*B*a*b^3*ln(sin(d*x+c))+4/3/d*A*a^3*b*cot(d*x+c)^3+3/d*A*a^2*b^2*cot(d*x+c)^2+6/d*B*cot(d*x+c)*a^2*b^2+4/d*A*cot(d*x+c)*a*b^3-4/d*A*cot(d*x+c)*a^3*b-a^4*A*ln(sin(d*x+c))/d","A"
267,1,211,125,0.227000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{B \left(\tan^{2}\left(d x +c \right)\right)}{2 b d}+\frac{A \tan \left(d x +c \right)}{d b}-\frac{a B \tan \left(d x +c \right)}{b^{2} d}-\frac{a^{3} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,b^{2} \left(a^{2}+b^{2}\right)}+\frac{a^{4} B \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{3} \left(a^{2}+b^{2}\right) d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a A}{2 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{A \arctan \left(\tan \left(d x +c \right)\right) b}{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)}"," ",0,"1/2*B*tan(d*x+c)^2/b/d+1/d/b*A*tan(d*x+c)-a*B*tan(d*x+c)/b^2/d-1/d/b^2*a^3/(a^2+b^2)*ln(a+b*tan(d*x+c))*A+a^4*B*ln(a+b*tan(d*x+c))/b^3/(a^2+b^2)/d-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*A-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b-1/d/(a^2+b^2)*A*arctan(tan(d*x+c))*b+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a","A"
268,1,179,101,0.217000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{B \tan \left(d x +c \right)}{b d}+\frac{a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d b \left(a^{2}+b^{2}\right)}-\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{\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) a B}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) a}{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)}"," ",0,"B*tan(d*x+c)/b/d+1/d/b*a^2/(a^2+b^2)*ln(a+b*tan(d*x+c))*A-a^3*B*ln(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d+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)*a*B-1/d/(a^2+b^2)*A*arctan(tan(d*x+c))*a-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b","A"
269,1,159,80,0.237000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","-\frac{a \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)}+\frac{a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right) b}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a A}{2 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{A \arctan \left(\tan \left(d x +c \right)\right) b}{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)}"," ",0,"-1/d*a/(a^2+b^2)*ln(a+b*tan(d*x+c))*A+1/d*a^2/(a^2+b^2)/b*ln(a+b*tan(d*x+c))*B+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*A+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b+1/d/(a^2+b^2)*A*arctan(tan(d*x+c))*b-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a","A"
270,1,153,58,0.250000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{\ln \left(a +b \tan \left(d x +c \right)\right) A b}{d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(a +b \tan \left(d x +c \right)\right) a B}{d \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) a B}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) a}{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)}"," ",0,"1/d/(a^2+b^2)*ln(a+b*tan(d*x+c))*A*b-1/d/(a^2+b^2)*ln(a+b*tan(d*x+c))*a*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)*a*B+1/d/(a^2+b^2)*A*arctan(tan(d*x+c))*a+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b","B"
271,1,174,80,0.677000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","-\frac{b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d a \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)}+\frac{A \ln \left(\tan \left(d x +c \right)\right)}{d a}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a A}{2 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{A \arctan \left(\tan \left(d x +c \right)\right) b}{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)}"," ",0,"-1/d*b^2/a/(a^2+b^2)*ln(a+b*tan(d*x+c))*A+1/d*b/(a^2+b^2)*ln(a+b*tan(d*x+c))*B+1/d*A/a*ln(tan(d*x+c))-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*A-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b-1/d/(a^2+b^2)*A*arctan(tan(d*x+c))*b+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a","B"
272,1,214,103,0.597000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{2} \left(a^{2}+b^{2}\right)}-\frac{b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d a \left(a^{2}+b^{2}\right)}-\frac{A}{d a \tan \left(d x +c \right)}-\frac{\ln \left(\tan \left(d x +c \right)\right) A b}{d \,a^{2}}+\frac{\ln \left(\tan \left(d x +c \right)\right) B}{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) a B}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) a}{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)}"," ",0,"1/d*b^3/a^2/(a^2+b^2)*ln(a+b*tan(d*x+c))*A-1/d*b^2/a/(a^2+b^2)*ln(a+b*tan(d*x+c))*B-1/d*A/a/tan(d*x+c)-1/d/a^2*ln(tan(d*x+c))*A*b+1/d/a*ln(tan(d*x+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)*a*B-1/d/(a^2+b^2)*A*arctan(tan(d*x+c))*a-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b","B"
273,1,266,135,0.689000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","-\frac{b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{3} \left(a^{2}+b^{2}\right)}+\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{A}{2 d a \tan \left(d x +c \right)^{2}}+\frac{A b}{d \,a^{2} \tan \left(d x +c \right)}-\frac{B}{d a \tan \left(d x +c \right)}-\frac{A \ln \left(\tan \left(d x +c \right)\right)}{d a}+\frac{\ln \left(\tan \left(d x +c \right)\right) A \,b^{2}}{d \,a^{3}}-\frac{\ln \left(\tan \left(d x +c \right)\right) B b}{d \,a^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a A}{2 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{A \arctan \left(\tan \left(d x +c \right)\right) b}{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)}"," ",0,"-1/d*b^4/a^3/(a^2+b^2)*ln(a+b*tan(d*x+c))*A+1/d*b^3/a^2/(a^2+b^2)*ln(a+b*tan(d*x+c))*B-1/2/d*A/a/tan(d*x+c)^2+1/d/a^2/tan(d*x+c)*A*b-1/d/a/tan(d*x+c)*B-1/d*A/a*ln(tan(d*x+c))+1/d/a^3*ln(tan(d*x+c))*A*b^2-1/d/a^2*ln(tan(d*x+c))*B*b+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*A+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b+1/d/(a^2+b^2)*A*arctan(tan(d*x+c))*b-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a","A"
274,1,337,165,0.654000," ","int(cot(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{b^{5} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{4} \left(a^{2}+b^{2}\right)}-\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{A b}{2 d \,a^{2} \tan \left(d x +c \right)^{2}}-\frac{B}{2 d a \tan \left(d x +c \right)^{2}}-\frac{A}{3 d a \tan \left(d x +c \right)^{3}}+\frac{\ln \left(\tan \left(d x +c \right)\right) A b}{d \,a^{2}}-\frac{\ln \left(\tan \left(d x +c \right)\right) A \,b^{3}}{d \,a^{4}}-\frac{\ln \left(\tan \left(d x +c \right)\right) B}{d a}+\frac{\ln \left(\tan \left(d x +c \right)\right) B \,b^{2}}{d \,a^{3}}+\frac{A}{d a \tan \left(d x +c \right)}-\frac{A \,b^{2}}{d \,a^{3} \tan \left(d x +c \right)}+\frac{B b}{d \,a^{2} \tan \left(d x +c \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) a B}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) a}{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)}"," ",0,"1/d*b^5/a^4/(a^2+b^2)*ln(a+b*tan(d*x+c))*A-1/d*b^4/a^3/(a^2+b^2)*ln(a+b*tan(d*x+c))*B+1/2/d/a^2/tan(d*x+c)^2*A*b-1/2/d/a/tan(d*x+c)^2*B-1/3/d*A/a/tan(d*x+c)^3+1/d/a^2*ln(tan(d*x+c))*A*b-1/d/a^4*ln(tan(d*x+c))*A*b^3-1/d/a*ln(tan(d*x+c))*B+1/d/a^3*ln(tan(d*x+c))*B*b^2+1/d*A/a/tan(d*x+c)-1/d/a^3/tan(d*x+c)*A*b^2+1/d/a^2/tan(d*x+c)*B*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)*a*B+1/d/(a^2+b^2)*A*arctan(tan(d*x+c))*a+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b","B"
275,1,364,208,0.218000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{B \tan \left(d x +c \right)}{d \,b^{2}}+\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) A}{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) A}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 a^{5} \ln \left(a +b \tan \left(d x +c \right)\right) B}{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) B}{d b \left(a^{2}+b^{2}\right)^{2}}+\frac{a^{3} A}{d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{4} B}{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} A}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{2}}{2 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{2 A \arctan \left(\tan \left(d x +c \right)\right) a b}{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}}"," ",0,"1/d*B/b^2*tan(d*x+c)+1/d/b^2*a^4/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A+3/d*a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A-2/d/b^3*a^5/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B-4/d/b*a^3/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B+1/d/b^2*a^3/(a^2+b^2)/(a+b*tan(d*x+c))*A-1/d/b^3*a^4/(a^2+b^2)/(a+b*tan(d*x+c))*B-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*A+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*A*b^2-1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*B*a*b-2/d/(a^2+b^2)^2*A*arctan(tan(d*x+c))*a*b+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","A"
276,1,313,157,0.277000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} A}{d b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{3} B}{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) A}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) B}{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) B}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A 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{A \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{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}}"," ",0,"-1/d*a^2/b/(a^2+b^2)/(a+b*tan(d*x+c))*A+1/d*a^3/b^2/(a^2+b^2)/(a+b*tan(d*x+c))*B-2/d*a/(a^2+b^2)^2*b*ln(a+b*tan(d*x+c))*A+1/d*a^4/(a^2+b^2)^2/b^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+1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*A*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*A*arctan(tan(d*x+c))*a^2+1/d/(a^2+b^2)^2*A*arctan(tan(d*x+c))*b^2-2/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*a*b","A"
277,1,305,115,0.273000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{a A}{d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{2} B}{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) A}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) A \,b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 \ln \left(a +b \tan \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} A}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{2}}{2 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{2 A \arctan \left(\tan \left(d x +c \right)\right) a b}{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}}"," ",0,"1/d*a/(a^2+b^2)/(a+b*tan(d*x+c))*A-1/d*a^2/(a^2+b^2)/b/(a+b*tan(d*x+c))*B-1/d*a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A+1/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A*b^2-2/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B*a*b+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*A-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*A*b^2+1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*B*a*b+2/d/(a^2+b^2)^2*A*arctan(tan(d*x+c))*a*b-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","B"
278,1,301,110,0.262000," ","int((A+B*tan(d*x+c))/(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 B}{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) A}{d \left(a^{2}+b^{2}\right)^{2}}-\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{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A 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{A \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{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}}"," ",0,"-1/d/(a^2+b^2)/(a+b*tan(d*x+c))*A*b+1/d/(a^2+b^2)/(a+b*tan(d*x+c))*a*B+2/d*a/(a^2+b^2)^2*b*ln(a+b*tan(d*x+c))*A-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-1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*A*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*A*arctan(tan(d*x+c))*a^2-1/d/(a^2+b^2)^2*A*arctan(tan(d*x+c))*b^2+2/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*a*b","B"
279,1,325,137,0.718000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","-\frac{3 \ln \left(a +b \tan \left(d x +c \right)\right) A \,b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \ln \left(a +b \tan \left(d x +c \right)\right) B a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{b^{2} A}{d a \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{b B}{d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}+\frac{A \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} A}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{2}}{2 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{2 A \arctan \left(\tan \left(d x +c \right)\right) a b}{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}}"," ",0,"-3/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A*b^2-1/d*b^4/a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A+2/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*B*a*b+1/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))*A-1/d*b/(a^2+b^2)/(a+b*tan(d*x+c))*B+1/a^2/d*A*ln(tan(d*x+c))-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*A+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*A*b^2-1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*B*a*b-2/d/(a^2+b^2)^2*A*arctan(tan(d*x+c))*a*b+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","B"
280,1,399,192,0.581000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{4 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d a \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right) A}{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} 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{b^{3} A}{d \,a^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{2} B}{d a \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{A}{d \,a^{2} \tan \left(d x +c \right)}-\frac{2 \ln \left(\tan \left(d x +c \right)\right) A b}{d \,a^{3}}+\frac{\ln \left(\tan \left(d x +c \right)\right) B}{d \,a^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A 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{A \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{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}}"," ",0,"4/d*b^3/a/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A+2/d*b^5/a^3/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A-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-1/d*b^3/a^2/(a^2+b^2)/(a+b*tan(d*x+c))*A+1/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))*B-1/d*A/a^2/tan(d*x+c)-2/d/a^3*ln(tan(d*x+c))*A*b+1/d/a^2*ln(tan(d*x+c))*B+1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*A*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*A*arctan(tan(d*x+c))*a^2+1/d/(a^2+b^2)^2*A*arctan(tan(d*x+c))*b^2-2/d/(a^2+b^2)^2*B*arctan(tan(d*x+c))*a*b","B"
281,1,457,246,0.692000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","-\frac{5 b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{3 b^{6} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{4} \left(a^{2}+b^{2}\right)^{2}}+\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{b^{4} A}{d \,a^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{3} B}{d \,a^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{A}{2 a^{2} d \tan \left(d x +c \right)^{2}}+\frac{2 A b}{d \,a^{3} \tan \left(d x +c \right)}-\frac{B}{a^{2} d \tan \left(d x +c \right)}-\frac{A \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}+\frac{3 \ln \left(\tan \left(d x +c \right)\right) A \,b^{2}}{d \,a^{4}}-\frac{2 \ln \left(\tan \left(d x +c \right)\right) B b}{d \,a^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} A}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{2}}{2 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{2 A \arctan \left(\tan \left(d x +c \right)\right) a b}{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}}"," ",0,"-5/d*b^4/a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A-3/d*b^6/a^4/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*A+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+1/d*b^4/a^3/(a^2+b^2)/(a+b*tan(d*x+c))*A-1/d*b^3/a^2/(a^2+b^2)/(a+b*tan(d*x+c))*B-1/2/a^2/d*A/tan(d*x+c)^2+2/d/a^3/tan(d*x+c)*A*b-1/a^2/d/tan(d*x+c)*B-1/a^2/d*A*ln(tan(d*x+c))+3/d/a^4*ln(tan(d*x+c))*A*b^2-2/d/a^3*ln(tan(d*x+c))*B*b+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*A-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*A*b^2+1/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*B*a*b+2/d/(a^2+b^2)^2*A*arctan(tan(d*x+c))*a*b-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","A"
282,1,619,327,0.250000," ","int(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\frac{B \tan \left(d x +c \right)}{d \,b^{3}}+\frac{a^{6} \ln \left(a +b \tan \left(d x +c \right)\right) A}{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) A}{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) A}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a^{7} \ln \left(a +b \tan \left(d x +c \right)\right) B}{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) B}{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) B}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{a^{4} A}{2 d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{5} B}{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} A}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 a^{3} A}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{6} B}{d \,b^{4} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{5 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 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{3}}{2 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{A \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{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}}"," ",0,"1/d*B/b^3*tan(d*x+c)+1/d/b^3*a^6/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A+3/d/b*a^4/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A+6/d*b*a^2/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A-3/d/b^4*a^7/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-9/d/b^2*a^5/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-10/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-1/2/d/b^3*a^4/(a^2+b^2)/(a+b*tan(d*x+c))^2*A+1/2/d/b^4*a^5/(a^2+b^2)/(a+b*tan(d*x+c))^2*B+2/d/b^3*a^5/(a^2+b^2)^2/(a+b*tan(d*x+c))*A+4/d/b*a^3/(a^2+b^2)^2/(a+b*tan(d*x+c))*A-3/d/b^4*a^6/(a^2+b^2)^2/(a+b*tan(d*x+c))*B-5/d/b^2*a^4/(a^2+b^2)^2/(a+b*tan(d*x+c))*B-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a^2*b+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*b^3+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+1/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a^3-3/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a*b^2+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","A"
283,1,566,248,0.268000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a \,b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{a^{6} \ln \left(a +b \tan \left(d x +c \right)\right) B}{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) B}{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) B}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{a^{4} A}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{2} A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\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{a^{3} A}{2 d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\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{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A 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) 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{3 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{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}}"," ",0,"1/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A-3/d*a/(a^2+b^2)^3*b^2*ln(a+b*tan(d*x+c))*A+1/d*a^6/(a^2+b^2)^3/b^3*ln(a+b*tan(d*x+c))*B+3/d*a^4/(a^2+b^2)^3/b*ln(a+b*tan(d*x+c))*B+6/d*a^2/(a^2+b^2)^3*b*ln(a+b*tan(d*x+c))*B-1/d*a^4/b^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*A-3/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*A+2/d*a^5/b^3/(a^2+b^2)^2/(a+b*tan(d*x+c))*B+4/d*a^3/b/(a^2+b^2)^2/(a+b*tan(d*x+c))*B+1/2/d*a^3/b^2/(a^2+b^2)/(a+b*tan(d*x+c))^2*A-1/2/d*a^4/b^3/(a^2+b^2)/(a+b*tan(d*x+c))^2*B-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a^3+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a*b^2-3/2/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-3/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a^2*b+1/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*b^3+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","B"
284,1,495,187,0.289000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","-\frac{a^{2} A}{2 d b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\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{3 b \,a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\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 \ln \left(a +b \tan \left(d x +c \right)\right) B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{2 a b A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\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{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{3}}{2 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{A \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{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}}"," ",0,"-1/2/d*a^2/b/(a^2+b^2)/(a+b*tan(d*x+c))^2*A+1/2/d*a^3/b^2/(a^2+b^2)/(a+b*tan(d*x+c))^2*B-3/d*b*a^2/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A+1/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A*b^3+1/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-3/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B*a*b^2+2/d*a/(a^2+b^2)^2*b/(a+b*tan(d*x+c))*A-1/d/b^2*a^4/(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+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a^2*b-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*b^3-1/2/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^2-1/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a^3+3/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a*b^2-3/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","B"
285,1,488,177,0.278000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\frac{a A}{2 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{2} B}{2 d \left(a^{2}+b^{2}\right) b \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{2} A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{A \,b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 B 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) A}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 a \,b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a^{2} b \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{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A 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) 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{3 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{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}}"," ",0,"1/2/d*a/(a^2+b^2)/(a+b*tan(d*x+c))^2*A-1/2/d*a^2/(a^2+b^2)/b/(a+b*tan(d*x+c))^2*B+1/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*A-1/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*A*b^2+2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*B*a*b-1/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A+3/d*a/(a^2+b^2)^3*b^2*ln(a+b*tan(d*x+c))*A-3/d*a^2/(a^2+b^2)^3*b*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+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a^3-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a*b^2+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+3/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a^2*b-1/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*b^3-1/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","B"
286,1,483,172,0.282000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\frac{3 b \,a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(d x +c \right)\right) A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\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 \ln \left(a +b \tan \left(d x +c \right)\right) B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{A b}{2 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a B}{2 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{2 a b A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\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{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{3}}{2 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{A \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{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}}"," ",0,"3/d*b*a^2/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A-1/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A*b^3-1/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B+3/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B*a*b^2-1/2/d/(a^2+b^2)/(a+b*tan(d*x+c))^2*A*b+1/2/d/(a^2+b^2)/(a+b*tan(d*x+c))^2*a*B-2/d*a/(a^2+b^2)^2*b/(a+b*tan(d*x+c))*A+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-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a^2*b+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*b^3+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+1/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a^3-3/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a*b^2+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","B"
287,1,540,213,0.775000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\frac{3 A \,b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{4} A}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 B 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) A}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d a \left(a^{2}+b^{2}\right)^{3}}-\frac{b^{6} \ln \left(a +b \tan \left(d x +c \right)\right) A}{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) 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{b^{2} A}{2 d a \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b B}{2 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{A \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A 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) 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{3 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{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}}"," ",0,"3/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*A*b^2+1/d*b^4/a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*A-2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*B*a*b-6/d*a/(a^2+b^2)^3*b^2*ln(a+b*tan(d*x+c))*A-3/d*b^4/a/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A-1/d*b^6/a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A+3/d*a^2/(a^2+b^2)^3*b*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+1/2/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))^2*A-1/2/d*b/(a^2+b^2)/(a+b*tan(d*x+c))^2*B+1/a^3/d*A*ln(tan(d*x+c))-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a^3+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a*b^2-3/2/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-3/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a^2*b+1/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*b^3+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","B"
288,1,651,285,0.692000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","-\frac{4 b^{3} A}{d a \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 b^{5} A}{d \,a^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\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{10 \ln \left(a +b \tan \left(d x +c \right)\right) A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{9 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right) A}{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) A}{d \,a^{4} \left(a^{2}+b^{2}\right)^{3}}-\frac{6 \ln \left(a +b \tan \left(d x +c \right)\right) B 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) 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{b^{3} A}{2 d \,a^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\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{A}{d \,a^{3} \tan \left(d x +c \right)}-\frac{3 \ln \left(\tan \left(d x +c \right)\right) A b}{d \,a^{4}}+\frac{\ln \left(\tan \left(d x +c \right)\right) B}{d \,a^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{3}}{2 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{A \arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{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}}"," ",0,"-4/d*b^3/a/(a^2+b^2)^2/(a+b*tan(d*x+c))*A-2/d*b^5/a^3/(a^2+b^2)^2/(a+b*tan(d*x+c))*A+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+10/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A*b^3+9/d*b^5/a^2/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A+3/d*b^7/a^4/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A-6/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B*a*b^2-3/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-1/2/d*b^3/a^2/(a^2+b^2)/(a+b*tan(d*x+c))^2*A+1/2/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))^2*B-1/d*A/a^3/tan(d*x+c)-3/d/a^4*ln(tan(d*x+c))*A*b+1/d/a^3*ln(tan(d*x+c))*B+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a^2*b-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*b^3-1/2/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^2-1/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a^3+3/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a*b^2-3/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","B"
289,1,713,348,0.760000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\frac{6 \ln \left(\tan \left(d x +c \right)\right) A \,b^{2}}{d \,a^{5}}-\frac{3 \ln \left(\tan \left(d x +c \right)\right) B b}{d \,a^{4}}+\frac{3 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{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{A \arctan \left(\tan \left(d x +c \right)\right) b^{3}}{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 A b}{d \,a^{4} \tan \left(d x +c \right)}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3}}{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{10 \ln \left(a +b \tan \left(d x +c \right)\right) b^{3} B}{d \left(a^{2}+b^{2}\right)^{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{A \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}-\frac{A}{2 d \,a^{3} \tan \left(d x +c \right)^{2}}-\frac{B}{d \,a^{3} \tan \left(d x +c \right)}+\frac{5 b^{4} A}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\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{3 b^{6} A}{d \,a^{4} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\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{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A a \,b^{2}}{2 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{6 b^{8} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{5} \left(a^{2}+b^{2}\right)^{3}}-\frac{15 b^{4} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d a \left(a^{2}+b^{2}\right)^{3}}-\frac{17 b^{6} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{3} \left(a^{2}+b^{2}\right)^{3}}-\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{b^{4} A}{2 d \,a^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\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}}"," ",0,"6/d/a^5*ln(tan(d*x+c))*A*b^2-3/d/a^4*ln(tan(d*x+c))*B*b+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b*B+3/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*a^2*b+3/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a*b^2+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a^3-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3*B-1/d/(a^2+b^2)^3*A*arctan(tan(d*x+c))*b^3-1/d/(a^2+b^2)^3*B*arctan(tan(d*x+c))*a^3+3/d/a^4/tan(d*x+c)*A*b+10/d/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*b^3*B-1/a^3/d*A*ln(tan(d*x+c))-1/2/d*A/a^3/tan(d*x+c)^2-1/d/a^3/tan(d*x+c)*B+5/d*b^4/a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))*A-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*A*a*b^2-1/2/d*b^3/a^2/(a^2+b^2)/(a+b*tan(d*x+c))^2*B+3/d*b^6/a^4/(a^2+b^2)^2/(a+b*tan(d*x+c))*A-4/d*b^3/a/(a^2+b^2)^2/(a+b*tan(d*x+c))*B+9/d*b^5/a^2/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B-6/d*b^8/a^5/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A-15/d*b^4/a/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A-17/d*b^6/a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*A-2/d*b^5/a^3/(a^2+b^2)^2/(a+b*tan(d*x+c))*B+1/2/d*b^4/a^3/(a^2+b^2)/(a+b*tan(d*x+c))^2*A+3/d*b^7/a^4/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*B","B"
290,1,854,347,0.282000," ","int(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","\frac{10 a^{3} B}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{5 a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4} B}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 a \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{6 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{a^{8} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{4} b^{4}}+\frac{4 a^{6} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{4} b^{2}}-\frac{a^{6} A}{d \,b^{3} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{4} A}{d b \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 a^{3} b \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{a^{5} A}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{2 a^{3} A}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 a^{6} B}{2 d \,b^{4} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{5} B}{3 d \,b^{4} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{5 a^{4} B}{2 d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{2} B}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{9 a^{5} B}{d \,b^{2} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{6 a^{2} b A}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 a^{7} B}{d \,b^{4} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{4} A}{3 d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{10 a^{2} b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"10/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))*B+5/d*a^4/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^4*B+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*b^4+1/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^4+1/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*b^4-4/d*a/(a^2+b^2)^4*b^3*ln(a+b*tan(d*x+c))*A-6/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^2*b^2+4/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^3*b-4/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a*b^3+1/d*a^8/(a^2+b^2)^4/b^4*ln(a+b*tan(d*x+c))*B+4/d*a^6/(a^2+b^2)^4/b^2*ln(a+b*tan(d*x+c))*B+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a*A*b^3-1/d*a^6/b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))*A-3/d*a^4/b/(a^2+b^2)^3/(a+b*tan(d*x+c))*A-3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^2*B+4/d*a^3/(a^2+b^2)^4*b*ln(a+b*tan(d*x+c))*A+1/d*a^5/b^3/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A+2/d*a^3/b/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A-3/2/d*a^6/b^4/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B+1/3/d*a^5/b^4/(a^2+b^2)/(a+b*tan(d*x+c))^3*B-5/2/d*a^4/b^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^3*b+9/d*a^5/b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))*B-6/d*a^2*b/(a^2+b^2)^3/(a+b*tan(d*x+c))*A+3/d*a^7/b^4/(a^2+b^2)^3/(a+b*tan(d*x+c))*B-1/3/d*a^4/b^3/(a^2+b^2)/(a+b*tan(d*x+c))^3*A+10/d*a^2/(a^2+b^2)^4*b^2*ln(a+b*tan(d*x+c))*B","B"
291,1,780,292,0.274000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","-\frac{6 B \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{3 a^{2} A}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{a^{3} A}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) A \,b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{a^{4} A}{2 d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{5} B}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{3} A}{3 d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{a^{4} B}{3 d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{2 a^{3} B}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) A \,a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{3 a \,b^{2} A}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{6} B}{d \left(a^{2}+b^{2}\right)^{3} b^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{3 a^{4} B}{d \left(a^{2}+b^{2}\right)^{3} b \left(a +b \tan \left(d x +c \right)\right)}-\frac{6 a^{2} b B}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{6 \ln \left(a +b \tan \left(d x +c \right)\right) A \,a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 \ln \left(a +b \tan \left(d x +c \right)\right) B \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 \ln \left(a +b \tan \left(d x +c \right)\right) B a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-6/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^2*b^2-3/2/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^4-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*b^4+1/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^4+1/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*b^4-1/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))*A+1/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A*b^4-1/2/d*a^4/b^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A+1/d*a^5/b^3/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B+1/3/d*a^3/b^2/(a^2+b^2)/(a+b*tan(d*x+c))^3*A-1/3/d*a^4/b^3/(a^2+b^2)/(a+b*tan(d*x+c))^3*B+2/d*a^3/b/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B+1/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A*a^4+3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^2*b^2+3/d*a/(a^2+b^2)^3*b^2/(a+b*tan(d*x+c))*A-1/d*a^6/(a^2+b^2)^3/b^3/(a+b*tan(d*x+c))*B-4/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^3*b+4/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a*b^3-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*a^3*b-3/d*a^4/(a^2+b^2)^3/b/(a+b*tan(d*x+c))*B-6/d*a^2/(a^2+b^2)^3*b/(a+b*tan(d*x+c))*B-6/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A*a^2*b^2+4/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*a^3*b-4/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*a*b^3+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*a*b^3","B"
292,1,709,257,0.280000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","-\frac{a^{2} A}{3 d b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{a^{3} B}{3 d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{3 a^{2} b A}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{3} B}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{4 a^{3} b \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 a \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{6 a^{2} b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) B \,b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{a b A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{4} B}{2 d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 a^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4} B}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{2} B}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{6 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/3/d*a^2/b/(a^2+b^2)/(a+b*tan(d*x+c))^3*A+1/3/d*a^3/b^2/(a^2+b^2)/(a+b*tan(d*x+c))^3*B+3/d*a^2*b/(a^2+b^2)^3/(a+b*tan(d*x+c))*A-1/d/(a^2+b^2)^3/(a+b*tan(d*x+c))*A*b^3-1/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))*B+3/d/(a^2+b^2)^3/(a+b*tan(d*x+c))*B*a*b^2-4/d*a^3/(a^2+b^2)^4*b*ln(a+b*tan(d*x+c))*A+4/d*a/(a^2+b^2)^4*b^3*ln(a+b*tan(d*x+c))*A+1/d*a^4/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B-6/d*a^2/(a^2+b^2)^4*b^2*ln(a+b*tan(d*x+c))*B+1/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*b^4+1/d*a/(a^2+b^2)^2*b/(a+b*tan(d*x+c))^2*A-1/2/d*a^4/b^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B-3/2/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^3*b-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a*A*b^3-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^4*B+3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^2*B-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*b^4-1/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^4+6/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^2*b^2-1/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*b^4-4/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^3*b+4/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a*b^3","B"
293,1,702,246,0.258000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","\frac{a A}{3 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{a^{2} B}{3 d \left(a^{2}+b^{2}\right) b \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{a^{2} A}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{A \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{B a b}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{3} A}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a \,b^{2} A}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 a^{2} b B}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{3} B}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{\ln \left(a +b \tan \left(d x +c \right)\right) A \,a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{6 \ln \left(a +b \tan \left(d x +c \right)\right) A \,a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(a +b \tan \left(d x +c \right)\right) A \,b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 \ln \left(a +b \tan \left(d x +c \right)\right) B \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 \ln \left(a +b \tan \left(d x +c \right)\right) B a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{6 B \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"1/3/d*a/(a^2+b^2)/(a+b*tan(d*x+c))^3*A-1/3/d*a^2/(a^2+b^2)/b/(a+b*tan(d*x+c))^3*B+1/2/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A-1/2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A*b^2+1/d/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B*a*b+1/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))*A-3/d*a/(a^2+b^2)^3*b^2/(a+b*tan(d*x+c))*A+3/d*a^2/(a^2+b^2)^3*b/(a+b*tan(d*x+c))*B-1/d/(a^2+b^2)^3/(a+b*tan(d*x+c))*b^3*B-1/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A*a^4+6/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A*a^2*b^2-1/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A*b^4-4/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*a^3*b+4/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*a*b^3+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^4-3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^2*b^2+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*b^4+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*a^3*b-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*a*b^3+4/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^3*b-4/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a*b^3-1/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^4+6/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^2*b^2-1/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*b^4","B"
294,1,695,240,0.264000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","-\frac{3 a^{2} b A}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{3} B}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 a^{3} b \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 a \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{6 a^{2} b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(a +b \tan \left(d x +c \right)\right) B \,b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{A b}{3 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{a B}{3 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{a b A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4} B}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{2} B}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{6 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-3/d*a^2*b/(a^2+b^2)^3/(a+b*tan(d*x+c))*A+1/d/(a^2+b^2)^3/(a+b*tan(d*x+c))*A*b^3+1/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))*B-3/d/(a^2+b^2)^3/(a+b*tan(d*x+c))*B*a*b^2+4/d*a^3/(a^2+b^2)^4*b*ln(a+b*tan(d*x+c))*A-4/d*a/(a^2+b^2)^4*b^3*ln(a+b*tan(d*x+c))*A-1/d*a^4/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B+6/d*a^2/(a^2+b^2)^4*b^2*ln(a+b*tan(d*x+c))*B-1/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*b^4-1/3/d/(a^2+b^2)/(a+b*tan(d*x+c))^3*A*b+1/3/d/(a^2+b^2)/(a+b*tan(d*x+c))^3*a*B-1/d*a/(a^2+b^2)^2*b/(a+b*tan(d*x+c))^2*A+1/2/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B-1/2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*b^2*B-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^3*b+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a*A*b^3+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^4*B-3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^2*B+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*b^4+1/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^4-6/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^2*b^2+1/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*b^4+4/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^3*b-4/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a*b^3","B"
295,1,789,298,0.793000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","\frac{A \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{4}}+\frac{3 A \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{b^{3} B}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{6 B \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{5 \ln \left(a +b \tan \left(d x +c \right)\right) A \,b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{B a b}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{6 a \,b^{2} A}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{b^{2} A}{3 d a \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{b B}{3 d \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{3 a^{2} b B}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{10 \ln \left(a +b \tan \left(d x +c \right)\right) A \,a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 \ln \left(a +b \tan \left(d x +c \right)\right) B \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 \ln \left(a +b \tan \left(d x +c \right)\right) B a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 b^{6} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{2} \left(a^{2}+b^{2}\right)^{4}}-\frac{b^{8} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{4} \left(a^{2}+b^{2}\right)^{4}}+\frac{b^{4} A}{2 d \,a^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{b^{6} A}{d \,a^{3} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 b^{4} A}{d a \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"1/d*A/a^4*ln(tan(d*x+c))+3/2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A*b^2+1/d/(a^2+b^2)^3/(a+b*tan(d*x+c))*b^3*B-6/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^2*b^2-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^4-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*b^4+1/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^4+1/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*b^4-5/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A*b^4-1/d/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B*a*b+3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^2*b^2+6/d*a/(a^2+b^2)^3*b^2/(a+b*tan(d*x+c))*A-4/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^3*b+4/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a*b^3+1/3/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))^3*A-1/3/d*b/(a^2+b^2)/(a+b*tan(d*x+c))^3*B-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*a^3*b-3/d*a^2/(a^2+b^2)^3*b/(a+b*tan(d*x+c))*B-10/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A*a^2*b^2+4/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*a^3*b-4/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*a*b^3+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*a*b^3-4/d*b^6/a^2/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A-1/d*b^8/a^4/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A+1/2/d*b^4/a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A+1/d*b^6/a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))*A+3/d*b^4/a/(a^2+b^2)^3/(a+b*tan(d*x+c))*A","B"
296,1,969,395,0.692000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","-\frac{A \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4} B}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{A}{d \,a^{4} \tan \left(d x +c \right)}+\frac{\ln \left(\tan \left(d x +c \right)\right) B}{d \,a^{4}}-\frac{10 A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 b^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{A \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{5 \ln \left(a +b \tan \left(d x +c \right)\right) B \,b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 \ln \left(\tan \left(d x +c \right)\right) A b}{d \,a^{5}}+\frac{20 a \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{6 A \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 B \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{2} B}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{6 B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{10 a^{2} b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{b^{8} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{4} \left(a^{2}+b^{2}\right)^{4}}-\frac{4 b^{6} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{2} \left(a^{2}+b^{2}\right)^{4}}+\frac{b^{6} B}{d \,a^{3} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{24 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d a \left(a^{2}+b^{2}\right)^{4}}+\frac{16 b^{7} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{3} \left(a^{2}+b^{2}\right)^{4}}+\frac{4 b^{9} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{5} \left(a^{2}+b^{2}\right)^{4}}-\frac{b^{5} A}{d \,a^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{b^{4} B}{2 d \,a^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{9 b^{5} A}{d \,a^{2} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{3} A}{3 d \,a^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{b^{2} B}{3 d a \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{3 b^{7} A}{d \,a^{4} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 b^{4} B}{d a \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 b^{3} A}{d a \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^4*B-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*b^4-1/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^4-1/d*A/a^4/tan(d*x+c)+1/d/a^4*ln(tan(d*x+c))*B-10/d/(a^2+b^2)^3/(a+b*tan(d*x+c))*A*b^3+3/2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*b^2*B-1/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*b^4-5/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*b^4-4/d/a^5*ln(tan(d*x+c))*A*b+20/d*a/(a^2+b^2)^4*b^3*ln(a+b*tan(d*x+c))*A+6/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^2*b^2-4/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^3*b+4/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a*b^3-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a*A*b^3+3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^2*B+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^3*b+6/d/(a^2+b^2)^3/(a+b*tan(d*x+c))*B*a*b^2-10/d*a^2/(a^2+b^2)^4*b^2*ln(a+b*tan(d*x+c))*B-1/d*b^8/a^4/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B-4/d*b^6/a^2/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B+1/d*b^6/a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))*B+24/d*b^5/a/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A+16/d*b^7/a^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A+4/d*b^9/a^5/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A-1/d*b^5/a^3/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A+1/2/d*b^4/a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B-9/d*b^5/a^2/(a^2+b^2)^3/(a+b*tan(d*x+c))*A-1/3/d*b^3/a^2/(a^2+b^2)/(a+b*tan(d*x+c))^3*A+1/3/d*b^2/a/(a^2+b^2)/(a+b*tan(d*x+c))^3*B-3/d*b^7/a^4/(a^2+b^2)^3/(a+b*tan(d*x+c))*A+3/d*b^4/a/(a^2+b^2)^3/(a+b*tan(d*x+c))*B-2/d*b^3/a/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A","B"
297,1,1030,469,0.784000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","\frac{6 b^{8} A}{d \,a^{5} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 b^{6} A}{2 d \,a^{4} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{A \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{4}}-\frac{10 b^{3} B}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{6 B \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{B \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{35 \ln \left(a +b \tan \left(d x +c \right)\right) A \,b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{B}{d \,a^{4} \tan \left(d x +c \right)}-\frac{A}{2 d \,a^{4} \tan \left(d x +c \right)^{2}}-\frac{b^{5} B}{d \,a^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 A \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) A \,a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{b^{3} B}{3 d \,a^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{10 b^{10} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{6} \left(a^{2}+b^{2}\right)^{4}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B \,a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) B a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{20 \ln \left(a +b \tan \left(d x +c \right)\right) B a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{56 b^{6} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{2} \left(a^{2}+b^{2}\right)^{4}}-\frac{39 b^{8} \ln \left(a +b \tan \left(d x +c \right)\right) A}{d \,a^{4} \left(a^{2}+b^{2}\right)^{4}}+\frac{5 b^{4} A}{2 d \,a^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{17 b^{6} A}{d \,a^{3} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{15 b^{4} A}{d a \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{16 b^{7} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{3} \left(a^{2}+b^{2}\right)^{4}}+\frac{4 b^{9} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \,a^{5} \left(a^{2}+b^{2}\right)^{4}}+\frac{24 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d a \left(a^{2}+b^{2}\right)^{4}}-\frac{3 b^{7} B}{d \,a^{4} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{4} A}{3 d \,a^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{9 b^{5} B}{d \,a^{2} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 b^{3} B}{d a \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{4 A b}{d \,a^{5} \tan \left(d x +c \right)}+\frac{10 \ln \left(\tan \left(d x +c \right)\right) A \,b^{2}}{d \,a^{6}}-\frac{4 \ln \left(\tan \left(d x +c \right)\right) B b}{d \,a^{5}}"," ",0,"6/d*b^8/a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))*A+3/2/d*b^6/a^4/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A-1/d*A/a^4*ln(tan(d*x+c))-10/d/(a^2+b^2)^3/(a+b*tan(d*x+c))*b^3*B+6/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^2*b^2+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^4+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*b^4-1/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*a^4-1/d/(a^2+b^2)^4*B*arctan(tan(d*x+c))*b^4-35/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A*b^4-1/d/a^4/tan(d*x+c)*B-1/2/d*A/a^4/tan(d*x+c)^2-1/d*b^5/a^3/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B-3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*A*a^2*b^2+4/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a^3*b-4/d/(a^2+b^2)^4*A*arctan(tan(d*x+c))*a*b^3-1/3/d*b^3/a^2/(a^2+b^2)/(a+b*tan(d*x+c))^3*B-10/d*b^10/a^6/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*a^3*b+20/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B*a*b^3-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*B*a*b^3-56/d*b^6/a^2/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A-39/d*b^8/a^4/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*A+5/2/d*b^4/a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*A+17/d*b^6/a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))*A+15/d*b^4/a/(a^2+b^2)^3/(a+b*tan(d*x+c))*A+16/d*b^7/a^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B+4/d*b^9/a^5/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B+24/d*b^5/a/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*B-3/d*b^7/a^4/(a^2+b^2)^3/(a+b*tan(d*x+c))*B+1/3/d*b^4/a^3/(a^2+b^2)/(a+b*tan(d*x+c))^3*A-9/d*b^5/a^2/(a^2+b^2)^3/(a+b*tan(d*x+c))*B-2/d*b^3/a/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*B+4/d/a^5/tan(d*x+c)*A*b+10/d/a^6*ln(tan(d*x+c))*A*b^2-4/d/a^5*ln(tan(d*x+c))*B*b","B"
298,1,33,27,0.175000," ","int(tan(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{B \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/2*B*tan(d*x+c)^2/d-1/2/d*B*ln(1+tan(d*x+c)^2)","A"
299,1,26,16,0.168000," ","int(tan(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{B \tan \left(d x +c \right)}{d}-\frac{B \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"B*tan(d*x+c)/d-1/d*B*arctan(tan(d*x+c))","A"
300,1,18,13,0.150000," ","int(tan(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{B \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*B*ln(1+tan(d*x+c)^2)","A"
301,1,4,3,0.017000," ","int((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","B x"," ",0,"B*x","A"
302,1,13,12,0.313000," ","int(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{B \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"B*ln(sin(d*x+c))/d","A"
303,1,22,17,0.291000," ","int(cot(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{B \left(-\cot \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*B*(-cot(d*x+c)-d*x-c)","A"
304,1,29,28,0.364000," ","int(cot(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","-\frac{B \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{B \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/2*B*cot(d*x+c)^2/d-B*ln(sin(d*x+c))/d","A"
305,1,27,29,0.360000," ","int(cot(d*x+c)^4*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{B \left(-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*B*(-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)","A"
306,1,115,100,0.273000," ","int(tan(d*x+c)^4*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{B \left(\tan^{2}\left(d x +c \right)\right)}{2 b d}-\frac{a B \tan \left(d x +c \right)}{b^{2} d}+\frac{a^{4} B \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{3} \left(a^{2}+b^{2}\right) d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B b}{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)}"," ",0,"1/2*B*tan(d*x+c)^2/b/d-a*B*tan(d*x+c)/b^2/d+a^4*B*ln(a+b*tan(d*x+c))/b^3/(a^2+b^2)/d-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a","A"
307,1,98,83,0.239000," ","int(tan(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{B \tan \left(d x +c \right)}{b d}-\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{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a 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)}"," ",0,"B*tan(d*x+c)/b/d-a^3*B*ln(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*B-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b","A"
308,1,83,81,0.266000," ","int(tan(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{a^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right) b}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) B b}{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)}"," ",0,"1/d*a^2/(a^2+b^2)/b*ln(a+b*tan(d*x+c))*B+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a","A"
309,1,78,48,0.260000," ","int(tan(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","-\frac{B a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \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{B \arctan \left(\tan \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}"," ",0,"-1/d*B*a/(a^2+b^2)*ln(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*B+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b","A"
310,1,77,47,0.203000," ","int((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{B b \ln \left(a +b \tan \left(d x +c \right)\right)}{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{B \arctan \left(\tan \left(d x +c \right)\right) a}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/d*B*b/(a^2+b^2)*ln(a+b*tan(d*x+c))-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a","A"
311,1,99,69,0.577000," ","int(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,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{\ln \left(\tan \left(d x +c \right)\right) B}{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{B \arctan \left(\tan \left(d x +c \right)\right) b}{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/a*ln(tan(d*x+c))*B-1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*B-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b","A"
312,1,117,85,0.523000," ","int(cot(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{B \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{2} \left(a^{2}+b^{2}\right)}-\frac{B}{d a \tan \left(d x +c \right)}-\frac{B 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) B b}{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)}"," ",0,"B/d*b^3/a^2/(a^2+b^2)*ln(a+b*tan(d*x+c))-B/d/a/tan(d*x+c)-B/d*b/a^2*ln(tan(d*x+c))+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*B*b-1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*a","A"
313,1,151,110,0.666000," ","int(cot(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,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}{2 d a \tan \left(d x +c \right)^{2}}-\frac{\ln \left(\tan \left(d x +c \right)\right) B}{d a}+\frac{\ln \left(\tan \left(d x +c \right)\right) B \,b^{2}}{d \,a^{3}}+\frac{B b}{d \,a^{2} \tan \left(d x +c \right)}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a 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)}"," ",0,"-1/d*b^4/a^3/(a^2+b^2)*ln(a+b*tan(d*x+c))*B-1/2/d/a/tan(d*x+c)^2*B-1/d/a*ln(tan(d*x+c))*B+1/d/a^3*ln(tan(d*x+c))*B*b^2+1/d/a^2/tan(d*x+c)*B*b+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*B+1/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b","A"
314,1,41,25,0.240000," ","int((3+tan(d*x+c))/(2-tan(d*x+c)),x)","-\frac{\ln \left(-2+\tan \left(d x +c \right)\right)}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{d x +c}{d}"," ",0,"-1/d*ln(-2+tan(d*x+c))+1/2/d*ln(1+tan(d*x+c)^2)+1/d*(d*x+c)","A"
315,1,142,58,0.258000," ","int((b*B/a+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","-\frac{B a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}+\frac{b^{2} \ln \left(a +b \tan \left(d x +c \right)\right) B}{d a \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{B \ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d a \left(a^{2}+b^{2}\right)}+\frac{2 B \arctan \left(\tan \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}"," ",0,"-1/d*B*a/(a^2+b^2)*ln(a+b*tan(d*x+c))+1/d*b^2/a/(a^2+b^2)*ln(a+b*tan(d*x+c))*B+1/2/d/(a^2+b^2)*ln(1+tan(d*x+c)^2)*a*B-1/2/d*B/a/(a^2+b^2)*ln(1+tan(d*x+c)^2)*b^2+2/d/(a^2+b^2)*B*arctan(tan(d*x+c))*b","B"
316,1,222,100,0.260000," ","int((a+b*tan(d*x+c))/(b+a*tan(d*x+c))^2,x)","-\frac{a^{2}}{d \left(a^{2}+b^{2}\right) \left(b +a \tan \left(d x +c \right)\right)}+\frac{b^{2}}{d \left(a^{2}+b^{2}\right) \left(b +a \tan \left(d x +c \right)\right)}+\frac{3 b \ln \left(b +a \tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{3} \ln \left(b +a \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \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^{3}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-1/d/(a^2+b^2)/(b+a*tan(d*x+c))*a^2+1/d/(a^2+b^2)/(b+a*tan(d*x+c))*b^2+3/d*b/(a^2+b^2)^2*ln(b+a*tan(d*x+c))*a^2-1/d*b^3/(a^2+b^2)^2*ln(b+a*tan(d*x+c))-3/2/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^3-1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^3+3/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a*b^2","B"
317,1,1099,201,0.370000," ","int((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^3*(A+B*tan(d*x+c)),x)","\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d \,b^{3}}+\frac{2 A \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d \,b^{2}}-\frac{4 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5 d \,b^{3}}-\frac{2 A \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3 d \,b^{2}}+\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3 d \,b^{3}}-\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 b d}-\frac{2 A \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/7/d/b^3*B*(a+b*tan(d*x+c))^(7/2)+2/5/d/b^2*A*(a+b*tan(d*x+c))^(5/2)-4/5/d/b^3*B*(a+b*tan(d*x+c))^(5/2)*a-2/3/d/b^2*A*(a+b*tan(d*x+c))^(3/2)*a+2/3/d/b^3*B*(a+b*tan(d*x+c))^(3/2)*a^2-2/3*B*(a+b*tan(d*x+c))^(3/2)/b/d-2*A*(a+b*tan(d*x+c))^(1/2)/d+1/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B","B"
318,1,1032,158,0.372000," ","int((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^2*(A+B*tan(d*x+c)),x)","\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d \,b^{2}}+\frac{2 A \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d b}-\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3 d \,b^{2}}-\frac{2 B \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/5/d/b^2*B*(a+b*tan(d*x+c))^(5/2)+2/3/d/b*A*(a+b*tan(d*x+c))^(3/2)-2/3/d/b^2*B*(a+b*tan(d*x+c))^(3/2)*a-2*B*(a+b*tan(d*x+c))^(1/2)/d+1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a","B"
319,1,989,122,0.278000," ","int((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)*(A+B*tan(d*x+c)),x)","\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 b d}+\frac{2 A \sqrt{a +b \tan \left(d x +c \right)}}{d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/3*B*(a+b*tan(d*x+c))^(3/2)/b/d+2*A*(a+b*tan(d*x+c))^(1/2)/d-1/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B","B"
320,1,968,102,0.270000," ","int((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\frac{2 B \sqrt{a +b \tan \left(d x +c \right)}}{d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2*B*(a+b*tan(d*x+c))^(1/2)/d-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a","B"
321,1,29038,107,2.358000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
322,1,50546,141,2.846000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
323,1,81275,185,3.396000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
324,1,118304,241,4.654000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
325,1,1729,182,0.374000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d b}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d b}+\frac{b^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5 d \,b^{2}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d \,b^{2}}-\frac{2 b A \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{2 A \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d b}-\frac{2 B \sqrt{a +b \tan \left(d x +c \right)}\, a}{d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d b}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d b}-\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}"," ",0,"1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/4/d*b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2/5/d/b^2*B*(a+b*tan(d*x+c))^(5/2)*a+1/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/2/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/2/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/4/d*b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+2/7/d/b^2*B*(a+b*tan(d*x+c))^(7/2)-2/d*b*A*(a+b*tan(d*x+c))^(1/2)+2/5/d/b*A*(a+b*tan(d*x+c))^(5/2)-2/d*B*(a+b*tan(d*x+c))^(1/2)*a-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)+2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)-2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-2/3*B*(a+b*tan(d*x+c))^(3/2)/d","B"
326,1,1686,147,0.322000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 b d}+\frac{2 A \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{2 A \sqrt{a +b \tan \left(d x +c \right)}\, a}{d}-\frac{2 b B \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 b d}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 b d}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 b d}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 b d}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/5*B*(a+b*tan(d*x+c))^(5/2)/b/d+2/3*A*(a+b*tan(d*x+c))^(3/2)/d+2/d*A*(a+b*tan(d*x+c))^(1/2)*a-2*b*B*(a+b*tan(d*x+c))^(1/2)/d+1/4*b/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+b/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)-2*b/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-1/4*b/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/2/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/b/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-b/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)+2*b/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-b^2/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+b^2/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/2/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/b/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+1/4/b/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a-1/4/b/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a","B"
327,1,1665,126,0.250000," ","int((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d b}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d}+\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d b}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d b}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d}+\frac{2 b A \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{2 B \sqrt{a +b \tan \left(d x +c \right)}\, a}{d}-\frac{b^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d b}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/2/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)-2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/2/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+2/d*b*A*(a+b*tan(d*x+c))^(1/2)+2/d*B*(a+b*tan(d*x+c))^(1/2)*a-1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/4/d*b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/4/d*b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)+2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+2/3*B*(a+b*tan(d*x+c))^(3/2)/d+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a","B"
328,1,41721,126,3.302000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
329,1,69534,143,3.390000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
330,1,102706,185,4.095000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
331,1,145176,240,5.206000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
332,1,2469,216,0.386000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","-\frac{3 b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d}-\frac{3 b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d}+\frac{b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b}-\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 B \,a^{2} \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{2 A \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d b}+\frac{2 b^{2} B \sqrt{a +b \tan \left(d x +c \right)}}{d}-\frac{2 b A \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{9}{2}}}{9 d \,b^{2}}-\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3 d}-\frac{3 \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d}+\frac{3 \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 a B \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d \,b^{2}}-\frac{b^{2} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 d b}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 d b}-\frac{4 b A a \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{b^{2} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{2 d}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{2 d}+\frac{3 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}"," ",0,"-3/4/d*b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-3/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+3/4/d*b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)-1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)-3/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+1/4/d*b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a-2/d*B*a^2*(a+b*tan(d*x+c))^(1/2)+2/7/d/b*A*(a+b*tan(d*x+c))^(7/2)+2/d*b^2*B*(a+b*tan(d*x+c))^(1/2)-2/3/d*b*A*(a+b*tan(d*x+c))^(3/2)+2/9/d/b^2*B*(a+b*tan(d*x+c))^(9/2)-2/3/d*B*(a+b*tan(d*x+c))^(3/2)*a-3/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+3/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3-2/7/d/b^2*a*B*(a+b*tan(d*x+c))^(7/2)-1/4/d*b^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^2+1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^2-4/d*b*A*a*(a+b*tan(d*x+c))^(1/2)+1/4/d*b^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/4/d*b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/2/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a^2+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a^2-1/2/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+3/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+3/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-2/5*B*(a+b*tan(d*x+c))^(5/2)/d","B"
333,1,2426,181,0.338000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\frac{3 \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d}-\frac{3 \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d}+\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 b d}-\frac{2 b B \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{2 b^{2} A \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 b d}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 b d}+\frac{2 A \sqrt{a +b \tan \left(d x +c \right)}\, a^{2}}{d}+\frac{2 A \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3 d}+\frac{b^{2} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{2} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 b B \sqrt{a +b \tan \left(d x +c \right)}\, a}{d}+\frac{b^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 b d}-\frac{b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{2 d}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{2 d}-\frac{3 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 b^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 b d}-\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}+\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}-\frac{3 b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 A \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}"," ",0,"3/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-3/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+2/7*B*(a+b*tan(d*x+c))^(7/2)/b/d-2/3*b*B*(a+b*tan(d*x+c))^(3/2)/d-2*b^2/d*A*(a+b*tan(d*x+c))^(1/2)+2*b/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3-2*b/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a+1/4/b/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^2-1/4/b/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^2+2/d*A*(a+b*tan(d*x+c))^(1/2)*a^2+2/3/d*A*(a+b*tan(d*x+c))^(3/2)*a+1/4*b^2/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3-1/4*b^2/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+b^3/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-b^3/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-4*b/d*B*(a+b*tan(d*x+c))^(1/2)*a+b^2/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)+3/4*b/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/b/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-b^2/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)+1/2/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/2/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-3*b/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+3*b/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+3*b^2/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-3*b^2/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/4/b/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4*b/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/4*b/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-3/4*b/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a^2+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a^2+2/5*A*(a+b*tan(d*x+c))^(5/2)/d","B"
334,1,2405,160,0.260000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\frac{3 b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d}+\frac{3 b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d}-\frac{b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b}+\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 B \,a^{2} \sqrt{a +b \tan \left(d x +c \right)}}{d}-\frac{2 b^{2} B \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{2 b A \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3 d}+\frac{3 \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d}-\frac{3 \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{2} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 d b}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 d b}+\frac{4 b A a \sqrt{a +b \tan \left(d x +c \right)}}{d}-\frac{b^{2} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{2 d}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{2 d}-\frac{3 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 b^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}"," ",0,"3/4/d*b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+3/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-3/4/d*b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)+1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)+3/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-1/4/d*b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a+2/d*B*a^2*(a+b*tan(d*x+c))^(1/2)-2/d*b^2*B*(a+b*tan(d*x+c))^(1/2)+2/3/d*b*A*(a+b*tan(d*x+c))^(3/2)+2/3/d*B*(a+b*tan(d*x+c))^(3/2)*a+3/4/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-3/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3+1/4/d*b^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^2-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^2+4/d*b*A*a*(a+b*tan(d*x+c))^(1/2)-1/4/d*b^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/4/d*b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/2/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a^2-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a^2+1/2/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-3/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-3/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+2/5*B*(a+b*tan(d*x+c))^(5/2)/d","B"
335,1,55566,152,5.819000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
336,1,88645,168,4.815000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
337,1,128221,186,4.795000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
338,1,171974,239,6.057000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
339,1,227162,300,7.241000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
340,1,1375,127,0.332000," ","int((-a+b*tan(d*x+c))*(a+b*tan(d*x+c))^(5/2),x)","\frac{2 b \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}-\frac{2 b \,a^{2} \sqrt{a +b \tan \left(d x +c \right)}}{d}-\frac{2 b^{3} \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{3}}{4 d b}+\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b}+\frac{b^{3} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{3}}{4 d b}-\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b}-\frac{b^{3} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/5*b*(a+b*tan(d*x+c))^(5/2)/d-2/d*b*a^2*(a+b*tan(d*x+c))^(1/2)-2/d*b^3*(a+b*tan(d*x+c))^(1/2)+1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^3+1/4/d*b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+1/4/d*b^3*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-2/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*(a^2+b^2)^(1/2)*a^2+1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*(a^2+b^2)^(1/2)-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^3-1/4/d*b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4-1/4/d*b^3*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+2/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*(a^2+b^2)^(1/2)*a^2-1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*(a^2+b^2)^(1/2)","B"
341,1,986,333,0.289000," ","int((-a+b*tan(d*x+c))*(a+b*tan(d*x+c))^(3/2),x)","\frac{2 b \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{4 d b}-\frac{b \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{4 d}-\frac{b \,a^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) a^{2}}{4 d b}+\frac{b \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{4 d}-\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right)}{4 d b}+\frac{b \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right)}{4 d}+\frac{b \,a^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{2}}{4 d b}-\frac{b \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right)}{4 d}+\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/3*b*(a+b*tan(d*x+c))^(3/2)/d-1/4/d/b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))-1/4/d*b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))-1/d*b*a^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/4/d/b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*a^2+1/4/d*b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))-1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/4/d/b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))+1/4/d*b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))+1/d*b*a^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/4/d/b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a^2-1/4/d*b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))+1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))","B"
342,1,2285,341,0.303000," ","int((-a+b*tan(d*x+c))*(a+b*tan(d*x+c))^(1/2),x)","\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)}-\frac{2 b^{5} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b^{5} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{6}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{4 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{5 b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{2 b \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)}-\frac{5 b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)}-\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{b^{3} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{6}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"1/2/d*b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/d*b^3/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/4/d*b^3/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b^3/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/4/d*b^3/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2/d*b^5/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+2/d*b^5/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^6+4/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+5/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+1/4/d/b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5+2*b*(a+b*tan(d*x+c))^(1/2)/d+1/2/d*b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-5/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+1/4/d/b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4-1/4/d/b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4-1/2/d*b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/4/d/b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5-1/2/d*b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*b^3/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4-2/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+1/4/d*b^3/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+2/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^6-4/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4","B"
343,1,4107,183,0.316000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"2/5/d/b^3*B*(a+b*tan(d*x+c))^(5/2)+2/3/d/b^2*A*(a+b*tan(d*x+c))^(3/2)+1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/d/b^2/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4+1/d*b^2/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/d/b^2*(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/4/d/b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+2/d/b^3*B*a^2*(a+b*tan(d*x+c))^(1/2)-2/d/b^2*A*(a+b*tan(d*x+c))^(1/2)*a+1/4/d*b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/b^2/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3-1/d/b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4-1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/4/d/b^2/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/d/b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4-1/4/d/b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/d/b^2*(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/4/d/b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d/b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/4/d/b^2/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/d*b^2/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4-4/3/d/b^3*B*(a+b*tan(d*x+c))^(3/2)*a-1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/4/d/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-1/4/d/b^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d/b^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d*b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/4/d*b^2/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/4/d*b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/4/d*b^2/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3+1/4/d/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3-1/4/d/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-2*B*(a+b*tan(d*x+c))^(1/2)/b/d","B"
344,1,4040,140,0.328000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/d/b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4+1/4/d/b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d*b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d*b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-1/4/d/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4+1/d/b^2*(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-1/d/b^2/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3+2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-1/4/d*b^2/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/4/d/b^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/4/d/b^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/d*b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/4/d*b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/4/d*b^2/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4-1/d/b^2*(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+1/d/b^2/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3+1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-1/4/d/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*A+1/d*b^2/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*B-1/4/d/b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/d/b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4+1/4/d/b^2/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d/b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/b^2/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d/b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*A-1/d*b^2/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*B+2/d/b*A*(a+b*tan(d*x+c))^(1/2)-1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3*B-2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/4/d/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3*B+2/3/d/b^2*B*(a+b*tan(d*x+c))^(3/2)-2/d/b^2*B*(a+b*tan(d*x+c))^(1/2)*a","B"
345,1,3997,104,0.289000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/d/b^2/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4-1/d*b^2/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-1/d/b^2*(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-1/4/d/b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/b^2/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3+1/d/b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4+1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/4/d/b^2/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/d/b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4+1/4/d/b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/b^2*(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/4/d/b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d*b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/4/d/b^2/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/d*b^2/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a+3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4+1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-1/4/d/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+1/4/d/b^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/b^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d*b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/4/d*b^2/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/4/d*b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/4/d*b^2/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3-1/4/d/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3+1/4/d/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+2*B*(a+b*tan(d*x+c))^(1/2)/b/d","B"
346,1,3976,84,0.258000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d/b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4-1/4/d/b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d*b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+1/4/d/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4-1/d/b^2*(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+1/d/b^2/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3-2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+1/4/d*b^2/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/4/d/b^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/4/d/b^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/d*b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/4/d*b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/4/d*b^2/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4+1/d/b^2*(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-1/d/b^2/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3-1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+1/4/d/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*A-1/d*b^2/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*B+1/4/d/b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/b^2/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4-1/4/d/b^2/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d/b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d*b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d/b^2/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d/b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*A+1/d*b^2/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*B+1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3*B+2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/4/d/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3*B","B"
347,1,33052,107,2.665000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
348,1,69579,143,3.411000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
349,1,111109,190,4.261000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
350,1,8025,236,0.373000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
351,1,7982,145,0.328000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
352,1,7956,121,0.294000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
353,1,7951,118,0.295000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
354,1,63947,145,3.387000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
355,1,119765,191,5.555000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
356,1,174426,247,6.310000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
357,1,12953,339,0.381000," ","int(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
358,1,12907,231,0.384000," ","int(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
359,1,12849,174,0.329000," ","int(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
360,1,12841,164,0.294000," ","int(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
361,1,12836,161,0.269000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
362,1,185602,194,10.447000," ","int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
363,1,339365,257,16.361000," ","int(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
364,1,467696,322,18.013000," ","int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
365,1,662,291,0.255000," ","int((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}-\frac{B \,a^{2} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d b \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}+\frac{B \left(a^{2}+b^{2}\right) \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d b \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}+\frac{B \,a^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d b \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}-\frac{B \left(a^{2}+b^{2}\right) \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d b \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d*B/b*a^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/d*B/b*(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d*B/b*a^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/d*B/b*(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))","B"
366,1,1575,327,0.247000," ","int((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d b \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{4}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d b \left(a^{2}+b^{2}\right)}-\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{4}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"1/4/d/b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/4/d*b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/4/d/b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4+3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/4/d/b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/4/d*b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/4/d/b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d*b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4-3/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-2/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B","B"
367,1,20195,97,1.960000," ","int(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
368,1,1955,103,0.256000," ","int((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\frac{B \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \left(a^{2}+b^{2}\right)^{2}}+\frac{B b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{B \,b^{3} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{B \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{B b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{B b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{B \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{B \,b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 B \,b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{4 B b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{B \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \left(a^{2}+b^{2}\right)^{2}}-\frac{B b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{B \,b^{3} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{B \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{B b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{B b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{B \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{B \,b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 B \,b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 B b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b B}{\left(a^{2}+b^{2}\right) d \sqrt{a +b \tan \left(d x +c \right)}}"," ",0,"1/4/d*B/b/(a^2+b^2)^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d*B*b/(a^2+b^2)^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d*B/b/(a^2+b^2)^(5/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+1/4/d*B*b^3/(a^2+b^2)^(5/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*B/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-1/d*B*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-1/d*B*b/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+1/d*B/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5-1/d*B*b^3/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+3/d*B*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+4/d*B*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-1/4/d*B/b/(a^2+b^2)^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*B*b/(a^2+b^2)^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d*B/b/(a^2+b^2)^(5/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4-1/4/d*B*b^3/(a^2+b^2)^(5/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*B/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+1/d*B*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+1/d*B*b/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-1/d*B/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5+1/d*B*b^3/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-3/d*B*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-4/d*B*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-2*b*B/(a^2+b^2)/d/(a+b*tan(d*x+c))^(1/2)","B"
369,1,39359,130,2.599000," ","int(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
370,1,1905,84,0.335000," ","int((-a+b*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \left(a^{2}+b^{2}\right)}-\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{b^{3} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{b^{3} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{4 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-1/4/d/b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*b/(a^2+b^2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d/b/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4-1/4/d*b^3/(a^2+b^2)^(3/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+1/d*b/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5+1/d*b^3/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-3/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-4/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+1/4/d/b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d*b/(a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/b/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+1/4/d*b^3/(a^2+b^2)^(3/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-1/d*b/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5-1/d*b^3/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+3/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+4/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3","B"
371,1,2291,112,0.312000," ","int((-a+b*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{6}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{4 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b^{5} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{5} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{3} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{2}}+\frac{3 b^{3} \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{3 b^{3} \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b^{3} \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{6}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{4 a b}{\left(a^{2}+b^{2}\right) d \sqrt{a +b \tan \left(d x +c \right)}}"," ",0,"-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4-2/d*b/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+1/2/d*b/(a^2+b^2)^(5/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/d*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+1/d/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^6+4/d*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+2/d*b^5/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-2/d*b^5/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/4/d*b^3/(a^2+b^2)^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/4/d*b^3/(a^2+b^2)^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/4/d/b/(a^2+b^2)^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+3/4/d*b^3/(a^2+b^2)^(5/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/b/(a^2+b^2)^(5/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5+1/d*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-4/d*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4-1/2/d*b/(a^2+b^2)^(5/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d/b/(a^2+b^2)^(5/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5-3/4/d*b^3/(a^2+b^2)^(5/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/b/(a^2+b^2)^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+2/d*b^3/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-2/d*b^3/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+2/d*b/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-1/d/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^6+4*a*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(1/2)","B"
372,1,3055,150,0.314000," ","int((-a+b*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/d*b^3/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)+1/d*b^5/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/4/d*b^5/(a^2+b^2)^(7/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/4/d*b^5/(a^2+b^2)^(7/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+6/d*b/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)*a^2-1/d*b^5/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-3/d*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-1/d/b/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^7+3/d*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+1/d/b/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^7+1/4/d/b/(a^2+b^2)^(7/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^6-5/4/d*b^3/(a^2+b^2)^(7/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-5/d*b^3/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+4/3*a*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-7/d*b^5/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-3/d*b/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+1/2/d*b/(a^2+b^2)^3*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/2/d*b/(a^2+b^2)^3*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+7/d*b^5/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+5/4/d*b^3/(a^2+b^2)^(7/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-2/d*b^3/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+3/4/d*b^3/(a^2+b^2)^3*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+2/d*b^3/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+1/4/d/b/(a^2+b^2)^3*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5-3/4/d*b^3/(a^2+b^2)^3*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/b/(a^2+b^2)^3*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5+5/4/d*b/(a^2+b^2)^(7/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+2/d*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+3/d*b/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5-5/4/d*b/(a^2+b^2)^(7/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4-2/d*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-3/d*b/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5-1/4/d/b/(a^2+b^2)^(7/2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^6+3/d*b/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4-1/d/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5+1/d/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5+5/d*b^3/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3","B"
373,1,1624,36,0.228000," ","int((1+I*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","-\frac{i \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) a}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}-\frac{i \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b^{2}}{d \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}-\frac{i \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{i \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a \,b^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{i \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{i \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{i \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{i \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{2} b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) b^{3}}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{i \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) b^{2}}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a b}{d \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2} b}{d \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b^{3}}{d \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*a-I/d/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b^2+1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*b-I/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a*b^2+1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+I/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a^2+I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a^3-1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))-1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a*b-1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a^2*b-1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*b^3+1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*b^2-1/d/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*b-1/d/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*b-1/d/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b^3","B"
374,1,1624,36,0.211000," ","int((1-I*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","-\frac{i \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{i \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) a}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}+\frac{\ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}-\frac{i \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{i \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) b^{2}}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{i \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b^{2}}{d \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{i \ln \left(b \tan \left(d x +c \right)+a +\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}-\frac{i \ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a \,b^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{i \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{2} b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{a +b \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \tan \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) b^{3}}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{i \arctan \left(\frac{2 \sqrt{a +b \tan \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a b}{d \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2} b}{d \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \tan \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b^{3}}{d \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a^2+1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*a+1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*b-I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a^3-1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*b^2+1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+I/d/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b^2+1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))-I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a*b^2-I/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a*b-1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*a^2*b-1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*b^3+I/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-1/d/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*b-1/d/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*b-1/d/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b^3","B"
375,1,54,25,0.177000," ","int((3+tan(x))/(4+3*tan(x))^(1/2),x)","\sqrt{2}\, \arctan \left(\frac{\left(2 \sqrt{4+3 \tan \left(x \right)}-3 \sqrt{2}\right) \sqrt{2}}{2}\right)+\sqrt{2}\, \arctan \left(\frac{\left(2 \sqrt{4+3 \tan \left(x \right)}+3 \sqrt{2}\right) \sqrt{2}}{2}\right)"," ",0,"2^(1/2)*arctan(1/2*(2*(4+3*tan(x))^(1/2)-3*2^(1/2))*2^(1/2))+2^(1/2)*arctan(1/2*(2*(4+3*tan(x))^(1/2)+3*2^(1/2))*2^(1/2))","B"
376,1,52,22,0.121000," ","int((1-3*tan(x))/(4+3*tan(x))^(1/2),x)","-\frac{\sqrt{2}\, \ln \left(9+3 \tan \left(x \right)-3 \sqrt{2}\, \sqrt{4+3 \tan \left(x \right)}\right)}{2}+\frac{\sqrt{2}\, \ln \left(9+3 \tan \left(x \right)+3 \sqrt{2}\, \sqrt{4+3 \tan \left(x \right)}\right)}{2}"," ",0,"-1/2*2^(1/2)*ln(9+3*tan(x)-3*2^(1/2)*(4+3*tan(x))^(1/2))+1/2*2^(1/2)*ln(9+3*tan(x)+3*2^(1/2)*(4+3*tan(x))^(1/2))","B"
377,1,142,71,0.322000," ","int((4-3*tan(b*x+a))/(4+3*tan(b*x+a))^(1/2),x)","-\frac{13 \sqrt{2}\, \ln \left(9+3 \tan \left(b x +a \right)-3 \sqrt{2}\, \sqrt{4+3 \tan \left(b x +a \right)}\right)}{20 b}+\frac{9 \sqrt{2}\, \arctan \left(\frac{\left(2 \sqrt{4+3 \tan \left(b x +a \right)}-3 \sqrt{2}\right) \sqrt{2}}{2}\right)}{10 b}+\frac{13 \sqrt{2}\, \ln \left(9+3 \tan \left(b x +a \right)+3 \sqrt{2}\, \sqrt{4+3 \tan \left(b x +a \right)}\right)}{20 b}+\frac{9 \sqrt{2}\, \arctan \left(\frac{\left(2 \sqrt{4+3 \tan \left(b x +a \right)}+3 \sqrt{2}\right) \sqrt{2}}{2}\right)}{10 b}"," ",0,"-13/20/b*2^(1/2)*ln(9+3*tan(b*x+a)-3*2^(1/2)*(4+3*tan(b*x+a))^(1/2))+9/10/b*2^(1/2)*arctan(1/2*(2*(4+3*tan(b*x+a))^(1/2)-3*2^(1/2))*2^(1/2))+13/20/b*2^(1/2)*ln(9+3*tan(b*x+a)+3*2^(1/2)*(4+3*tan(b*x+a))^(1/2))+9/10/b*2^(1/2)*arctan(1/2*(2*(4+3*tan(b*x+a))^(1/2)+3*2^(1/2))*2^(1/2))","A"
378,1,527,236,0.106000," ","int(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{2 b B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}+\frac{2 A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) b}{5 d}+\frac{2 a B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{2 a A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}-\frac{2 b B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}-\frac{2 A \left(\sqrt{\tan}\left(d x +c \right)\right) b}{d}-\frac{2 a B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}"," ",0,"2/7*b*B*tan(d*x+c)^(7/2)/d+2/5/d*A*tan(d*x+c)^(5/2)*b+2/5/d*a*B*tan(d*x+c)^(5/2)+2/3/d*a*A*tan(d*x+c)^(3/2)-2/3*b*B*tan(d*x+c)^(3/2)/d-2/d*A*tan(d*x+c)^(1/2)*b-2/d*a*B*tan(d*x+c)^(1/2)+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b","B"
379,1,497,216,0.102000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{2 b B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{2 A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b}{3 d}+\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a}{3 d}+\frac{2 A \left(\sqrt{\tan}\left(d x +c \right)\right) a}{d}-\frac{2 b B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d}-\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d}-\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}"," ",0,"2/5*b*B*tan(d*x+c)^(5/2)/d+2/3/d*A*tan(d*x+c)^(3/2)*b+2/3/d*B*tan(d*x+c)^(3/2)*a+2/d*A*tan(d*x+c)^(1/2)*a-2*b*B*tan(d*x+c)^(1/2)/d-1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","B"
380,1,467,195,0.106000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{2 b B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{2 A \left(\sqrt{\tan}\left(d x +c \right)\right) b}{d}+\frac{2 a B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}-\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}"," ",0,"2/3*b*B*tan(d*x+c)^(3/2)/d+2/d*A*tan(d*x+c)^(1/2)*b+2/d*a*B*tan(d*x+c)^(1/2)-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b","B"
381,1,437,175,0.101000," ","int((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\frac{2 b B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}+\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d}"," ",0,"2*b*B*tan(d*x+c)^(1/2)/d+1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a","B"
382,1,437,175,0.103000," ","int((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","-\frac{2 a A}{d \sqrt{\tan \left(d x +c \right)}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}+\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}"," ",0,"-2*a*A/d/tan(d*x+c)^(1/2)+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/4/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b","B"
383,1,467,195,0.115000," ","int((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","-\frac{2 A b}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 a B}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 a A}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d}-\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}"," ",0,"-2/d/tan(d*x+c)^(1/2)*A*b-2/d/tan(d*x+c)^(1/2)*a*B-2/3*a*A/d/tan(d*x+c)^(3/2)-1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
384,1,497,216,0.112000," ","int((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","-\frac{2 A b}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 a B}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 a A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 B b}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 a A}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}-\frac{a B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{a A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{a A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d}"," ",0,"-2/3/d/tan(d*x+c)^(3/2)*A*b-2/3/d/tan(d*x+c)^(3/2)*a*B+2*a*A/d/tan(d*x+c)^(1/2)-2/d/tan(d*x+c)^(1/2)*B*b-2/5*a*A/d/tan(d*x+c)^(5/2)-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d*a*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/4/d*a*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2/d*a*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b","B"
385,1,858,348,0.110000," ","int(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\frac{4 A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) a b}{5 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{2 b^{2} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{2 b^{2} B \left(\tan^{\frac{9}{2}}\left(d x +c \right)\right)}{9 d}-\frac{2 B \,a^{2} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{2 A \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right) b^{2}}{7 d}-\frac{2 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) b^{2}}{5 d}+\frac{2 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) a^{2}}{5 d}-\frac{2 A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{2}}{3 d}+\frac{2 a^{2} A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{4 B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right) a b}{7 d}-\frac{4 A \left(\sqrt{\tan}\left(d x +c \right)\right) a b}{d}-\frac{4 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a b}{3 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}"," ",0,"4/7/d*B*tan(d*x+c)^(7/2)*a*b+4/5/d*A*tan(d*x+c)^(5/2)*a*b-1/2/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2-1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-4/3/d*B*tan(d*x+c)^(3/2)*a*b-4/d*A*tan(d*x+c)^(1/2)*a*b-2/5/d*B*tan(d*x+c)^(5/2)*b^2+2/5/d*B*tan(d*x+c)^(5/2)*a^2-2/3/d*A*tan(d*x+c)^(3/2)*b^2+2/3/d*a^2*A*tan(d*x+c)^(3/2)+2/9/d*b^2*B*tan(d*x+c)^(9/2)-2/d*B*a^2*tan(d*x+c)^(1/2)+2/7/d*A*tan(d*x+c)^(7/2)*b^2+1/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/2/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+1/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/2/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+2*b^2*B*tan(d*x+c)^(1/2)/d","B"
386,1,810,318,0.112000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{2 A \left(\sqrt{\tan}\left(d x +c \right)\right) b^{2}}{d}+\frac{2 a^{2} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{2}}{3 d}+\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a^{2}}{3 d}+\frac{2 b^{2} B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}+\frac{2 A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) b^{2}}{5 d}+\frac{4 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) a b}{5 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}-\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{4 A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a b}{3 d}-\frac{4 B \left(\sqrt{\tan}\left(d x +c \right)\right) a b}{d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}"," ",0,"1/2/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/2/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/2/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+4/5/d*B*tan(d*x+c)^(5/2)*a*b+1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+4/3/d*A*tan(d*x+c)^(3/2)*a*b-4/d*B*tan(d*x+c)^(1/2)*a*b-2/d*A*tan(d*x+c)^(1/2)*b^2+2/d*a^2*A*tan(d*x+c)^(1/2)-2/3/d*B*tan(d*x+c)^(3/2)*b^2+2/3/d*B*tan(d*x+c)^(3/2)*a^2+2/7/d*b^2*B*tan(d*x+c)^(7/2)+2/5/d*A*tan(d*x+c)^(5/2)*b^2-1/4/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b","B"
387,1,762,288,0.104000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\frac{2 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) b^{2}}{5 d}+\frac{2 A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{2}}{3 d}+\frac{4 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a b}{3 d}+\frac{4 A \left(\sqrt{\tan}\left(d x +c \right)\right) a b}{d}+\frac{2 B \,a^{2} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 b^{2} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}"," ",0,"2/5/d*B*tan(d*x+c)^(5/2)*b^2+2/3/d*A*tan(d*x+c)^(3/2)*b^2+4/3/d*B*tan(d*x+c)^(3/2)*a*b+4/d*A*tan(d*x+c)^(1/2)*a*b+2/d*B*a^2*tan(d*x+c)^(1/2)-2*b^2*B*tan(d*x+c)^(1/2)/d-1/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/2/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/2/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/2/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2-1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/2/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b","B"
388,1,710,258,0.105000," ","int((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{2}}{3 d}+\frac{2 A \left(\sqrt{\tan}\left(d x +c \right)\right) b^{2}}{d}+\frac{4 B \left(\sqrt{\tan}\left(d x +c \right)\right) a b}{d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}"," ",0,"2/3/d*B*tan(d*x+c)^(3/2)*b^2+2/d*A*tan(d*x+c)^(1/2)*b^2+4/d*B*tan(d*x+c)^(1/2)*a*b+1/2/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/4/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/2/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/2/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/2/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+1/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/4/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/2/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2","B"
389,1,692,244,0.115000," ","int((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\frac{2 b^{2} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} A}{d \sqrt{\tan \left(d x +c \right)}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}"," ",0,"2*b^2*B*tan(d*x+c)^(1/2)/d-2*a^2*A/d/tan(d*x+c)^(1/2)+1/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/2/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+1/2/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2-1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/2/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+1/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b","B"
390,1,710,249,0.115000," ","int((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","-\frac{4 a A b}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 a^{2} B}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 a^{2} A}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{a^{2} A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}-\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{a^{2} B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}"," ",0,"-4/d*a/tan(d*x+c)^(1/2)*A*b-2/d*a^2/tan(d*x+c)^(1/2)*B-2/3*a^2*A/d/tan(d*x+c)^(3/2)-1/2/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/d*a^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/2/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/2/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+1/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/2/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/2/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/d*a^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/2/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2","B"
391,1,762,279,0.112000," ","int((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","\frac{2 a^{2} A}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 A \,b^{2}}{d \sqrt{\tan \left(d x +c \right)}}-\frac{4 B a b}{d \sqrt{\tan \left(d x +c \right)}}-\frac{4 a A b}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 a^{2} B}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 a^{2} A}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{a^{2} B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{a^{2} A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d}"," ",0,"2*a^2*A/d/tan(d*x+c)^(1/2)-2/d/tan(d*x+c)^(1/2)*A*b^2-4/d/tan(d*x+c)^(1/2)*B*a*b-4/3/d*a/tan(d*x+c)^(3/2)*A*b-2/3/d*a^2/tan(d*x+c)^(3/2)*B-2/5*a^2*A/d/tan(d*x+c)^(5/2)-1/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/2/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/2/d*a^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d*a^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2-1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/2/d*a^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*a^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b","B"
392,1,1147,417,0.102000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a \,b^{2}}{d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{6 B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right) a \,b^{2}}{7 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}+\frac{2 A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a^{2} b}{d}+\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right) b^{3}}{d}+\frac{2 B \left(\tan^{\frac{9}{2}}\left(d x +c \right)\right) b^{3}}{9 d}-\frac{2 A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{3}}{3 d}+\frac{2 a^{3} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{6 B \left(\sqrt{\tan}\left(d x +c \right)\right) a^{2} b}{d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a^{3}}{3 d}-\frac{2 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) b^{3}}{5 d}+\frac{2 A \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right) b^{3}}{7 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{6 A \left(\sqrt{\tan}\left(d x +c \right)\right) a \,b^{2}}{d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{6 A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) a \,b^{2}}{5 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}+\frac{6 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) a^{2} b}{5 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}+\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}"," ",0,"-6/d*A*tan(d*x+c)^(1/2)*a*b^2-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-2/d*B*tan(d*x+c)^(3/2)*a*b^2+3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+6/7/d*B*tan(d*x+c)^(7/2)*a*b^2+2/d*B*tan(d*x+c)^(1/2)*b^3+2/3/d*B*tan(d*x+c)^(3/2)*a^3-2/5/d*B*tan(d*x+c)^(5/2)*b^3+2/7/d*A*tan(d*x+c)^(7/2)*b^3+2/9/d*B*tan(d*x+c)^(9/2)*b^3-2/3/d*A*tan(d*x+c)^(3/2)*b^3-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+6/5/d*A*tan(d*x+c)^(5/2)*a*b^2-1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+2/d*A*tan(d*x+c)^(3/2)*a^2*b-6/d*B*tan(d*x+c)^(1/2)*a^2*b+6/5/d*B*tan(d*x+c)^(5/2)*a^2*b+1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+2*a^3*A*tan(d*x+c)^(1/2)/d+3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+3/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+3/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b","B"
393,1,1077,379,0.102000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}+\frac{6 A \left(\sqrt{\tan}\left(d x +c \right)\right) a^{2} b}{d}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}+\frac{2 A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a \,b^{2}}{d}+\frac{2 A \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) b^{3}}{5 d}+\frac{2 B \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right) b^{3}}{7 d}-\frac{2 A \left(\sqrt{\tan}\left(d x +c \right)\right) b^{3}}{d}+\frac{2 a^{3} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{6 B \left(\sqrt{\tan}\left(d x +c \right)\right) a \,b^{2}}{d}-\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{3}}{3 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{6 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) a \,b^{2}}{5 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a^{2} b}{d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}"," ",0,"-3/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+3/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-3/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+2/d*B*tan(d*x+c)^(3/2)*a^2*b+3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-2/3/d*B*tan(d*x+c)^(3/2)*b^3+2/5/d*A*tan(d*x+c)^(5/2)*b^3+2/7/d*B*tan(d*x+c)^(7/2)*b^3-2/d*A*tan(d*x+c)^(1/2)*b^3+2/d*A*tan(d*x+c)^(3/2)*a*b^2+1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-6/d*B*tan(d*x+c)^(1/2)*a*b^2+6/5/d*B*tan(d*x+c)^(5/2)*a*b^2+1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+6/d*A*tan(d*x+c)^(1/2)*a^2*b+1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+2*a^3*B*tan(d*x+c)^(1/2)/d-3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b","B"
394,1,1007,340,0.121000," ","int((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","-\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a \,b^{2}}{d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}+\frac{2 A \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{3}}{3 d}-\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right) b^{3}}{d}+\frac{6 B \left(\sqrt{\tan}\left(d x +c \right)\right) a^{2} b}{d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{2 B \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) b^{3}}{5 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{6 A \left(\sqrt{\tan}\left(d x +c \right)\right) a \,b^{2}}{d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}"," ",0,"6/d*A*tan(d*x+c)^(1/2)*a*b^2+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+2/d*B*tan(d*x+c)^(3/2)*a*b^2-3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-2/d*B*tan(d*x+c)^(1/2)*b^3+2/5/d*B*tan(d*x+c)^(5/2)*b^3+2/3/d*A*tan(d*x+c)^(3/2)*b^3+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+6/d*B*tan(d*x+c)^(1/2)*a^2*b-1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b","B"
395,1,971,338,0.111000," ","int((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}+\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}-\frac{2 A \,a^{3}}{d \sqrt{\tan \left(d x +c \right)}}+\frac{2 A \left(\sqrt{\tan}\left(d x +c \right)\right) b^{3}}{d}+\frac{6 B \left(\sqrt{\tan}\left(d x +c \right)\right) a \,b^{2}}{d}+\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{3}}{3 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}"," ",0,"3/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+3/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+3/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+2/3/d*B*tan(d*x+c)^(3/2)*b^3+2/d*A*tan(d*x+c)^(1/2)*b^3-2/d*A*a^3/tan(d*x+c)^(1/2)-1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+6/d*B*tan(d*x+c)^(1/2)*a*b^2-1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b","B"
396,1,971,332,0.118000," ","int((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}+\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right) b^{3}}{d}-\frac{2 a^{3} B}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 A \,a^{3}}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{6 a^{2} A b}{d \sqrt{\tan \left(d x +c \right)}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}+\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}"," ",0,"-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-2/d*a^3/tan(d*x+c)^(1/2)*B-2/3/d*A*a^3/tan(d*x+c)^(3/2)+2/d*B*tan(d*x+c)^(1/2)*b^3-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-6/d*a^2/tan(d*x+c)^(1/2)*A*b-1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+3/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+3/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b","B"
397,1,1007,340,0.108000," ","int((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","-\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}-\frac{2 a^{2} A b}{d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d}-\frac{2 a^{3} B}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 A \,a^{3}}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}+\frac{2 A \,a^{3}}{d \sqrt{\tan \left(d x +c \right)}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{6 a A \,b^{2}}{d \sqrt{\tan \left(d x +c \right)}}-\frac{6 a^{2} B b}{d \sqrt{\tan \left(d x +c \right)}}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}"," ",0,"-3/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+3/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-3/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-2/d*a^2/tan(d*x+c)^(3/2)*A*b+3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-2/3/d*a^3/tan(d*x+c)^(3/2)*B-2/5/d*A*a^3/tan(d*x+c)^(5/2)+2/d*A*a^3/tan(d*x+c)^(1/2)+1/4/d*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/4/d*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/4/d*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/4/d*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-6/d*a/tan(d*x+c)^(1/2)*A*b^2-6/d*a^2/tan(d*x+c)^(1/2)*B*b-3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b","B"
398,1,666,281,0.414000," ","int(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 b d}+\frac{2 A \left(\sqrt{\tan}\left(d x +c \right)\right)}{d b}-\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right) a}{d \,b^{2}}-\frac{2 a^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d b \left(a^{2}+b^{2}\right) \sqrt{a b}}+\frac{2 a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \,b^{2} \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"2/3*B*tan(d*x+c)^(3/2)/b/d+2/d/b*A*tan(d*x+c)^(1/2)-2/d/b^2*B*tan(d*x+c)^(1/2)*a-2/d/b*a^3/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+2/d/b^2*a^4/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b","B"
399,1,628,257,0.423000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{b d}+\frac{2 a^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{2 a^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d b \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"2*B*tan(d*x+c)^(1/2)/b/d+2/d*a^2/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-2/d/b*a^3/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a","B"
400,1,607,240,0.444000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","-\frac{2 a \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A b}{d \left(a^{2}+b^{2}\right) \sqrt{a b}}+\frac{2 a^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right) \sqrt{a b}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"-2/d*a/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A*b+2/d*a^2/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b","B"
401,1,607,240,0.376000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x)","\frac{2 b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{2 b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) a B}{d \left(a^{2}+b^{2}\right) \sqrt{a b}}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}"," ",0,"2/d*b^2/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-2/d*b/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*a*B+1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a","B"
402,1,628,257,0.345000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x)","-\frac{2 b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d a \left(a^{2}+b^{2}\right) \sqrt{a b}}+\frac{2 b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{2 A}{a d \sqrt{\tan \left(d x +c \right)}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"-2/d/a*b^3/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+2/d*b^2/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-2*A/a/d/tan(d*x+c)^(1/2)-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b","B"
403,1,666,281,0.359000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x)","\frac{2 b^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \,a^{2} \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{2 b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d a \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{2 A}{3 a d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 A b}{d \,a^{2} \sqrt{\tan \left(d x +c \right)}}-\frac{2 B}{a d \sqrt{\tan \left(d x +c \right)}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}"," ",0,"2/d/a^2*b^4/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-2/d/a*b^3/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-2/3*A/a/d/tan(d*x+c)^(3/2)+2/d/a^2/tan(d*x+c)^(1/2)*A*b-2*B/a/d/tan(d*x+c)^(1/2)-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d/(a^2+b^2)*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/4/d/(a^2+b^2)*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a","B"
404,1,1160,394,0.441000," ","int(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a^{4} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{5} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d b \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,b^{2}}+\frac{5 a^{2} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{3 a^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a^{2} b \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{7 a^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d*a^2*b/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A-1/d*a^4/b/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A+1/d*a^5/b^2/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B+1/d*a^4/b/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+5/d*a^2*b/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-3/d*a^5/b^2/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/2/d/(a^2+b^2)^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/2/d/(a^2+b^2)^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+2/d*B/b^2*tan(d*x+c)^(1/2)+1/d*a^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B-7/d*a^3/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2-1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2","B"
405,1,1136,351,0.456000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a^{2} b \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a \,b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right)^{2} b \sqrt{a b}}+\frac{5 a^{2} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{a^{4} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2} b \left(a +b \tan \left(d x +c \right)\right)}+\frac{a \,b^{2} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{a^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"5/d*a^2/(a^2+b^2)^2*b/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/d*a^4/(a^2+b^2)^2/b*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B+1/d*a/(a^2+b^2)^2*b^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A+1/2/d/(a^2+b^2)^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/d*a^2/(a^2+b^2)^2*b*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B-3/d*a/(a^2+b^2)^2*b^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+1/d*a^4/(a^2+b^2)^2/b/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/2/d/(a^2+b^2)^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/d*a^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A+1/d*a^3/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2","B"
406,1,1128,351,0.460000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{2} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a^{2} b \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{a^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{\arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}"," ",0,"-3/d/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B*a*b^2+1/d/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B*a*b^2+1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d*a^2*b/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A-3/d*a^2*b/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+1/2/d/(a^2+b^2)^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+1/2/d/(a^2+b^2)^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d*a^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B+1/d*a^3/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2-1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/d/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A*b^3+1/d/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A*b^3","B"
407,1,1136,351,0.370000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x)","-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a^{2} b \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{5 a \,b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{3 a^{2} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{a \,b^{2} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{b^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right)^{2} a \sqrt{a b}}+\frac{b^{4} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{2} a \left(a +b \tan \left(d x +c \right)\right)}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"-3/d*a^2/(a^2+b^2)^2*b/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+1/d*a/(a^2+b^2)^2*b^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A-1/2/d/(a^2+b^2)^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/d*a^2/(a^2+b^2)^2*b*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B+5/d*a/(a^2+b^2)^2*b^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+1/d*b^4/(a^2+b^2)^2/a/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+1/d*b^4/(a^2+b^2)^2/a*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A+1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/2/d/(a^2+b^2)^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+1/d*b^3/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/d*b^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2-1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2-1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2","B"
408,1,1160,395,0.349000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x)","-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{3 b^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right)^{2} a^{2} \sqrt{a b}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{4} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2} a \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 A}{d \,a^{2} \sqrt{\tan \left(d x +c \right)}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{5} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{2} a^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right)^{2} a \sqrt{a b}}+\frac{5 \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{7 \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}"," ",0,"-3/d*b^5/(a^2+b^2)^2/a^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+5/d/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B*a*b^2-1/d*b^5/(a^2+b^2)^2/a^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A+1/d*b^4/(a^2+b^2)^2/a/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+1/d*b^4/(a^2+b^2)^2/a*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B+1/d/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B*a*b^2-2/d*A/a^2/tan(d*x+c)^(1/2)-1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/2/d/(a^2+b^2)^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/2/d/(a^2+b^2)^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2-1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/d/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A*b^3-7/d/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A*b^3","B"
409,1,1198,447,0.367000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x)","\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{9 b^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \left(a^{2}+b^{2}\right)^{2} a \sqrt{a b}}+\frac{4 A b}{d \,a^{3} \sqrt{\tan \left(d x +c \right)}}-\frac{2 A}{3 d \,a^{2} \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 B}{d \,a^{2} \sqrt{\tan \left(d x +c \right)}}+\frac{b^{4} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d \left(a^{2}+b^{2}\right)^{2} a \left(a +b \tan \left(d x +c \right)\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{5} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{6} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{d \,a^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 b^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \,a^{2} \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{5 b^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{d \,a^{3} \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a b}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{7 b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"-1/d*b^5/a^2/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B+1/d*b^6/a^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A-3/d*b^5/a^2/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+5/d*b^6/a^3/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+1/2/d/(a^2+b^2)^2*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b+9/d*b^4/(a^2+b^2)^2/a/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+1/d*b^4/(a^2+b^2)^2/a*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*A-1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+4/d/a^3/tan(d*x+c)^(1/2)*A*b-2/3/d*A/a^2/tan(d*x+c)^(3/2)-2/d/a^2/tan(d*x+c)^(1/2)*B+1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b+1/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b-1/2/d/(a^2+b^2)^2*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b-7/d*b^3/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/d*b^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*B-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d/(a^2+b^2)^2*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2-1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2+1/4/d/(a^2+b^2)^2*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^2","B"
410,1,1864,548,0.465000," ","int(tan(d*x+c)^(7/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\frac{3 a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a^{7} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \,b^{2} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{11 a^{3} b^{2} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{9 a^{7} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \,b^{2} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{17 a^{3} b^{2} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{15 a^{4} b B \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \,b^{2} \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{23 a^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{2 d b \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{63 a^{3} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{11 a^{6} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{2 d b \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{5 a^{6} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d b \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{9 a^{4} b \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{13 a^{2} b^{3} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{35 a^{2} b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{15 a^{7} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d \,b^{3} \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{7 a^{8} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \,b^{3} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{7 a^{5} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,b^{3}}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{13 a^{5} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"-3/4/d*a^7/b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*A*tan(d*x+c)^(1/2)-11/4/d*a^3*b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*A*tan(d*x+c)^(1/2)+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+9/4/d*a^7/b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*B+17/4/d*a^3*b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*B-3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+15/4/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*B*tan(d*x+c)^(1/2)+3/4/d*a^6/b^2/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-23/2/d*a^5/b/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-63/4/d*a^3*b/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+35/4/d*a^2*b^2/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-15/4/d*a^7/b^3/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+7/4/d*a^8/b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*B*tan(d*x+c)^(1/2)+11/2/d*a^6/b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*B*tan(d*x+c)^(1/2)-5/4/d*a^6/b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A-9/2/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A-13/4/d*a^2*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-7/2/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*A*tan(d*x+c)^(1/2)+3/2/d*a^4/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+2/d*B/b^3*tan(d*x+c)^(1/2)+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+13/2/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*B","B"
411,1,1843,486,0.438000," ","int(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{5 a^{3} b^{2} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{9 a^{3} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{15 a \,b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{9 a \,b^{4} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{5 a^{6} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} b}-\frac{9 a^{4} b \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{13 a^{2} b^{3} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{11 a^{3} b^{2} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a^{4} b \left(\sqrt{\tan}\left(d x +c \right)\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{7 a^{2} b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 a^{7} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} b^{2}}+\frac{35 a^{2} b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{a^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} b \sqrt{a b}}+\frac{3 a^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} b^{2} \sqrt{a b}}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{a^{6} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} b}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{a^{5} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{7 a^{5} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/4/d*a^6/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/b*tan(d*x+c)^(1/2)*A-3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-11/4/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^2*tan(d*x+c)^(1/2)*B+3/2/d*a^4/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b*tan(d*x+c)^(1/2)*A+7/4/d*a^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^3*tan(d*x+c)^(1/2)*A-3/4/d*a^7/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/b^2*tan(d*x+c)^(1/2)*B+35/4/d*a^2/(a^2+b^2)^3*b^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+1/4/d*a^5/(a^2+b^2)^3/b/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+3/4/d*a^6/(a^2+b^2)^3/b^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+5/2/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^2*tan(d*x+c)^(3/2)*A+9/2/d*a^3/(a^2+b^2)^3*b/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-15/4/d*a/(a^2+b^2)^3*b^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+9/4/d*a/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^4*tan(d*x+c)^(3/2)*A-5/4/d*a^6/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/b*tan(d*x+c)^(3/2)*B-9/2/d*a^4/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b*tan(d*x+c)^(3/2)*B-13/4/d*a^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^3*tan(d*x+c)^(3/2)*B-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/4/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A-7/2/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*B+3/2/d*a^4/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3-1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3","B"
412,1,1835,485,0.429000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\frac{3 a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{a^{3} b^{2} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{9 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a \,b^{4} B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{5 a^{3} b^{2} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 a^{4} b B \left(\sqrt{\tan}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{a^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d b \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{9 a^{3} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{15 b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) a B}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{3 a \,b^{4} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{7 a^{2} b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{6} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d b \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a^{4} b \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{2} b^{3} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{13 a^{2} b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 b^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{5 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A \,b^{5}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{5 a^{5} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{a^{5} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"1/2/d*a^3*b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*A*tan(d*x+c)^(1/2)-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-15/4/d/(a^2+b^2)^3*b^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*a*B-3/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*a*b^4*tan(d*x+c)^(1/2)*A+7/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*a^2*b^3*tan(d*x+c)^(1/2)*B+5/2/d*a^3*b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*B+3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*B*tan(d*x+c)^(1/2)+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+9/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*a*b^4*B+1/4/d*a^5/b/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+9/2/d*a^3*b/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-13/2/d*a^2*b^2/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/4/d*a^6/b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*B*tan(d*x+c)^(1/2)+3/4/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A-1/2/d*a^2*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/4/d/(a^2+b^2)^3*b^4/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-5/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A*b^5+5/4/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*A*tan(d*x+c)^(1/2)+3/4/d*a^4/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3-1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/4/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*B","B"
413,1,1835,483,0.454000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{b^{6} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} a}-\frac{7 a^{3} b^{2} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{15 a^{3} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{9 a \,b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a \,b^{4} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a^{4} b \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{2} b^{3} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{3} b^{2} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{9 a^{4} b \left(\sqrt{\tan}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{5 a^{2} b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{13 a^{2} b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A \,b^{5}}{4 d \left(a^{2}+b^{2}\right)^{3} a \sqrt{a b}}-\frac{3 \left(\sqrt{\tan}\left(d x +c \right)\right) a \,b^{4} B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{5 a^{5} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{5 b^{5} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) A \,b^{5}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) b^{4} B}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+1/2/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^2*tan(d*x+c)^(1/2)*B-9/4/d*a^4/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b*tan(d*x+c)^(1/2)*A-5/2/d*a^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^3*tan(d*x+c)^(1/2)*A-13/2/d*a^2/(a^2+b^2)^3*b^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-7/4/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^2*tan(d*x+c)^(3/2)*A-15/4/d*a^3/(a^2+b^2)^3*b/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+9/2/d*a/(a^2+b^2)^3*b^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^6/a*tan(d*x+c)^(3/2)*A-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/2/d*a/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^4*tan(d*x+c)^(3/2)*A+3/4/d*a^4/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b*tan(d*x+c)^(3/2)*B-1/2/d*a^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^3*tan(d*x+c)^(3/2)*B+1/4/d/(a^2+b^2)^3/a/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A*b^5-3/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*a*b^4*B+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+5/4/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*B+3/4/d*a^4/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3-1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-5/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^5*tan(d*x+c)^(3/2)*B-1/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*A*b^5+3/4/d/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*b^4*B+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3","B"
414,1,1843,486,0.476000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x)","\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{13 a^{3} b^{2} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{5 b^{6} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} a}+\frac{3 b^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} a^{2} \sqrt{a b}}-\frac{3 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a \,b^{4} B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{b^{6} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} a}-\frac{7 a^{3} b^{2} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{9 a^{4} b B \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{15 a^{3} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{b^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} a \sqrt{a b}}+\frac{9 b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) a B}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{9 a \,b^{4} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{5 a^{2} b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 b^{7} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} a^{2}}+\frac{11 a^{2} b^{3} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{35 a^{2} b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 b^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{7 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A \,b^{5}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{b^{5} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/4/d*b^6/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/a*tan(d*x+c)^(3/2)*B+1/4/d*b^5/(a^2+b^2)^3/a/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+5/4/d*b^6/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/a*tan(d*x+c)^(1/2)*A+3/4/d*b^6/(a^2+b^2)^3/a^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+13/4/d*a^3*b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*A*tan(d*x+c)^(1/2)+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b+9/2/d/(a^2+b^2)^3*b^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*a*B+9/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*a*b^4*tan(d*x+c)^(1/2)*A-5/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*a^2*b^3*tan(d*x+c)^(1/2)*B+3/4/d*b^7/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/a^2*tan(d*x+c)^(3/2)*A-7/4/d*a^3*b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*B-3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-9/4/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*B*tan(d*x+c)^(1/2)-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*a*b^4*B-15/4/d*a^3*b/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+35/4/d*a^2*b^2/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+11/4/d*a^2*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-1/4/d*b^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*B+3/2/d/(a^2+b^2)^3*b^4/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A+7/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A*b^5+1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3","B"
415,1,1864,549,0.424000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x)","-\frac{2 A}{d \,a^{3} \sqrt{\tan \left(d x +c \right)}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{7 b^{5} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{11 b^{6} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} a}+\frac{5 b^{6} B \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \left(a^{2}+b^{2}\right)^{3} a \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 b^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} a^{2} \sqrt{a b}}-\frac{63 a \,b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 b^{7} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} a^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{7 b^{8} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} a^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{15 b^{7} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} a^{3} \sqrt{a b}}-\frac{9 b^{7} A \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \left(a^{2}+b^{2}\right)^{3} a^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{15 a \,b^{4} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{11 a^{2} b^{3} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{13 a^{3} b^{2} \left(\sqrt{\tan}\left(d x +c \right)\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{17 a^{2} b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right) A}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{35 a^{2} b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{23 \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) A \,b^{5}}{2 d \left(a^{2}+b^{2}\right)^{3} a \sqrt{a b}}+\frac{9 \left(\sqrt{\tan}\left(d x +c \right)\right) a \,b^{4} B}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{13 \left(\sqrt{\tan}\left(d x +c \right)\right) A \,b^{5}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) b^{4} B}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{A \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a*b^2+13/4/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^2*tan(d*x+c)^(1/2)*B-17/4/d*a^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^3*tan(d*x+c)^(1/2)*A+35/4/d*a^2/(a^2+b^2)^3*b^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-63/4/d*a/(a^2+b^2)^3*b^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-2/d*A/a^3/tan(d*x+c)^(1/2)-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+5/4/d*b^6/(a^2+b^2)^3/a/(a+b*tan(d*x+c))^2*B*tan(d*x+c)^(1/2)+3/4/d*b^6/(a^2+b^2)^3/a^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+3/4/d*b^7/(a^2+b^2)^3/a^2/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*B-7/4/d*b^8/(a^2+b^2)^3/a^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*A-11/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^6/a*tan(d*x+c)^(3/2)*A-15/4/d*b^7/(a^2+b^2)^3/a^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A-9/4/d*b^7/(a^2+b^2)^3/a^2/(a+b*tan(d*x+c))^2*A*tan(d*x+c)^(1/2)+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-3/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^2*b-15/4/d*a/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^4*tan(d*x+c)^(3/2)*A+11/4/d*a^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^3*tan(d*x+c)^(3/2)*B-23/2/d/(a^2+b^2)^3/a/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*A*b^5+9/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*a*b^4*B-3/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3+1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/4/d/(a^2+b^2)^3*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b^3-1/4/d/(a^2+b^2)^3*A*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+7/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*b^5*tan(d*x+c)^(3/2)*B-13/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*A*b^5+3/2/d/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*b^4*B-1/2/d/(a^2+b^2)^3*A*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+1/2/d/(a^2+b^2)^3*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3","B"
416,1,118,124,0.127000," ","int(tan(d*x+c)^(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{2 B \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}-\frac{B \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}-\frac{B \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}"," ",0,"2/3*B*tan(d*x+c)^(3/2)/d-1/2*B*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)-1/2*B*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)-1/4*B/d*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))","A"
417,1,118,124,0.163000," ","int(tan(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{B \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}-\frac{B \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}"," ",0,"2*B*tan(d*x+c)^(1/2)/d-1/2*B*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)-1/2*B*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)-1/4*B/d*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))","A"
418,1,104,110,0.206000," ","int(tan(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{B \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}+\frac{B \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}"," ",0,"1/4*B/d*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2*B*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)+1/2*B*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)","A"
419,1,104,110,0.174000," ","int((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x)","\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}+\frac{B \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}+\frac{B \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}"," ",0,"1/4*B/d*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))+1/2*B*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)+1/2*B*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)","A"
420,1,118,124,0.141000," ","int((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x)","-\frac{2 B}{d \sqrt{\tan \left(d x +c \right)}}-\frac{B \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{B \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}"," ",0,"-2*B/d/tan(d*x+c)^(1/2)-1/2*B*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)-1/4*B/d*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2*B*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)","A"
421,1,118,124,0.138000," ","int((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x)","-\frac{2 B}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{B \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right)}{4 d}-\frac{B \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) \sqrt{2}}{2 d}"," ",0,"-2/3*B/d/tan(d*x+c)^(3/2)-1/2*B*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)-1/4*B/d*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))-1/2*B*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))/d*2^(1/2)","A"
422,1,325,216,0.333000," ","int(tan(d*x+c)^(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{2 B \left(\sqrt{\tan}\left(d x +c \right)\right)}{b d}-\frac{2 a^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d b \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}"," ",0,"2*B*tan(d*x+c)^(1/2)/b/d-2/d/b*a^3/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a","A"
423,1,305,199,0.341000," ","int(tan(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\frac{2 a^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"2/d*a^2/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b","A"
424,1,304,199,0.353000," ","int(tan(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","-\frac{2 b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) a B}{d \left(a^{2}+b^{2}\right) \sqrt{a b}}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"-2/d*b/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*a*B+1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b+1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a","A"
425,1,305,199,0.314000," ","int((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x)","\frac{2 b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d \left(a^{2}+b^{2}\right) \sqrt{a b}}+\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}+\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"2/d*b^2/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a+1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a+1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b","A"
426,1,325,216,0.293000," ","int((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x)","-\frac{2 b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) B}{d a \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{2 B}{a d \sqrt{\tan \left(d x +c \right)}}-\frac{B \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) b}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \left(d x +c \right)}\right) a}{4 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"-2/d/a*b^3/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*B-2*B/a/d/tan(d*x+c)^(1/2)-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b-1/4/d/(a^2+b^2)*B*2^(1/2)*ln((1-2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c))/(1+2^(1/2)*tan(d*x+c)^(1/2)+tan(d*x+c)))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a-1/2/d/(a^2+b^2)*B*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a","A"
427,1,2181075,220,1.031000," ","int((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
428,1,2179610,167,1.035000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
429,1,2175963,139,0.937000," ","int((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
430,1,2176205,128,0.951000," ","int((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
431,1,2178959,165,0.886000," ","int((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
432,1,2181012,210,0.940000," ","int((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
433,1,2184224,268,1.179000," ","int((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
434,1,2400808,273,1.081000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
435,1,2398581,223,1.086000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
436,1,2396041,170,1.054000," ","int((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
437,1,2394883,174,1.013000," ","int((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
438,1,2396482,162,0.999000," ","int((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
439,1,2398570,218,1.058000," ","int((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
440,1,2400710,265,1.045000," ","int((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
441,1,2404245,330,1.060000," ","int((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
442,1,2656933,341,1.188000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
443,1,2655805,266,1.368000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
444,1,2653581,216,1.150000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
445,1,2651144,203,1.096000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
446,1,2651450,200,1.121000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
447,1,2652302,207,1.120000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
448,1,2654465,263,1.187000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
449,1,2658134,326,1.211000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
450,1,2660696,402,1.408000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(13/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
451,1,1490268,211,0.886000," ","int((a+b*tan(d*x+c))^(5/2)*(3/2*b*B/a+B*tan(d*x+c))/tan(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
452,1,1889462,172,1.082000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
453,1,1886894,138,1.085000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
454,1,1879756,101,1.003000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
455,1,1887164,133,1.028000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
456,1,1888895,169,1.066000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
457,1,1891860,216,1.448000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
458,1,1560668,185,1.986000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
459,1,1559493,144,1.992000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
460,1,1559531,149,1.935000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
461,1,1560429,186,1.856000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
462,1,1563272,236,1.883000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
463,1,2979638,242,2.427000," ","int(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
464,1,2975178,210,2.511000," ","int(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
465,1,2976700,210,2.403000," ","int(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
466,1,2975233,213,2.458000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
467,1,2978232,263,2.394000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
468,1,2981039,315,3.263000," ","int((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
469,1,943902,127,0.744000," ","int(tan(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
470,1,940031,95,0.780000," ","int(tan(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
471,1,939796,91,0.960000," ","int((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
472,1,943929,124,0.750000," ","int((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
473,1,101,301,0.903000," ","int((a+b*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x)","\frac{3 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{2 d}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3} a +a^{2}+b^{2}\right)}{\sum}\frac{\left(\left(A b +a B \right) \textit{\_R}^{4}+B \left(-a^{2}-b^{2}\right) \textit{\_R} \right) \ln \left(\left(a +b \tan \left(d x +c \right)\right)^{\frac{1}{3}}-\textit{\_R} \right)}{\textit{\_R}^{5}-\textit{\_R}^{2} a}}{2 d}"," ",0,"3/2*B*(a+b*tan(d*x+c))^(2/3)/d+1/2/d*sum(((A*b+B*a)*_R^4+B*(-a^2-b^2)*_R)/(_R^5-_R^2*a)*ln((a+b*tan(d*x+c))^(1/3)-_R),_R=RootOf(_Z^6-2*_Z^3*a+a^2+b^2))","C"
474,1,99,301,0.330000," ","int((a+b*tan(d*x+c))^(1/3)*(A+B*tan(d*x+c)),x)","\frac{3 B \left(a +b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{d}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3} a +a^{2}+b^{2}\right)}{\sum}\frac{\left(\left(A b +a B \right) \textit{\_R}^{3}-a^{2} B -b^{2} B \right) \ln \left(\left(a +b \tan \left(d x +c \right)\right)^{\frac{1}{3}}-\textit{\_R} \right)}{\textit{\_R}^{5}-\textit{\_R}^{2} a}}{2 d}"," ",0,"3*B*(a+b*tan(d*x+c))^(1/3)/d+1/2/d*sum(((A*b+B*a)*_R^3-a^2*B-b^2*B)/(_R^5-_R^2*a)*ln((a+b*tan(d*x+c))^(1/3)-_R),_R=RootOf(_Z^6-2*_Z^3*a+a^2+b^2))","C"
475,1,72,283,0.319000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/3),x)","\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3} a +a^{2}+b^{2}\right)}{\sum}\frac{\left(B \,\textit{\_R}^{4}+\left(A b -a B \right) \textit{\_R} \right) \ln \left(\left(a +b \tan \left(d x +c \right)\right)^{\frac{1}{3}}-\textit{\_R} \right)}{\textit{\_R}^{5}-\textit{\_R}^{2} a}}{2 d}"," ",0,"1/2/d*sum((B*_R^4+(A*b-B*a)*_R)/(_R^5-_R^2*a)*ln((a+b*tan(d*x+c))^(1/3)-_R),_R=RootOf(_Z^6-2*_Z^3*a+a^2+b^2))","C"
476,1,69,283,0.306000," ","int((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(2/3),x)","\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3} a +a^{2}+b^{2}\right)}{\sum}\frac{\left(B \,\textit{\_R}^{3}+A b -a B \right) \ln \left(\left(a +b \tan \left(d x +c \right)\right)^{\frac{1}{3}}-\textit{\_R} \right)}{\textit{\_R}^{5}-\textit{\_R}^{2} a}}{2 d}"," ",0,"1/2/d*sum((B*_R^3+A*b-B*a)/(_R^5-_R^2*a)*ln((a+b*tan(d*x+c))^(1/3)-_R),_R=RootOf(_Z^6-2*_Z^3*a+a^2+b^2))","C"
477,1,42,116,0.326000," ","int((-tan(f*x+e)+I)/(c+d*tan(f*x+e))^(1/3),x)","-\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{3}+i d -c \right)}{\sum}\frac{\ln \left(\left(c +d \tan \left(f x +e \right)\right)^{\frac{1}{3}}-\textit{\_R} \right)}{\textit{\_R}}}{f}"," ",0,"-1/f*sum(1/_R*ln((c+d*tan(f*x+e))^(1/3)-_R),_R=RootOf(_Z^3+I*d-c))","C"
478,1,72,231,0.309000," ","int((d-c*tan(f*x+e))/(c+d*tan(f*x+e))^(2/3),x)","-\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3} c +c^{2}+d^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{3} c -c^{2}-d^{2}\right) \ln \left(\left(c +d \tan \left(f x +e \right)\right)^{\frac{1}{3}}-\textit{\_R} \right)}{\textit{\_R}^{5}-\textit{\_R}^{2} c}}{2 f}"," ",0,"-1/2/f*sum((_R^3*c-c^2-d^2)/(_R^5-_R^2*c)*ln((c+d*tan(f*x+e))^(1/3)-_R),_R=RootOf(_Z^6-2*_Z^3*c+c^2+d^2))","C"
479,0,0,399,1.690000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{4} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x)","F"
480,0,0,263,1.441000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{3} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","F"
481,0,0,190,1.260000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{2} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","F"
482,0,0,123,1.979000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","F"
483,0,0,183,3.805000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{a +b \tan \left(d x +c \right)}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","F"
484,0,0,280,3.939000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +b \tan \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","F"
485,0,0,430,4.168000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +b \tan \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","F"
486,0,0,649,4.323000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +b \tan \left(d x +c \right)\right)^{4}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x)","F"
487,0,0,173,1.413000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","F"
488,0,0,169,1.379000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","F"
489,0,0,167,1.483000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \sqrt{a +b \tan \left(d x +c \right)}\, \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","F"
490,0,0,167,1.519000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(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)\right)}{\sqrt{a +b \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","F"
491,0,0,173,1.462000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","F"
492,0,0,173,1.448000," ","int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\int \frac{\left(\tan^{m}\left(d x +c \right)\right) \left(A +B \tan \left(d x +c \right)\right)}{\left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","F"
493,0,0,175,1.362000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^m*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
494,0,0,381,1.208000," ","int(tan(d*x+c)^4*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{4}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^4*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
495,0,0,285,1.153000," ","int(tan(d*x+c)^3*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{3}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^3*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
496,0,0,213,1.062000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{2}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^2*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
497,0,0,162,0.941000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \tan \left(d x +c \right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
498,0,0,137,1.414000," ","int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
499,0,0,186,1.569000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \cot \left(d x +c \right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
500,0,0,224,1.122000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^2*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
501,0,0,282,1.622000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^3*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
502,1,2945,84,1.802000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/15*a/d*(15*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+18*A*2^(1/2)*cos(d*x+c)^3-15*A*2^(1/2)*cos(d*x+c)+15*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+15*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-15*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+5*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+5*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-15*I*B*2^(1/2)*cos(d*x+c)^3+15*I*B*2^(1/2)*cos(d*x+c)+15*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2+15*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-15*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)-15*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-15*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+15*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^3+15*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-15*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-15*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-15*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-15*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+15*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^3-15*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2+15*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+15*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-15*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c))*(cos(d*x+c)/sin(d*x+c))^(7/2)*sin(d*x+c)/cos(d*x+c)^4*2^(1/2)","C"
503,1,1538,64,1.806000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-\frac{a \left(-3 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+3 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-3 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-3 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-3 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-3 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+3 B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right) \sqrt{2}}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"-1/3*a/d*(-3*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-3*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)-3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)-3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+3*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)+A*2^(1/2)*cos(d*x+c)^2+3*B*2^(1/2)*cos(d*x+c)*sin(d*x+c))*(cos(d*x+c)/sin(d*x+c))^(5/2)*sin(d*x+c)/cos(d*x+c)^3*2^(1/2)","C"
504,1,1425,44,1.676000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","-\frac{a \left(i A \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-i A \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i B \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-A \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)+i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right)-B \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)-A \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-B \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+A \sqrt{2}\, \cos \left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}}{d \cos \left(d x +c \right)^{2}}"," ",0,"-a/d*(I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)-B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+A*2^(1/2)*cos(d*x+c))*(cos(d*x+c)/sin(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)^2*2^(1/2)","C"
505,1,784,45,1.777000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{a \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+i B \cos \left(d x +c \right) \sqrt{2}-i B \sqrt{2}\right) \sqrt{2}}{d \cos \left(d x +c \right) \sin \left(d x +c \right)^{3}}"," ",0,"a/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)+B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+I*B*cos(d*x+c)*2^(1/2)-I*B*2^(1/2))/cos(d*x+c)/sin(d*x+c)^3*2^(1/2)","C"
506,1,889,65,1.657000," ","int((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\frac{a \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(3 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i A \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+3 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-3 B \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 i A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-3 i A \cos \left(d x +c \right) \sqrt{2}-i B \sin \left(d x +c \right) \sqrt{2}+3 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-3 B \sqrt{2}\, \cos \left(d x +c \right)\right) \sqrt{2}}{3 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{4} \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"1/3*a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-3*B*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*I*A*2^(1/2)*cos(d*x+c)^2+I*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)-3*I*A*cos(d*x+c)*2^(1/2)-I*B*sin(d*x+c)*2^(1/2)+3*B*2^(1/2)*cos(d*x+c)^2-3*B*2^(1/2)*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)^4/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
507,1,971,85,1.615000," ","int((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x)","\frac{a \left(-1+\cos \left(d x +c \right)\right) \left(3 i B \cos \left(d x +c \right) \sqrt{2}+15 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-15 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+15 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-15 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+18 i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-15 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 i A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-5 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+5 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-15 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-18 i B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-5 B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i B \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{15 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{5} \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/15*a/d*(-1+cos(d*x+c))*(-15*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*B*cos(d*x+c)*2^(1/2)+18*I*B*2^(1/2)*cos(d*x+c)^2+15*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-15*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-5*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)+15*A*2^(1/2)*cos(d*x+c)^3-18*I*B*2^(1/2)*cos(d*x+c)^3+5*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-15*A*2^(1/2)*cos(d*x+c)^2+15*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-5*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-3*I*2^(1/2)*B)*(1+cos(d*x+c))^2/cos(d*x+c)/sin(d*x+c)^5/(cos(d*x+c)/sin(d*x+c))^(3/2)*2^(1/2)","C"
508,1,2947,108,1.898000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"1/15*a^2/d*(-30*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-33*A*2^(1/2)*cos(d*x+c)^3+30*A*2^(1/2)*cos(d*x+c)+30*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-30*I*B*cos(d*x+c)*2^(1/2)+30*I*B*cos(d*x+c)^3*2^(1/2)-30*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-30*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+30*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-5*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+30*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+30*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-30*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^3+30*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+30*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-30*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2-30*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-30*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+30*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)+30*I*A*cos(d*x+c)^3*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-30*I*A*cos(d*x+c)^3*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-30*I*B*cos(d*x+c)^3*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+30*I*A*cos(d*x+c)^2*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-30*I*A*cos(d*x+c)^2*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-30*I*B*cos(d*x+c)^2*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-30*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+30*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+30*I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+30*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-10*I*A*cos(d*x+c)^2*sin(d*x+c)*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(7/2)*sin(d*x+c)/cos(d*x+c)^4*2^(1/2)","C"
509,1,1541,86,1.909000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\frac{a^{2} \left(6 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+6 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-6 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+6 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-6 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+6 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+6 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-6 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+6 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-6 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+6 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+6 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-6 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-3 B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right) \sqrt{2}}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"1/3*a^2/d*(6*I*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+6*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+6*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+6*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+6*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)+6*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-6*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)-A*2^(1/2)*cos(d*x+c)^2-3*B*2^(1/2)*cos(d*x+c)*sin(d*x+c))*(cos(d*x+c)/sin(d*x+c))^(5/2)*sin(d*x+c)/cos(d*x+c)^3*2^(1/2)","C"
510,1,1440,85,2.002000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{a^{2} \left(2 i A \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-2 i A \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 i B \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 A \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)+2 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-2 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right)-2 B \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)+2 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 A \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-2 B \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+A \sqrt{2}\, \cos \left(d x +c \right)+B \sin \left(d x +c \right) \sqrt{2}\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}}{d \cos \left(d x +c \right)^{2}}"," ",0,"-a^2/d*(2*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+2*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)-2*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+2*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+A*2^(1/2)*cos(d*x+c)+B*sin(d*x+c)*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)^2*2^(1/2)","C"
511,1,888,87,2.058000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","-\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(-6 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-6 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+6 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+6 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-6 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-6 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-6 i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+3 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+6 i B \cos \left(d x +c \right) \sqrt{2}-3 A \sqrt{2}\, \cos \left(d x +c \right)-B \sin \left(d x +c \right) \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}}{3 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{3}}"," ",0,"-1/3*a^2/d*(-1+cos(d*x+c))*(-6*I*A*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*I*B*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+6*I*B*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-6*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-6*I*B*cos(d*x+c)^2*2^(1/2)+3*A*2^(1/2)*cos(d*x+c)^2+B*2^(1/2)*cos(d*x+c)*sin(d*x+c)+6*I*B*cos(d*x+c)*2^(1/2)-3*A*2^(1/2)*cos(d*x+c)-B*sin(d*x+c)*2^(1/2))*(1+cos(d*x+c))^2*(cos(d*x+c)/sin(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)^3*2^(1/2)","C"
512,1,971,109,1.774000," ","int((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(30 i A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-10 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-30 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+30 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-30 B \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+30 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+30 i A \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-30 i A \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+10 i B \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-5 A \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-30 i A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+33 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+5 A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-33 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-3 B \sqrt{2}\, \cos \left(d x +c \right)+3 B \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{15 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{4} \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"1/15*a^2/d*(-1+cos(d*x+c))*(-30*I*A*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+30*I*A*2^(1/2)*cos(d*x+c)^3-10*I*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)+30*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-30*B*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+30*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-30*I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+30*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+10*I*B*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2-5*A*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2-30*I*A*2^(1/2)*cos(d*x+c)^2+33*B*2^(1/2)*cos(d*x+c)^3+5*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)-33*B*2^(1/2)*cos(d*x+c)^2-3*B*2^(1/2)*cos(d*x+c)+3*B*2^(1/2))*(1+cos(d*x+c))^2/cos(d*x+c)^2/sin(d*x+c)^4/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
513,1,3132,145,2.204000," ","int(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/105*a^3/d*(-420*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+155*A*2^(1/2)*cos(d*x+c)^4-140*A*2^(1/2)*cos(d*x+c)^2-420*A*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+420*A*cos(d*x+c)^3*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-420*B*cos(d*x+c)^3*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+420*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-420*I*B*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+420*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+420*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+441*B*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-105*I*B*cos(d*x+c)^4*2^(1/2)+105*I*B*cos(d*x+c)^2*2^(1/2)-420*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)+420*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)+420*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-420*I*A*cos(d*x+c)^2*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+420*I*B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-420*I*B*cos(d*x+c)^2*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-420*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+420*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+420*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+420*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-420*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-420*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+483*I*A*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-420*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)+420*I*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-420*I*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-420*I*A*cos(d*x+c)^3*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+420*I*B*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-420*I*B*cos(d*x+c)^3*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*(cos(d*x+c)/sin(d*x+c))^(9/2)*sin(d*x+c)/cos(d*x+c)^5*2^(1/2)","C"
514,1,2947,123,2.195000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"1/15*a^3/d*(-60*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-63*A*2^(1/2)*cos(d*x+c)^3+60*A*2^(1/2)*cos(d*x+c)+60*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+60*I*A*cos(d*x+c)^3*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-60*I*A*cos(d*x+c)^3*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-60*I*B*cos(d*x+c)^3*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+60*I*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-60*I*A*cos(d*x+c)^2*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-60*I*B*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-60*I*A*cos(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+60*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+60*I*B*cos(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-60*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-60*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+60*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-5*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+60*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+60*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-60*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^3+60*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+60*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-60*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2-60*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-60*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+60*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)+60*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-45*I*B*cos(d*x+c)*2^(1/2)+45*I*B*cos(d*x+c)^3*2^(1/2)-15*I*A*cos(d*x+c)^2*sin(d*x+c)*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(7/2)*sin(d*x+c)/cos(d*x+c)^4*2^(1/2)","C"
515,1,1562,116,2.160000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{a^{3} \left(12 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+12 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+9 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-12 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+12 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-12 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-12 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-12 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-12 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+12 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-12 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-12 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-12 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 i B \sqrt{2}+A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+3 B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right) \sqrt{2}}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"-1/3*a^3/d*(12*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+12*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+9*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)-12*I*B*cos(d*x+c)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+12*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-12*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+3*I*B*2^(1/2)-12*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-12*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+12*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-12*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)-12*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-12*I*A*cos(d*x+c)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*B*2^(1/2)*cos(d*x+c)^2+A*2^(1/2)*cos(d*x+c)^2+3*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-12*I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*(cos(d*x+c)/sin(d*x+c))^(5/2)*sin(d*x+c)/cos(d*x+c)^3*2^(1/2)","C"
516,1,1539,118,2.209000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{a^{3} \left(12 i B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+12 i A \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+12 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-12 A \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-12 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-12 B \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+12 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)+i B \sqrt{2}-12 A \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)-12 B \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)+12 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right)+12 i B \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-12 i A \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+9 B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"-1/3*a^3/d*(-12*I*A*cos(d*x+c)^2*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+12*I*B*cos(d*x+c)^2*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)-12*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+12*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2+I*B*2^(1/2)-12*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-12*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+12*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)+12*I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*I*A*cos(d*x+c)^2*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*A*2^(1/2)*cos(d*x+c)^2+9*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-I*B*2^(1/2)*cos(d*x+c)^2)*(cos(d*x+c)/sin(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)^3*2^(1/2)","C"
517,1,973,124,3.980000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","-\frac{a^{3} \left(-1+\cos \left(d x +c \right)\right) \left(-3 i B \sqrt{2}+60 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+3 i B \cos \left(d x +c \right) \sqrt{2}-60 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+60 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-60 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-5 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+63 i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-60 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+45 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-63 i B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+15 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-45 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-60 i A \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-15 B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+5 i A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}}{15 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{3}}"," ",0,"-1/15*a^3/d*(-1+cos(d*x+c))*(-3*I*2^(1/2)*B+60*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+3*I*B*cos(d*x+c)*2^(1/2)-60*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+60*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-60*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)+63*I*B*2^(1/2)*cos(d*x+c)^2-60*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+45*A*2^(1/2)*cos(d*x+c)^3-60*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+15*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-45*A*2^(1/2)*cos(d*x+c)^2-63*I*B*2^(1/2)*cos(d*x+c)^3-15*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)+5*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c))*(1+cos(d*x+c))^2*(cos(d*x+c)/sin(d*x+c))^(1/2)/sin(d*x+c)^3/cos(d*x+c)^3*2^(1/2)","C"
518,1,1043,146,1.900000," ","int((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\frac{a^{3} \left(-1+\cos \left(d x +c \right)\right) \left(15 i B \sin \left(d x +c \right) \sqrt{2}-441 i A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+155 i B \sin \left(d x +c \right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+420 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+420 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-420 B \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-15 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-420 i B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+441 i A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)-105 A \sin \left(d x +c \right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+420 i A \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+483 B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)-420 i A \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+105 A \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-155 i B \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-483 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+21 i A \cos \left(d x +c \right) \sqrt{2}-21 i A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-63 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+63 B \sqrt{2}\, \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{105 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)^{4} \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"1/105*a^3/d*(-1+cos(d*x+c))*(15*I*B*sin(d*x+c)*2^(1/2)-441*I*A*2^(1/2)*cos(d*x+c)^3+155*I*B*sin(d*x+c)*2^(1/2)*cos(d*x+c)^3+420*A*cos(d*x+c)^3*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+420*B*cos(d*x+c)^3*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-420*B*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-15*I*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)+441*I*A*2^(1/2)*cos(d*x+c)^4-420*I*A*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-105*A*sin(d*x+c)*2^(1/2)*cos(d*x+c)^3-155*I*B*sin(d*x+c)*2^(1/2)*cos(d*x+c)^2+483*B*2^(1/2)*cos(d*x+c)^4-420*I*B*cos(d*x+c)^3*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+105*A*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2+21*I*A*cos(d*x+c)*2^(1/2)-483*B*2^(1/2)*cos(d*x+c)^3+420*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-21*I*A*2^(1/2)*cos(d*x+c)^2-63*B*2^(1/2)*cos(d*x+c)^2+63*B*2^(1/2)*cos(d*x+c))*(1+cos(d*x+c))^2/cos(d*x+c)^3/sin(d*x+c)^4/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
519,1,2598,246,4.452000," ","int(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"1/12/a/d*(cos(d*x+c)/sin(d*x+c))^(5/2)*sin(d*x+c)*(-3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+3*A*2^(1/2)*cos(d*x+c)^4-7*A*2^(1/2)*cos(d*x+c)^2+3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*B*2^(1/2)*cos(d*x+c)^2+3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+3*I*B*2^(1/2)*cos(d*x+c)^4+3*B*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-15*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)+21*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)-3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+21*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-18*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-18*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+9*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-3*I*A*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+15*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)-18*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-18*I*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+9*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2)))/cos(d*x+c)^3*2^(1/2)","C"
520,1,2437,222,4.229000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/4/a/d*(cos(d*x+c)/sin(d*x+c))^(3/2)*sin(d*x+c)*(-A*2^(1/2)*cos(d*x+c)^3+5*A*2^(1/2)*cos(d*x+c)+I*B*cos(d*x+c)*2^(1/2)-4*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-I*B*2^(1/2)*cos(d*x+c)^3-A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)-I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)-2*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)-2*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+4*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)+4*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)-2*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c))/cos(d*x+c)^2*2^(1/2)","C"
521,1,1139,192,4.391000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{\sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-2 i A \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-2 A \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+i B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-i A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \sqrt{2}}{4 a d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}"," ",0,"1/4/a/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)+3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)-A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-2*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*B*2^(1/2)*cos(d*x+c)^2+B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+A*2^(1/2)*cos(d*x+c)^3+I*B*cos(d*x+c)^3*2^(1/2)+B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-A*2^(1/2)*cos(d*x+c)^2-B*2^(1/2)*cos(d*x+c)*sin(d*x+c))/sin(d*x+c)^3/cos(d*x+c)*2^(1/2)","C"
522,1,2966,190,1.867000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"1/4*I/a/d*(-1+cos(d*x+c))*(-I*A*cos(d*x+c)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+A*2^(1/2)*cos(d*x+c)^2-A*2^(1/2)*cos(d*x+c)+I*B*cos(d*x+c)^2*2^(1/2)-I*B*2^(1/2)*cos(d*x+c)-2*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*B*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*B*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*A*cos(d*x+c)^2*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2-I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*B*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-2*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*B*cos(d*x+c)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*B*cos(d*x+c)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2)))*(1+cos(d*x+c))^2/(I*sin(d*x+c)+cos(d*x+c))/(cos(d*x+c)/sin(d*x+c))^(1/2)/sin(d*x+c)^4*2^(1/2)","C"
523,1,3717,228,1.862000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/4/a/d*(-1+cos(d*x+c))*(2*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+A*2^(1/2)*cos(d*x+c)^2-A*2^(1/2)*cos(d*x+c)+4*B*sin(d*x+c)*2^(1/2)-2*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2-I*B*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2+I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2+4*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-5*I*B*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-4*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*I*B*cos(d*x+c)^2*2^(1/2)-5*I*B*2^(1/2)*cos(d*x+c)+I*A*cos(d*x+c)^2*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+5*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-5*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2+4*B*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2+2*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)-A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+2*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-4*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*cos(d*x+c)*(1+cos(d*x+c))^2/(I*sin(d*x+c)+cos(d*x+c))/sin(d*x+c)^5/(cos(d*x+c)/sin(d*x+c))^(3/2)*2^(1/2)","C"
524,1,3871,252,1.954000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/12/a/d*(-1+cos(d*x+c))*(3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+15*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-11*B*2^(1/2)*cos(d*x+c)^3+11*B*2^(1/2)*cos(d*x+c)^2-4*B*2^(1/2)*cos(d*x+c)+12*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+4*B*2^(1/2)-8*I*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+8*I*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)-15*I*A*2^(1/2)*cos(d*x+c)^2+15*I*A*2^(1/2)*cos(d*x+c)^3-18*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-15*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+3*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-3*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-3*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+3*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+12*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-15*I*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-3*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-18*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-12*A*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2+12*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)-18*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+3*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-12*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+3*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+15*B*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*B*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-12*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+18*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+12*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-18*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-12*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+15*I*B*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-3*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+18*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3)*cos(d*x+c)*(1+cos(d*x+c))^2/(I*sin(d*x+c)+cos(d*x+c))/(cos(d*x+c)/sin(d*x+c))^(5/2)/sin(d*x+c)^6*2^(1/2)","C"
525,1,2507,261,4.405000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","\text{Expression too large to display}"," ",0,"-1/16/a^2/d*(cos(d*x+c)/sin(d*x+c))^(3/2)*sin(d*x+c)*(-4*A*2^(1/2)*cos(d*x+c)^5-21*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)-7*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+23*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)-5*A*2^(1/2)*cos(d*x+c)^3+25*A*2^(1/2)*cos(d*x+c)-7*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-23*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-7*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*B*2^(1/2)*cos(d*x+c)^3+5*I*B*2^(1/2)*cos(d*x+c)-4*B*2^(1/2)*cos(d*x+c)^4*sin(d*x+c)-4*I*B*2^(1/2)*cos(d*x+c)^5-2*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+9*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-3*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-2*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-2*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+9*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)+2*I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+4*I*A*2^(1/2)*cos(d*x+c)^4*sin(d*x+c)+7*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-23*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)-7*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+23*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-21*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))/cos(d*x+c)^2*2^(1/2)","C"
526,1,1517,235,4.474000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x)","-\frac{\sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(-i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+7 i A \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 i B \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-9 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+i B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+4 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+4 i B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)-5 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+5 i A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-2 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+4 A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)-4 A \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)+3 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+4 i A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 i A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+7 A \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+B \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-2 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-2 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-i B \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{2}}{16 a^{2} d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}"," ",0,"-1/16/a^2/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(2*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-4*A*2^(1/2)*cos(d*x+c)^5+4*A*2^(1/2)*cos(d*x+c)^4-3*A*2^(1/2)*cos(d*x+c)^3+3*A*2^(1/2)*cos(d*x+c)^2+4*I*B*cos(d*x+c)^4*2^(1/2)-2*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)+7*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+4*B*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-4*B*2^(1/2)*cos(d*x+c)^4*sin(d*x+c)-4*I*B*2^(1/2)*cos(d*x+c)^5+B*2^(1/2)*cos(d*x+c)*sin(d*x+c)+5*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-I*B*2^(1/2)*cos(d*x+c)^2-B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-9*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)+I*B*cos(d*x+c)^3*2^(1/2)+4*I*A*2^(1/2)*cos(d*x+c)^4*sin(d*x+c)-5*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)-4*I*A*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)+7*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2)))/sin(d*x+c)^3/cos(d*x+c)*2^(1/2)","C"
527,1,5032,229,2.059000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
528,1,5042,235,2.086000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
529,1,5063,263,2.034000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
530,1,2577,305,4.948000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"1/48/a^3/d*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(3/2)*(84*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+8*A*2^(1/2)*cos(d*x+c)^5+18*A*2^(1/2)*cos(d*x+c)^3-90*A*2^(1/2)*cos(d*x+c)+16*A*cos(d*x+c)^7*2^(1/2)+16*B*cos(d*x+c)^6*sin(d*x+c)*2^(1/2)+16*I*B*cos(d*x+c)^7*2^(1/2)+3*I*B*cos(d*x+c)^3*2^(1/2)-15*I*B*2^(1/2)*cos(d*x+c)-87*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+18*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+87*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+18*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+4*B*2^(1/2)*cos(d*x+c)^4*sin(d*x+c)-4*I*B*2^(1/2)*cos(d*x+c)^5+3*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-21*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+7*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+3*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+3*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-21*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)+3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+87*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+18*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)-16*I*A*cos(d*x+c)^6*sin(d*x+c)*2^(1/2)-16*I*A*cos(d*x+c)^4*sin(d*x+c)*2^(1/2)-28*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+84*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-87*I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+18*I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2)))/cos(d*x+c)^2*2^(1/2)","C"
531,1,1581,264,5.086000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x)","\frac{\sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(2 i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+16 i A \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-18 i A \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-8 i B \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-16 B \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-16 i B \left(\cos^{6}\left(d x +c \right)\right) \sqrt{2}+21 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+16 A \left(\cos^{7}\left(d x +c \right)\right) \sqrt{2}-2 i B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+8 i B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+15 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+16 B \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+16 i B \left(\cos^{7}\left(d x +c \right)\right) \sqrt{2}-15 i A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-3 A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-4 A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+4 A \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-7 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-12 i A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+12 i A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-6 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)-18 A \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 B \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-16 A \left(\cos^{6}\left(d x +c \right)\right) \sqrt{2}-16 i A \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+7 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+3 i A \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 i B \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 i B \sin \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{2}}{48 a^{3} d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}"," ",0,"1/48/a^3/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(-3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+4*A*2^(1/2)*cos(d*x+c)^5-4*A*2^(1/2)*cos(d*x+c)^4+7*A*2^(1/2)*cos(d*x+c)^3-7*A*2^(1/2)*cos(d*x+c)^2+16*A*cos(d*x+c)^7*2^(1/2)+16*B*cos(d*x+c)^6*sin(d*x+c)*2^(1/2)+16*I*B*cos(d*x+c)^7*2^(1/2)+3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+16*I*A*cos(d*x+c)^5*sin(d*x+c)*2^(1/2)-12*I*A*cos(d*x+c)^4*sin(d*x+c)*2^(1/2)+12*I*A*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)+21*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)+3*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-18*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-16*I*B*cos(d*x+c)^6*2^(1/2)-8*I*B*cos(d*x+c)^5*2^(1/2)+8*I*B*cos(d*x+c)^4*2^(1/2)-2*I*B*cos(d*x+c)^3*2^(1/2)+2*I*B*cos(d*x+c)^2*2^(1/2)-16*B*cos(d*x+c)^5*sin(d*x+c)*2^(1/2)-16*A*cos(d*x+c)^6*2^(1/2)-15*I*A*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)+15*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)-16*I*A*cos(d*x+c)^6*sin(d*x+c)*2^(1/2)-18*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-6*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2)))/sin(d*x+c)^3/cos(d*x+c)*2^(1/2)","C"
532,1,5075,260,4.099000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
533,1,4520,258,4.445000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"1/48/a^3/d*(-1+cos(d*x+c))*(-12*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+6*A*2^(1/2)*cos(d*x+c)^4-6*A*2^(1/2)*cos(d*x+c)^3-3*A*2^(1/2)*cos(d*x+c)^2+3*A*2^(1/2)*cos(d*x+c)+3*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+15*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2-12*A*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+12*A*cos(d*x+c)^3*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*B*cos(d*x+c)^3*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*I*B*sin(d*x+c)*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*B*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-12*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-6*I*B*cos(d*x+c)^4*2^(1/2)+6*I*B*cos(d*x+c)^3*2^(1/2)+6*I*B*cos(d*x+c)^2*2^(1/2)-6*I*B*2^(1/2)*cos(d*x+c)+2*B*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-3*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+15*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*B*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+9*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-9*I*B*sin(d*x+c)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-12*I*A*sin(d*x+c)*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-9*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+9*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+9*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)+9*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-12*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*sin(d*x+c)+9*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+10*I*A*sin(d*x+c)*cos(d*x+c)^3*2^(1/2)-10*I*A*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)-12*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4-3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-12*B*sin(d*x+c)*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*I*A*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+12*I*B*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*I*B*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*A*cos(d*x+c)^2*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-15*I*B*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*I*B*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*(1+cos(d*x+c))^2*cos(d*x+c)/(4*I*cos(d*x+c)^2*sin(d*x+c)+4*cos(d*x+c)^3-I*sin(d*x+c)-3*cos(d*x+c))/(cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^5*2^(1/2)","C"
534,1,5731,260,4.017000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
535,1,6350,305,4.282000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
536,1,2243,161,4.439000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/30/d*(15*I*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+34*A*2^(1/2)*cos(d*x+c)^3-32*A*2^(1/2)*cos(d*x+c)^2-28*A*2^(1/2)*cos(d*x+c)-10*B*sin(d*x+c)*2^(1/2)+30*I*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+26*A*2^(1/2)-15*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-30*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+30*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+30*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+15*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+34*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-2*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)-30*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-30*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-15*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-30*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-15*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-30*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-30*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+30*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+15*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+30*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-30*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-30*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-15*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-20*I*B*cos(d*x+c)^3*2^(1/2)+10*I*B*cos(d*x+c)^2*2^(1/2)-26*I*A*sin(d*x+c)*2^(1/2)+20*I*B*2^(1/2)*cos(d*x+c)-10*I*B*2^(1/2)-10*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)+20*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+30*I*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+30*I*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+15*I*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+30*I*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1))*(cos(d*x+c)/sin(d*x+c))^(7/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^3*2^(1/2)","B"
537,1,2016,126,4.227000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(-6 i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-2 A \sqrt{2}\, \cos \left(d x +c \right)-6 B \sin \left(d x +c \right) \sqrt{2}-2 A \sqrt{2}-2 i A \sin \left(d x +c \right) \sqrt{2}+6 B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-6 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-3 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)+6 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)+6 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+6 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+3 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right) \left(\cos^{2}\left(d x +c \right)\right)+6 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+6 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+6 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+3 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right) \left(\cos^{2}\left(d x +c \right)\right)+6 i B \sqrt{2}-6 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)-6 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+4 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-6 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-3 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)+4 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+3 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right) \left(\cos^{2}\left(d x +c \right)\right)-6 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-3 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right) \left(\cos^{2}\left(d x +c \right)\right)-6 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+6 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+6 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{6 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/6/d*(4*A*2^(1/2)*cos(d*x+c)^2-2*A*2^(1/2)*cos(d*x+c)-6*B*sin(d*x+c)*2^(1/2)+3*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2-6*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2-6*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+4*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)+6*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+6*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-2*A*2^(1/2)-6*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-3*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-2*I*A*sin(d*x+c)*2^(1/2)+6*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+6*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+6*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2+6*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+6*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+6*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+3*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2-6*I*B*cos(d*x+c)^2*2^(1/2)+6*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-6*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-6*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-6*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-3*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+6*I*B*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(5/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^2*2^(1/2)","B"
538,1,1048,91,4.189000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(2 i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)+2 i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)-2 A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-2 A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)+2 i A \sin \left(d x +c \right) \sqrt{2}+2 B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)+2 A \sqrt{2}\, \cos \left(d x +c \right)-2 A \sqrt{2}\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)}"," ",0,"-1/2/d*(2*I*A*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+2*I*B*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-2*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+2*I*A*sin(d*x+c)*2^(1/2)+2*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+2*A*2^(1/2)*cos(d*x+c)-2*A*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)*2^(1/2)","B"
539,1,895,121,4.113000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","-\frac{\sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(-i B \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 i B \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right)-2 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+2 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+2 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-2 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+B \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-2 B \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right)-B \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+i A \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)-i B \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)+i B \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+A \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)+2 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+B \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)+2 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)\right) \sqrt{2}}{2 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"-1/2/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(-I*B*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*I*B*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-2*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+B*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-2*B*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-B*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+I*B*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+2*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+2*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1))/(I*sin(d*x+c)+cos(d*x+c)-1)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)","B"
540,1,3889,155,4.170000," ","int((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"1/4/d*(2*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)*sin(d*x+c)-2*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)*sin(d*x+c)+4*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+4*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)+4*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)+2*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)*sin(d*x+c)+2*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)-2*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)-4*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)-2*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2+2*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2+4*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2+2*B*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+4*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+2*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2+4*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+4*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+2*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2-4*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)-4*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)-2*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)-4*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)-4*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)-2*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)+2*I*B*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)+2*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)-2*B*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)-4*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)-2*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)*sin(d*x+c)+B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)-B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2+B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2-2*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2+2*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2+4*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)+4*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)+2*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)-4*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)-4*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)-2*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)-4*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2-4*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-2*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2-2*B*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+4*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)*sin(d*x+c)-I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)*sin(d*x+c)+2*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)*sin(d*x+c)+2*I*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)*sin(d*x+c)-4*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)-2*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)*sin(d*x+c)+2*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)-2*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)+4*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)-4*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)-4*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)-2*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)*sin(d*x+c)-I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)+2*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)+2*I*B*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2+2*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)*sin(d*x+c)-2*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)*sin(d*x+c)-4*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)*sin(d*x+c)+I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)+B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)*sin(d*x+c)-B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)*sin(d*x+c)+2*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)*sin(d*x+c)+2*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2+2*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2-4*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2-I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2-2*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2-2*I*B*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*cos(d*x+c)+I*sin(d*x+c)-1+I+cos(d*x+c)-sin(d*x+c))/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/(cos(d*x+c)/sin(d*x+c))^(1/2)/sin(d*x+c)*2^(1/2)","B"
541,1,3124,200,4.091000," ","int(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/105/d*(211*A*2^(1/2)*cos(d*x+c)^4-53*A*2^(1/2)*cos(d*x+c)^3-330*A*2^(1/2)*cos(d*x+c)^2+38*A*2^(1/2)*cos(d*x+c)+210*I*A*cos(d*x+c)^4*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+210*I*A*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+105*I*A*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-210*I*B*cos(d*x+c)^4*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-210*I*B*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-105*I*B*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+211*I*A*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)+126*B*sin(d*x+c)*2^(1/2)+134*A*2^(1/2)-420*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-420*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-420*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-210*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2+134*I*A*sin(d*x+c)*2^(1/2)+210*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+210*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+105*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-210*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-210*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-105*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-189*I*B*cos(d*x+c)^4*2^(1/2)+42*I*B*cos(d*x+c)^3*2^(1/2)+315*I*B*cos(d*x+c)^2*2^(1/2)+210*A*cos(d*x+c)^4*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+210*A*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+105*A*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+210*B*cos(d*x+c)^4*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+210*B*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+105*B*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-42*I*B*cos(d*x+c)*2^(1/2)-126*I*B*2^(1/2)-420*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-210*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2+189*B*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-168*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-147*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+210*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+105*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+210*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+210*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+210*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+105*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-158*I*A*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)-420*I*A*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-420*I*A*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-210*I*A*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+420*I*B*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+420*I*B*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+210*I*B*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-172*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(9/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^4*a*2^(1/2)","B"
542,1,2244,164,4.202000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"1/15/d*(-30*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*sin(d*x+c)-27*A*2^(1/2)*cos(d*x+c)^3+21*A*2^(1/2)*cos(d*x+c)^2+24*A*2^(1/2)*cos(d*x+c)+20*B*sin(d*x+c)*2^(1/2)-18*A*2^(1/2)-30*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*sin(d*x+c)-30*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-15*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-30*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+30*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+30*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+15*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+5*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-25*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+25*I*B*cos(d*x+c)^3*2^(1/2)-20*I*B*cos(d*x+c)^2*2^(1/2)+18*I*A*sin(d*x+c)*2^(1/2)-25*I*B*cos(d*x+c)*2^(1/2)+20*I*B*2^(1/2)-15*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-27*I*A*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)+30*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)+30*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)+15*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+6*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)+15*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+30*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)+30*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)+30*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+15*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+30*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-30*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-30*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-15*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2*sin(d*x+c)-15*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-30*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*sin(d*x+c)-30*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*sin(d*x+c))*(cos(d*x+c)/sin(d*x+c))^(7/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^3*a*2^(1/2)","B"
543,1,2017,128,4.229000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(-3 i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-A \sqrt{2}\, \cos \left(d x +c \right)-3 B \sin \left(d x +c \right) \sqrt{2}-4 A \sqrt{2}-4 i A \sin \left(d x +c \right) \sqrt{2}+3 B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-6 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-3 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)+6 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)+6 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+6 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+3 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right) \left(\cos^{2}\left(d x +c \right)\right)+6 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+6 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+6 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+3 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right) \left(\cos^{2}\left(d x +c \right)\right)+3 i B \sqrt{2}-6 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)-6 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+5 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-6 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-3 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)+5 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+3 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right) \left(\cos^{2}\left(d x +c \right)\right)-6 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-3 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right) \left(\cos^{2}\left(d x +c \right)\right)-6 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+6 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+6 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) a \sqrt{2}}{3 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/3/d*(5*A*2^(1/2)*cos(d*x+c)^2-A*2^(1/2)*cos(d*x+c)-3*B*sin(d*x+c)*2^(1/2)-4*A*2^(1/2)+6*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+6*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+6*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+3*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2+6*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2-3*I*B*2^(1/2)*cos(d*x+c)^2-4*I*A*sin(d*x+c)*2^(1/2)+3*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-6*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-6*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-6*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-3*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-6*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-3*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+6*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+6*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+3*I*B*2^(1/2)+3*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2-6*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2-6*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+6*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+6*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+5*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(5/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^2*a*2^(1/2)","B"
544,1,1366,150,4.201000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(4 i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+4 i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)+4 i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+4 i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-2 i B \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-B \sin \left(d x +c \right) \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+B \sin \left(d x +c \right) \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 B \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 i A \sin \left(d x +c \right) \sqrt{2}+i B \sin \left(d x +c \right) \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i B \sin \left(d x +c \right) \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)-4 A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-4 A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-2 A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)+4 B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+4 B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+2 B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)+2 A \sqrt{2}\, \cos \left(d x +c \right)-2 A \sqrt{2}\right) \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a \sqrt{2}}{2 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)}"," ",0,"-1/2/d*(4*I*B*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*I*B*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+4*I*A*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*I*A*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*I*B*sin(d*x+c)*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-B*sin(d*x+c)*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+B*sin(d*x+c)*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*B*sin(d*x+c)*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*A*sin(d*x+c)*2^(1/2)+I*B*sin(d*x+c)*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*B*sin(d*x+c)*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-4*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-4*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-2*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+4*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+4*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+2*A*2^(1/2)*cos(d*x+c)-2*A*2^(1/2))*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)*a*2^(1/2)","B"
545,1,1306,158,4.139000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-4 A \cos \left(d x +c \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)-4 B \cos \left(d x +c \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)-8 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right)-8 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right)-8 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right)-8 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right)+2 B \sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 B \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 A \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sqrt{2}\, \cos \left(d x +c \right)-2 A \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{2}\, \cos \left(d x +c \right)+4 A \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{2}\, \cos \left(d x +c \right)+3 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{2}\, \cos \left(d x +c \right)+6 B \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{2}\, \cos \left(d x +c \right)-3 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sqrt{2}\, \cos \left(d x +c \right)-8 i A \cos \left(d x +c \right) \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-8 i A \cos \left(d x +c \right) \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-4 i A \cos \left(d x +c \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right)+8 i B \cos \left(d x +c \right) \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+8 i B \cos \left(d x +c \right) \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+4 i B \cos \left(d x +c \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right)+2 i A \cos \left(d x +c \right) \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-2 i A \cos \left(d x +c \right) \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+3 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{2}\, \cos \left(d x +c \right)-6 i B \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right)-3 i B \cos \left(d x +c \right) \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+4 i A \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{2}\, \cos \left(d x +c \right)+2 i B \sqrt{2}\, \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\, a}{4 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"1/4/d*(-1+cos(d*x+c))*(-4*A*cos(d*x+c)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-4*B*cos(d*x+c)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-8*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)-8*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)-8*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)-8*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)+2*B*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*A*cos(d*x+c)*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-8*I*A*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-8*I*A*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-4*I*A*cos(d*x+c)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+8*I*B*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+8*I*B*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+4*I*B*cos(d*x+c)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+2*B*cos(d*x+c)*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)-2*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)+4*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)+3*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)+6*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)-3*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)-2*I*A*cos(d*x+c)*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+3*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)-6*I*B*cos(d*x+c)*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-3*I*B*cos(d*x+c)*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+4*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)+2*I*B*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)/sin(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*a","B"
546,1,4490,194,4.013000," ","int((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"1/16/d*(8*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-32*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3-8*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)-32*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2-32*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-16*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2-32*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2-32*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-16*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2-4*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)+14*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^3+8*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^3+32*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3+32*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3+16*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^3+32*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3+32*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3+16*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^3+24*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3-12*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3+12*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3+16*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2*sin(d*x+c)-32*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*sin(d*x+c)-32*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*sin(d*x+c)-16*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2*sin(d*x+c)-22*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3-11*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3+11*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3+32*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*sin(d*x+c)+32*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*sin(d*x+c)+12*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2-12*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2-24*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2-4*B*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+14*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-12*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+22*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-11*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+11*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-8*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)*sin(d*x+c)-14*B*cos(d*x+c)*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+10*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)*sin(d*x+c)+24*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+12*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+4*B*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*B*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+11*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2-11*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2+22*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2-32*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3-16*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^3+32*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3+32*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3+16*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^3-32*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-16*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2+32*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+32*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+16*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2-32*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2-24*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+12*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+4*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^2+14*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)-8*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-8*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)*sin(d*x+c)-24*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3-12*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3+12*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3+8*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^3-22*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3+11*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3-11*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3-14*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^3-12*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+22*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+11*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-11*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+14*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-32*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*sin(d*x+c)-32*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*sin(d*x+c)-16*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2*sin(d*x+c)+24*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2+12*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2-12*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2-32*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*sin(d*x+c)-32*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*sin(d*x+c)+22*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2-11*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2+11*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2-16*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2*sin(d*x+c)-8*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)-4*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*sin(d*x+c)-10*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*cos(d*x+c)+I*sin(d*x+c)-1+I+cos(d*x+c)-sin(d*x+c))/cos(d*x+c)/(cos(d*x+c)/sin(d*x+c))^(1/2)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/sin(d*x+c)*2^(1/2)*a","B"
547,1,3412,244,4.058000," ","int(cot(d*x+c)^(11/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/315/d*(1260*I*A*cos(d*x+c)^4*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1292*A*2^(1/2)*cos(d*x+c)^5-961*A*2^(1/2)*cos(d*x+c)^4-2281*A*2^(1/2)*cos(d*x+c)^3+1714*A*2^(1/2)*cos(d*x+c)^2+1024*A*2^(1/2)*cos(d*x+c)+780*B*sin(d*x+c)*2^(1/2)-788*A*2^(1/2)+630*I*A*cos(d*x+c)^4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-1260*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-630*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-1260*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+1260*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+1260*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+630*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+1200*B*2^(1/2)*cos(d*x+c)^4*sin(d*x+c)-1695*I*B*cos(d*x+c)^2*2^(1/2)-1260*A*cos(d*x+c)^4*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-630*A*cos(d*x+c)^4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-1260*A*cos(d*x+c)^4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+1260*B*cos(d*x+c)^4*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+630*B*cos(d*x+c)^4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+1260*B*cos(d*x+c)^4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+1292*I*A*cos(d*x+c)^4*sin(d*x+c)*2^(1/2)-331*I*A*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-1950*I*A*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)-285*B*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)+788*I*A*sin(d*x+c)*2^(1/2)-1020*I*B*cos(d*x+c)*2^(1/2)-1200*I*B*cos(d*x+c)^5*2^(1/2)+915*I*B*cos(d*x+c)^4*2^(1/2)+2220*I*B*cos(d*x+c)^3*2^(1/2)+780*I*B*2^(1/2)+240*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-1935*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+236*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)+1260*I*A*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+630*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+1260*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+1260*I*B*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+630*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+1260*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+1260*I*A*cos(d*x+c)^4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+1260*I*B*cos(d*x+c)^4*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+630*I*B*cos(d*x+c)^4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+1260*I*B*cos(d*x+c)^4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2520*I*A*cos(d*x+c)^2*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1260*I*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-2520*I*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2520*I*B*cos(d*x+c)^2*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1260*I*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-2520*I*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-1260*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+2520*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+1260*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+2520*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-2520*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2520*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1))*(cos(d*x+c)/sin(d*x+c))^(11/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^5*2^(1/2)*a^2","B"
548,1,3126,206,4.177000," ","int(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/105/d*(400*A*2^(1/2)*cos(d*x+c)^4-95*A*2^(1/2)*cos(d*x+c)^3-645*A*2^(1/2)*cos(d*x+c)^2+80*A*2^(1/2)*cos(d*x+c)+266*B*sin(d*x+c)*2^(1/2)+260*A*2^(1/2)-840*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-840*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-840*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-420*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2+420*A*cos(d*x+c)^4*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+420*A*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+210*A*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+420*B*cos(d*x+c)^4*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+420*B*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+210*B*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-840*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-420*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2+260*I*A*2^(1/2)*sin(d*x+c)+420*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+420*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-266*I*B*2^(1/2)+210*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-420*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-420*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-210*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-364*I*B*2^(1/2)*cos(d*x+c)^4+77*I*B*2^(1/2)*cos(d*x+c)^3+630*I*B*2^(1/2)*cos(d*x+c)^2-77*I*B*2^(1/2)*cos(d*x+c)+364*B*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-343*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-287*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+420*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+210*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+420*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+420*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+420*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+210*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-340*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)+420*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+420*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^4+210*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^4-420*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4-420*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^4-210*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^4+400*I*A*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-305*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-840*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-840*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-420*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2+840*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+840*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+420*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2)*(cos(d*x+c)/sin(d*x+c))^(9/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^4*2^(1/2)*a^2","B"
549,1,2246,168,4.328000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/15/d*(60*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*sin(d*x+c)+52*A*2^(1/2)*cos(d*x+c)^3-41*A*2^(1/2)*cos(d*x+c)^2-49*A*2^(1/2)*cos(d*x+c)-35*B*sin(d*x+c)*2^(1/2)+38*A*2^(1/2)+30*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2*sin(d*x+c)+60*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*sin(d*x+c)+60*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*sin(d*x+c)+30*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2*sin(d*x+c)+60*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*sin(d*x+c)+60*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+30*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+60*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-60*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-60*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-30*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-40*I*B*2^(1/2)*cos(d*x+c)^3+35*I*B*2^(1/2)*cos(d*x+c)^2-38*I*A*2^(1/2)*sin(d*x+c)+40*I*B*2^(1/2)*cos(d*x+c)-5*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)+40*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+52*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-60*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)-60*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)-30*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-11*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)-60*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)-60*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)-30*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+30*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-60*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-30*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-60*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+60*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+60*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-35*I*B*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(7/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^3*2^(1/2)*a^2","B"
550,1,2629,186,4.171000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/6/d*(-3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*2^(1/2)+16*A*2^(1/2)*cos(d*x+c)^2-2*A*2^(1/2)*cos(d*x+c)-6*B*sin(d*x+c)*2^(1/2)-14*A*2^(1/2)+24*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+24*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+24*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+12*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2+3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*2^(1/2)+24*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+12*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2-6*I*B*cos(d*x+c)^2*2^(1/2)+6*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)-24*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-24*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-12*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))-14*I*A*sin(d*x+c)*2^(1/2)+24*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+24*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+12*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))+3*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)-3*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)+6*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)-24*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-12*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))-24*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-24*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-24*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-12*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))+6*I*B*2^(1/2)+6*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)^2*2^(1/2)-3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)-6*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)-3*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*2^(1/2)+3*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*2^(1/2)-6*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)^2*2^(1/2)+24*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+24*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+12*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2-24*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-24*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2-12*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2+16*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)+3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(5/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^2*2^(1/2)*a^2","B"
551,1,1896,193,4.127000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(5 B \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-16 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-8 A \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-16 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+8 B \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+16 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+16 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 i B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-4 A \sqrt{2}\, \cos \left(d x +c \right)-2 B \sin \left(d x +c \right) \sqrt{2}-10 B \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 B \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+8 i A \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+16 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+16 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+16 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+8 i B \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+16 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 i B \sqrt{2}+4 i A \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+4 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-5 B \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 A \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 A \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 A \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 i A \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 i A \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 i A \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-5 i B \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-10 i B \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+5 i B \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}\, a^{2}}{4 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/4/d*(5*B*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-16*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-8*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-16*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+8*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+16*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+16*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*I*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)+4*A*2^(1/2)*cos(d*x+c)^2-4*A*2^(1/2)*cos(d*x+c)-2*B*sin(d*x+c)*2^(1/2)-10*B*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*I*B*2^(1/2)*cos(d*x+c)^2+2*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)+2*I*B*2^(1/2)-5*B*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*A*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*A*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*A*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+8*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+16*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+16*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+16*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+8*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+16*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*A*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*I*A*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*I*A*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-5*I*B*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-10*I*B*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+5*I*B*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*(cos(d*x+c)/sin(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^2*2^(1/2)*a^2","B"
552,1,1530,196,4.168000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(4 B \sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+64 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \left(\cos^{2}\left(d x +c \right)\right)+64 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \left(\cos^{2}\left(d x +c \right)\right)+32 B \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right) \left(\cos^{2}\left(d x +c \right)\right)+64 A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+32 A \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right) \left(\cos^{2}\left(d x +c \right)\right)+64 B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)-20 A \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+20 A \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-40 A \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-32 i B \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}\right) \left(\cos^{2}\left(d x +c \right)\right)-64 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \left(\cos^{2}\left(d x +c \right)\right)-64 i B \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+64 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \left(\cos^{2}\left(d x +c \right)\right)+64 i A \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+32 i A \ln \left(-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)+\sin \left(d x +c \right)-1}{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)-\sin \left(d x +c \right)+1}\right) \left(\cos^{2}\left(d x +c \right)\right)-22 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+23 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-23 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-46 B \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-18 B \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-22 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-23 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+46 i B \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+20 i A \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-20 i A \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-40 i A \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-8 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 i B \sqrt{2}\, \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+8 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-8 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\, \cos \left(d x +c \right)+23 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{2}\, a^{2}}{16 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)^{2}}"," ",0,"-1/16/d*(-1+cos(d*x+c))*(-22*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*2^(1/2)-20*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2+20*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2-40*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2+4*B*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-32*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2-64*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2-64*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+64*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+64*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+32*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2+32*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^2+32*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^2-18*B*cos(d*x+c)*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-22*B*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+23*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2-23*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^2-46*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^2+64*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+64*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+64*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+64*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+8*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)*sin(d*x+c)-8*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)-4*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*sin(d*x+c)+23*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^2-23*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*2^(1/2)+46*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)^2*2^(1/2)+20*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*2^(1/2)-20*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2*2^(1/2)-40*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)^2*2^(1/2)-8*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/cos(d*x+c)^2*2^(1/2)*a^2","B"
553,1,4851,234,4.092000," ","int((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"1/96/d*(384*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3+24*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)+52*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^3-24*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^3-24*I*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-68*I*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-276*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3+138*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3-138*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3+270*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3+135*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3-135*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3+16*B*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+384*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^4+192*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^4-384*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^4-384*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^4-192*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^4+384*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^4-52*B*cos(d*x+c)*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-198*B*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+16*B*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-138*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+276*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+138*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+132*I*A*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+135*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+270*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-135*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+182*I*B*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-108*I*A*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+130*I*B*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+384*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3+192*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^3-384*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3-384*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3-192*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^3-108*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+24*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)*sin(d*x+c)-130*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-68*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-192*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^3*sin(d*x+c)+384*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^4+384*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^4+192*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^4+384*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^4+384*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^4+192*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^4-384*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3+132*A*2^(1/2)*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+182*B*2^(1/2)*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-384*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3-192*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^3-384*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3-384*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3-192*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^3-16*I*B*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+135*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^4-270*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^4-135*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^4+384*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3*sin(d*x+c)+384*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3*sin(d*x+c)-132*A*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+138*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^4+276*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^4-138*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^4+192*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^3*sin(d*x+c)-384*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3*sin(d*x+c)-384*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3*sin(d*x+c)-132*A*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-138*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-276*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+138*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-135*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+270*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+135*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+182*B*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-384*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3*sin(d*x+c)-192*I*A*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1))*cos(d*x+c)^3*sin(d*x+c)-138*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3+276*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3+138*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3+24*I*A*2^(1/2)*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-384*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3*sin(d*x+c)-384*I*B*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3*sin(d*x+c)+135*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^3+270*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^3-135*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^3-192*I*B*ln(-(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)+sin(d*x+c)-1)/(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-cos(d*x+c)-sin(d*x+c)+1))*cos(d*x+c)^3*sin(d*x+c)+52*I*B*2^(1/2)*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-132*I*A*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+198*I*B*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-24*I*A*2^(1/2)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-52*I*B*2^(1/2)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-16*I*B*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+138*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^4-276*I*A*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^4-138*I*A*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^4+132*I*A*2^(1/2)*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-135*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*cos(d*x+c)^4-270*I*B*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*cos(d*x+c)^4+135*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*cos(d*x+c)^4-182*I*B*2^(1/2)*cos(d*x+c)^4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-384*I*A*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*cos(d*x+c)+I*sin(d*x+c)-1+I+cos(d*x+c)-sin(d*x+c))/cos(d*x+c)^2/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/sin(d*x+c)/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)*a^2","B"
554,1,683,171,4.339000," ","int(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(-\frac{1}{6}-\frac{i}{6}\right) \left(3 i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 i A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 i A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+3 B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+5 i A \left(\cos^{2}\left(d x +c \right)\right)+3 B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 i A \cos \left(d x +c \right) \sin \left(d x +c \right)-7 i A -6 i B \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-5 A \left(\cos^{2}\left(d x +c \right)\right)-2 A \cos \left(d x +c \right) \sin \left(d x +c \right)-9 B \left(\cos^{2}\left(d x +c \right)\right)+6 B \cos \left(d x +c \right) \sin \left(d x +c \right)-9 i B \left(\cos^{2}\left(d x +c \right)\right)+9 i B +7 A +9 B \right) \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{2} a}"," ",0,"(-1/6-1/6*I)/d*(3*I*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*I*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*I*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)+3*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)+5*I*A*cos(d*x+c)^2+3*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-3*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*I*A*cos(d*x+c)*sin(d*x+c)-7*I*A-6*I*B*cos(d*x+c)*sin(d*x+c)-3*I*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-5*A*cos(d*x+c)^2-2*A*cos(d*x+c)*sin(d*x+c)-9*B*cos(d*x+c)^2+6*B*cos(d*x+c)*sin(d*x+c)-9*I*B*cos(d*x+c)^2+9*I*B+7*A+9*B)*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(5/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c)^2/a","B"
555,1,482,133,4.220000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(-\frac{1}{2}-\frac{i}{2}\right) \left(i A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-i B \sqrt{2}\, \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+A \sqrt{2}\, \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 i A \cos \left(d x +c \right)+3 i A \sin \left(d x +c \right)+i B \sin \left(d x +c \right)+2 A \cos \left(d x +c \right)+3 A \sin \left(d x +c \right)-B \sin \left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)}{d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right) \cos \left(d x +c \right) a}"," ",0,"(-1/2-1/2*I)/d*(I*A*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-I*B*2^(1/2)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+A*2^(1/2)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-I*B*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*I*A*cos(d*x+c)+3*I*A*sin(d*x+c)+I*B*sin(d*x+c)+2*A*cos(d*x+c)+3*A*sin(d*x+c)-B*sin(d*x+c))*(cos(d*x+c)/sin(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c)/a","B"
556,1,431,95,4.195000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(-\frac{1}{2}-\frac{i}{2}\right) \left(i A \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-i B \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+A \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+B \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a}"," ",0,"(-1/2-1/2*I)/d*(I*A*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-I*B*cos(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+A*cos(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+B*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*(cos(d*x+c)/sin(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c))/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/a","B"
557,1,805,155,4.117000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right) \cos \left(d x +c \right)-i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}+i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right) \cos \left(d x +c \right)-i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{2}+i B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{2}-i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sqrt{2}+i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sqrt{2}+A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right) \sin \left(d x +c \right)+i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right)-i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right)+B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sin \left(d x +c \right)+B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right) \sin \left(d x +c \right)-B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}-B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sin \left(d x +c \right)-B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \cos \left(d x +c \right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a}"," ",0,"(1/2+1/2*I)/d*(-I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)-I*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)-I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)+I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)-I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)+I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+I*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*sin(d*x+c)+I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)-I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)+B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)+B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*sin(d*x+c)-B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)-B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c))/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/sin(d*x+c)/(cos(d*x+c)/sin(d*x+c))^(1/2)/a","B"
558,1,648,172,4.165000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(-\frac{1}{12}-\frac{i}{12}\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(25 A +7 B +4 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+11 A \cos \left(d x +c \right) \sin \left(d x +c \right)-5 B \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-9 A \left(\cos^{2}\left(d x +c \right)\right)+4 i A \left(\cos^{4}\left(d x +c \right)\right)+11 i A \cos \left(d x +c \right) \sin \left(d x +c \right)+4 i A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+5 i B \cos \left(d x +c \right) \sin \left(d x +c \right)+7 i B +4 i B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-3 i B \sqrt{2}\, \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-4 A \left(\cos^{4}\left(d x +c \right)\right)+9 i A \left(\cos^{2}\left(d x +c \right)\right)+3 A \sqrt{2}\, \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-3 i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 i B \left(\cos^{4}\left(d x +c \right)\right)-3 i B \left(\cos^{2}\left(d x +c \right)\right)-3 B \left(\cos^{2}\left(d x +c \right)\right)-25 i A -4 B \left(\cos^{4}\left(d x +c \right)\right)\right)}{d \cos \left(d x +c \right) a^{2}}"," ",0,"(-1/12-1/12*I)/d*(cos(d*x+c)/sin(d*x+c))^(3/2)*sin(d*x+c)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(25*A+7*B-3*B*cos(d*x+c)^2-9*A*cos(d*x+c)^2-3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+11*A*cos(d*x+c)*sin(d*x+c)+7*I*B-4*A*cos(d*x+c)^4-4*B*cos(d*x+c)^4-3*I*B*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-3*I*A*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-5*B*cos(d*x+c)*sin(d*x+c)-4*B*cos(d*x+c)^3*sin(d*x+c)+3*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*I*B*cos(d*x+c)^4+4*A*cos(d*x+c)^3*sin(d*x+c)+4*I*A*cos(d*x+c)^4+9*I*A*cos(d*x+c)^2-3*I*B*cos(d*x+c)^2+4*I*A*cos(d*x+c)^3*sin(d*x+c)+4*I*B*cos(d*x+c)^3*sin(d*x+c)+11*I*A*cos(d*x+c)*sin(d*x+c)+5*I*B*cos(d*x+c)*sin(d*x+c)+3*A*2^(1/2)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-3*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-25*I*A)/cos(d*x+c)/a^2","B"
559,1,853,134,4.155000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(-\frac{1}{12}+\frac{i}{12}\right) \left(-3 i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}+7 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-9 i A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 i B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{2}+i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-3 i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sqrt{2}-3 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+6 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-7 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-7 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-9 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{2}-B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sqrt{2}+6 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+6 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-3 B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}+7 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(2 i \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a^{2}}"," ",0,"(-1/12+1/12*I)/d*(-3*I*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+7*I*A*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-9*I*A*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)+I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-3*I*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)-3*I*B*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*B*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+6*B*cos(d*x+c)^2*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-7*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-7*A*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-9*A*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)-B*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*B*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+6*I*A*cos(d*x+c)^2*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+6*I*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-3*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+7*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*(cos(d*x+c)/sin(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/a^2","B"
560,1,867,136,4.254000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(\frac{1}{12}-\frac{i}{12}\right) \left(i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 i A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 i A \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-3 i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-6 A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+5 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+6 i B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-6 i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+3 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 A \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+5 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-5 i B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 B \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-3 i B \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-5 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \cos \left(d x +c \right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(2 i \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a^{2}}"," ",0,"(1/12-1/12*I)/d*(I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)+3*I*A*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-3*I*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-6*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)+5*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+6*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)-6*I*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)-6*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+A*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*A*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*A*cos(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+5*B*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*B*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-5*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*B*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-3*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)-A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-5*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/sin(d*x+c)/(cos(d*x+c)/sin(d*x+c))^(1/2)/a^2","B"
561,1,1516,192,4.084000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(-\frac{1}{12}-\frac{i}{12}\right) \left(3 A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-6 B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+6 i B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+3 A \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-3 i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+3 B \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-6 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right) \cos \left(d x +c \right)+6 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right) \cos \left(d x +c \right)-5 A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+11 B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-6 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right) \sin \left(d x +c \right)+6 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sin \left(d x +c \right)-6 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sin \left(d x +c \right)+6 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right) \sin \left(d x +c \right)+12 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \left(\cos^{2}\left(d x +c \right)\right)-12 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right) \left(\cos^{2}\left(d x +c \right)\right)-12 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{2}\left(d x +c \right)\right)+12 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right) \left(\cos^{2}\left(d x +c \right)\right)+5 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+11 i B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-11 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+5 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-11 i B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-5 i A \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)+6 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+3 i A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-9 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 i A \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-3 i B \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-9 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+6 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-6 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+6 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right)-6 B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right)-6 i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+12 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-12 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+12 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-12 i B \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right) \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(2 i \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{2} a^{2}}"," ",0,"(-1/12-1/12*I)/d*(-6*I*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+3*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+3*A*cos(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+3*B*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-5*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+11*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+12*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)*sin(d*x+c)-9*I*B*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-12*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)*sin(d*x+c)+12*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)-12*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)*sin(d*x+c)+3*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)+5*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+11*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-6*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*sin(d*x+c)+6*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)-6*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)+6*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*sin(d*x+c)-3*A*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-9*B*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)-3*I*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-6*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)+6*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-6*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+6*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)+5*A*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-11*B*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-5*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-11*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+12*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)^2-12*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+12*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2-12*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)^2-6*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)+6*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)-6*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)+6*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)+6*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)-6*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-3*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+3*I*A*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)))*cos(d*x+c)^2*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/(cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^2/a^2","B"
562,1,764,210,4.097000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(\frac{1}{120}+\frac{i}{120}\right) \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-317 A -67 B +48 B \left(\cos^{6}\left(d x +c \right)\right)-56 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+16 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-151 A \cos \left(d x +c \right) \sin \left(d x +c \right)+41 B \cos \left(d x +c \right) \sin \left(d x +c \right)-48 i A \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-48 i B \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+48 A \left(\cos^{6}\left(d x +c \right)\right)+117 A \left(\cos^{2}\left(d x +c \right)\right)-32 i A \left(\cos^{4}\left(d x +c \right)\right)-151 i A \cos \left(d x +c \right) \sin \left(d x +c \right)-56 i A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-15 A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-67 i B +48 i B \left(\cos^{6}\left(d x +c \right)\right)+48 B \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-48 A \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-48 i A \left(\cos^{6}\left(d x +c \right)\right)-41 i B \cos \left(d x +c \right) \sin \left(d x +c \right)-16 i B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i B \sqrt{2}\, \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+32 A \left(\cos^{4}\left(d x +c \right)\right)-117 i A \left(\cos^{2}\left(d x +c \right)\right)-15 A \sqrt{2}\, \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+15 i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+15 B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+317 i A -8 i B \left(\cos^{4}\left(d x +c \right)\right)+27 i B \left(\cos^{2}\left(d x +c \right)\right)+27 B \left(\cos^{2}\left(d x +c \right)\right)-8 B \left(\cos^{4}\left(d x +c \right)\right)\right)}{d \cos \left(d x +c \right) a^{3}}"," ",0,"(1/120+1/120*I)/d*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-317*A-67*B+27*B*cos(d*x+c)^2+48*A*cos(d*x+c)^6+48*B*cos(d*x+c)^6+117*A*cos(d*x+c)^2-151*A*cos(d*x+c)*sin(d*x+c)+32*A*cos(d*x+c)^4-8*B*cos(d*x+c)^4+15*I*A*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+41*B*cos(d*x+c)*sin(d*x+c)+15*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+15*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+16*B*cos(d*x+c)^3*sin(d*x+c)-15*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-56*A*cos(d*x+c)^3*sin(d*x+c)-48*I*A*cos(d*x+c)^6+48*I*B*cos(d*x+c)^6-32*I*A*cos(d*x+c)^4-8*I*B*cos(d*x+c)^4-117*I*A*cos(d*x+c)^2+27*I*B*cos(d*x+c)^2-48*A*cos(d*x+c)^5*sin(d*x+c)+48*B*cos(d*x+c)^5*sin(d*x+c)-48*I*A*cos(d*x+c)^5*sin(d*x+c)-48*I*B*cos(d*x+c)^5*sin(d*x+c)-56*I*A*cos(d*x+c)^3*sin(d*x+c)-16*I*B*cos(d*x+c)^3*sin(d*x+c)-151*I*A*cos(d*x+c)*sin(d*x+c)-41*I*B*cos(d*x+c)*sin(d*x+c)-15*A*2^(1/2)*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+15*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+317*I*A-67*I*B)/cos(d*x+c)/a^3","B"
563,1,1078,172,4.261000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-\frac{1}{120}+\frac{i}{120}\right) \left(67 i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+67 A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+15 B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}-30 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+15 i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}+15 A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{2}-45 B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sqrt{2}-30 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+30 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-160 i A \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-172 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+12 B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+160 i A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+60 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+160 A \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-30 i B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+60 i B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-160 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-172 i A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-12 i B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-60 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+60 i A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-15 i B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{2}-45 i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(4 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \left(\cos^{3}\left(d x +c \right)\right)-i \sin \left(d x +c \right)-3 \cos \left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a^{3}}"," ",0,"(-1/120+1/120*I)/d*(60*I*B*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+67*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+15*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-30*I*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+15*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)-45*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+30*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+160*I*A*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-160*I*A*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+67*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+60*B*cos(d*x+c)^3*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-172*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+12*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+15*I*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-30*B*cos(d*x+c)^2*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-160*A*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+160*A*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-60*A*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+60*I*A*cos(d*x+c)^3*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-172*I*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-30*I*A*cos(d*x+c)^2*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-12*I*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-45*I*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)-15*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(4*I*cos(d*x+c)^2*sin(d*x+c)+4*cos(d*x+c)^3-I*sin(d*x+c)-3*cos(d*x+c))/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/a^3","B"
564,1,1092,174,4.103000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-\frac{1}{120}+\frac{i}{120}\right) \left(15 A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-30 B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+30 i B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-3 i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-45 A \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+13 i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-15 i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-15 B \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+3 A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+13 B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-30 A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-40 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-15 i A \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+45 i B \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+12 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-28 B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-40 i B \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+60 A \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}+40 i B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+40 B \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+60 i A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}-30 i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-12 i A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-28 i B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+60 B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}-60 i B \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}\right) \cos \left(d x +c \right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(4 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \left(\cos^{3}\left(d x +c \right)\right)-i \sin \left(d x +c \right)-3 \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a^{3}}"," ",0,"(-1/120+1/120*I)/d*(60*I*A*cos(d*x+c)^2*sin(d*x+c)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+3*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+15*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+13*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-45*A*cos(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-15*B*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-30*I*A*cos(d*x+c)*sin(d*x+c)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-15*I*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+60*A*cos(d*x+c)^3*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+40*I*B*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-40*I*B*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+13*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+12*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-28*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-30*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)-40*B*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+40*B*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+60*B*cos(d*x+c)^2*sin(d*x+c)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-15*I*A*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+45*I*B*cos(d*x+c)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-60*I*B*cos(d*x+c)^3*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-12*I*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-28*I*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+30*I*B*cos(d*x+c)^2*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-30*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2))*cos(d*x+c)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(4*I*cos(d*x+c)^2*sin(d*x+c)+4*cos(d*x+c)^3-I*sin(d*x+c)-3*cos(d*x+c))/sin(d*x+c)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/(cos(d*x+c)/sin(d*x+c))^(1/2)/a^3","B"
565,1,1212,172,4.049000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-\frac{1}{120}-\frac{i}{120}\right) \left(-15 A \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+30 B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-30 i B \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-13 i A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+45 A \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-37 i B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+15 i B \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+15 B \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)+13 A \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-37 B \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+30 A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+40 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+15 i A \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-45 i B \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right)-40 i A \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-28 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+52 B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+40 i A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+40 i B \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-60 A \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}-40 i B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-40 A \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-40 B \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-60 i A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}+40 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+30 i A \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+28 i A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+52 i B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-60 B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}+60 i B \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}\right) \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(4 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \left(\cos^{3}\left(d x +c \right)\right)-i \sin \left(d x +c \right)-3 \cos \left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2} \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} a^{3}}"," ",0,"(-1/120-1/120*I)/d*(-60*I*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*cos(d*x+c)^2+13*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-15*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-37*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+45*A*cos(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+15*B*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+30*I*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-60*A*cos(d*x+c)^3*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-28*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+52*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+40*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-40*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-13*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-40*I*A*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-37*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+40*I*B*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+15*I*B*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+30*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)^2*2^(1/2)+40*A*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-40*A*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+40*B*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-40*B*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+60*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^3+28*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*I*A*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+52*I*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-30*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2-45*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)-60*B*cos(d*x+c)^2*sin(d*x+c)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+30*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2))*cos(d*x+c)^2*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(4*I*cos(d*x+c)^2*sin(d*x+c)+4*cos(d*x+c)^3-I*sin(d*x+c)-3*cos(d*x+c))/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/sin(d*x+c)^2/(cos(d*x+c)/sin(d*x+c))^(3/2)/a^3","B"
566,1,2158,230,4.090000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"(-1/120-1/120*I)/d*(60*I*B*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-37*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+147*B*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+60*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*sin(d*x+c)-60*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)-60*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*sin(d*x+c)+15*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+60*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)-30*I*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+15*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)-45*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)-240*B*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)+240*B*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)-240*B*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*sin(d*x+c)+30*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+52*A*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-252*B*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+240*B*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*sin(d*x+c)+120*B*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)-120*B*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)+120*B*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*sin(d*x+c)-120*B*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*sin(d*x+c)+40*I*A*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-40*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+240*I*B*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-240*I*B*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+240*I*B*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-240*I*B*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)+240*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-120*I*B*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+120*I*B*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-120*I*B*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)+120*I*B*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-180*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)+180*I*B*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-180*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)+180*I*B*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-37*I*A*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-240*I*B*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-147*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+60*B*cos(d*x+c)^3*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+15*I*A*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-30*B*cos(d*x+c)^2*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+40*A*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-40*A*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+240*B*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-240*B*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+60*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-60*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+60*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-60*I*B*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)+52*I*A*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+252*I*B*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-60*A*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))+60*I*A*cos(d*x+c)^3*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-30*I*A*cos(d*x+c)^2*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-45*I*A*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)-15*I*B*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2))*cos(d*x+c)^3*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(4*I*cos(d*x+c)^2*sin(d*x+c)+4*cos(d*x+c)^3-I*sin(d*x+c)-3*cos(d*x+c))/(cos(d*x+c)/sin(d*x+c))^(5/2)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/sin(d*x+c)^3/a^3","B"
567,0,0,172,191.778000," ","int(cot(d*x+c)^m*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\cot^{m}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^m*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
568,0,0,215,3.722000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\cot^{\frac{5}{2}}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
569,0,0,172,3.752000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\cot^{\frac{3}{2}}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
570,0,0,139,3.730000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\sqrt{\cot}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
571,0,0,193,3.507000," ","int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\sqrt{\cot \left(d x +c \right)}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","F"
572,0,0,261,1.786000," ","int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\cot \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x)","F"
573,0,0,349,2.041000," ","int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(5/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\cot \left(d x +c \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(5/2),x)","F"
574,1,4490,195,1.689000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/6/d*(-3*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+6*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b+3*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+3*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-6*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a-3*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+3*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+3*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-6*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a-3*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+6*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b+3*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+3*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*I*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+3*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+3*I*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+6*A*2^(1/2)*cos(d*x+c)*sin(d*x+c)*b+6*B*2^(1/2)*cos(d*x+c)*sin(d*x+c)*a+2*A*2^(1/2)*cos(d*x+c)^2*a+3*I*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+3*I*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*I*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*I*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+3*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+3*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b)*(cos(d*x+c)/sin(d*x+c))^(5/2)*sin(d*x+c)/cos(d*x+c)^3*2^(1/2)","C"
575,1,4230,175,1.654000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/2/d*(-B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+2*A*2^(1/2)*cos(d*x+c)*a+I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-I*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+I*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+2*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a-A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+2*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b+B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+2*A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b+I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+2*B*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a+I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-A*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a)*(cos(d*x+c)/sin(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)^2*2^(1/2)","C"
576,1,2223,175,1.706000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/2/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(-I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a+I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b+I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a-I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a+I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a-I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b-I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b+I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b+A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-2*A*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a-B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+2*B*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b-2*B*cos(d*x+c)*2^(1/2)*b+2*B*2^(1/2)*b)/cos(d*x+c)/sin(d*x+c)^3*2^(1/2)","C"
577,1,2401,195,1.592000," ","int((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/6/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(3*I*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+3*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a+3*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b+3*I*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b-3*I*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*I*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a-3*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*A*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+6*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b-3*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+3*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+3*B*cos(d*x+c)*sin(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+6*B*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a-6*A*2^(1/2)*cos(d*x+c)^2*b-6*B*2^(1/2)*cos(d*x+c)^2*a-2*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*b+6*A*cos(d*x+c)*2^(1/2)*b+6*B*cos(d*x+c)*2^(1/2)*a+2*B*sin(d*x+c)*2^(1/2)*b)/cos(d*x+c)/sin(d*x+c)^4/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
578,1,13170,288,2.109000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
579,1,6783,258,1.855000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
580,1,6423,244,1.844000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
581,1,3582,249,1.921000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"1/6/d*(-1+cos(d*x+c))*(-6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*b^2+3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2-3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*b^2+3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2-3*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*b^2-3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2+3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*b^2-3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2+3*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*b^2+6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2-12*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b+3*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2+6*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b-12*B*cos(d*x+c)*2^(1/2)*a*b+6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b+12*B*cos(d*x+c)^2*2^(1/2)*a*b+2*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*b^2+6*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b+6*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b-6*A*cos(d*x+c)*2^(1/2)*b^2+6*A*cos(d*x+c)^2*2^(1/2)*b^2+6*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b-6*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b-6*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b+6*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b-3*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*b^2-3*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2+3*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*b^2+3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2-3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*b^2-3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2+3*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*b^2-2*B*sin(d*x+c)*2^(1/2)*b^2)*(1+cos(d*x+c))^2*(cos(d*x+c)/sin(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)^3*2^(1/2)","C"
582,1,3748,279,1.776000," ","int((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"-1/30/d*(-1+cos(d*x+c))*(-20*B*sin(d*x+c)*2^(1/2)*cos(d*x+c)^2*a*b-60*A*2^(1/2)*cos(d*x+c)^3*a*b-10*A*sin(d*x+c)*2^(1/2)*b^2*cos(d*x+c)^2+60*A*2^(1/2)*cos(d*x+c)^2*a*b+10*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*b^2-15*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+30*B*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-30*B*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+20*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*a*b-30*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a*b+30*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a*b-30*I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a*b+30*I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a*b-36*B*2^(1/2)*b^2*cos(d*x+c)^2-6*B*cos(d*x+c)*2^(1/2)*b^2-30*B*2^(1/2)*a^2*cos(d*x+c)^3+36*B*2^(1/2)*b^2*cos(d*x+c)^3+30*B*2^(1/2)*a^2*cos(d*x+c)^2+6*b^2*B*2^(1/2)+30*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a*b+15*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*I*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*I*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-30*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a*b-30*A*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a*b+60*A*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a*b+30*B*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a*b)*(1+cos(d*x+c))^2/cos(d*x+c)^2/sin(d*x+c)^4/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
583,1,18631,379,2.679000," ","int(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
584,1,17628,340,2.441000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
585,1,9099,338,2.235000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
586,1,8955,332,2.262000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
587,1,4947,340,2.370000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"1/30/d*(-1+cos(d*x+c))*(30*2^(1/2)*B*cos(d*x+c)^2*sin(d*x+c)*a*b^2-30*2^(1/2)*sin(d*x+c)*B*cos(d*x+c)*a*b^2-15*sin(d*x+c)*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-15*sin(d*x+c)*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+10*2^(1/2)*A*cos(d*x+c)^2*sin(d*x+c)*b^3-6*B*2^(1/2)*b^3-15*sin(d*x+c)*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-15*sin(d*x+c)*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+30*sin(d*x+c)*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2*a^3+15*sin(d*x+c)*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*a^3-15*sin(d*x+c)*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*b^3+15*sin(d*x+c)*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*a^3-15*sin(d*x+c)*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*b^3+30*sin(d*x+c)*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2*b^3+6*2^(1/2)*B*cos(d*x+c)*b^3-36*2^(1/2)*B*cos(d*x+c)^3*b^3+36*B*2^(1/2)*cos(d*x+c)^2*b^3-90*2^(1/2)*A*cos(d*x+c)^2*b^2*a-10*2^(1/2)*sin(d*x+c)*A*cos(d*x+c)*b^3-90*2^(1/2)*B*cos(d*x+c)^2*a^2*b+45*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-45*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2-45*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b+45*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2-45*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-45*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2+45*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b+45*I*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a+45*sin(d*x+c)*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b+45*sin(d*x+c)*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a+45*sin(d*x+c)*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b+45*sin(d*x+c)*A*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a-90*sin(d*x+c)*A*cos(d*x+c)^2*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a+45*sin(d*x+c)*B*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b-45*sin(d*x+c)*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*a*b^2+45*sin(d*x+c)*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*a^2*b-45*sin(d*x+c)*B*cos(d*x+c)^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*a-90*sin(d*x+c)*B*cos(d*x+c)^2*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*b+90*A*cos(d*x+c)^3*2^(1/2)*a*b^2+90*B*cos(d*x+c)^3*2^(1/2)*a^2*b+15*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3-15*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3-15*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3+15*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3-15*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3-15*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3+15*I*A*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3+15*I*B*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3)*(1+cos(d*x+c))^2*(cos(d*x+c)/sin(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)^3*2^(1/2)","C"
588,1,5111,379,2.097000," ","int((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
589,1,22300,281,5.503000," ","int(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
590,1,20614,257,4.811000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
591,1,4107,240,4.771000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/2/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b^2+3*I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b^2+2*a^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3*B-2*a^4*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b*B-2*a^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3*B-2*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(3/2)*a^2-2*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(3/2)*b^2+2*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*a^4+2*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*b^4+A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2+A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2-A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^4-A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^4-2*a^3*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*A*b^2-2*a*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*b^4*A+2*a^3*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*A*b^2+2*a*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^4*A-B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2-B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^4+B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^4+2*a^4*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*b*B-3*I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b^2-I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^3+3*I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3*b+I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3*b+I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^3-I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b^2-I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^3+I*A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b+I*B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b-I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3*b-I*B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b+I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^3-3*I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3*b-I*A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b+B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3*b-B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b^2-B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^3+B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3*b-B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b^2-B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^3-I*A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2-I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^4-I*B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2-I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^4+4*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*a^3*b-3*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3*b-3*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b^2-A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^3+B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b+B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b-2*a^3*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*b*B*(a^2+b^2)^(1/2)+I*A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2-A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^3+I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^4+I*B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2+I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^4-2*a^3*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b*B*(a^2+b^2)^(1/2)+2*a^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2*B*(a^2+b^2)^(1/2)+2*a^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2*B*(a^2+b^2)^(1/2)+4*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*a^2*b^2+4*A*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*a*b^3+A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b+A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b+2*a^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*A*b^2*(a^2+b^2)^(1/2)-2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3*A*(a^2+b^2)^(1/2)*a+2*a^2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*A*b^2*(a^2+b^2)^(1/2)-2*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3*A*(a^2+b^2)^(1/2)*a-3*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3*b-3*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b^2)/sin(d*x+c)^2/cos(d*x+c)*(1+cos(d*x+c))^2*2^(1/2)/a/(a^2+b^2)^(3/2)/(a+b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a)","C"
592,1,3684,240,1.839000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/2/d*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(2*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^3-2*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^3*b-2*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^3-B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+2*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*a^3+2*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^3+B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3+B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3+B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3+B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3-2*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2*b^2+2*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b^2-A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3-A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3+A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3-A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3+2*A*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*a^3*b+I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b+I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2+2*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^4-2*B*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*a^4-2*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b-I*B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3-I*B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+I*B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3+3*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2+A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b-A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2+A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b-A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2-I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3-I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3-I*A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-I*A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-3*I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b-3*I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2+3*I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b+3*I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2-I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2-I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b-I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3+I*A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+I*A*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3+I*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3+I*B*(a^2+b^2)^(3/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+I*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3+3*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b+3*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2+3*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b-2*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2*b+2*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2-2*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b+2*A*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2-2*B*(a^2+b^2)^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2*b)/sin(d*x+c)^3/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)/(a^2+b^2)^(3/2)/(a+b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a)","C"
593,1,9867,257,1.731000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
594,1,12107,281,3.691000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
595,1,57954,396,5.904000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
596,1,36065,352,5.759000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
597,1,40753,350,4.259000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
598,1,40751,352,4.035000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
599,1,42740,395,4.148000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
600,1,159217,549,10.877000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
601,1,100811,486,8.880000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
602,1,102206,486,5.809000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
603,1,102262,482,5.306000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
604,1,102135,486,5.999000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
605,1,104936,548,5.706000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
606,1,1275,124,0.883000," ","int(cot(d*x+c)^(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","-\frac{B \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}}{6 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)^{3}}"," ",0,"-1/6*B/d*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+2*cos(d*x+c)^2*2^(1/2))*(1+cos(d*x+c))^2*(cos(d*x+c)/sin(d*x+c))^(5/2)/cos(d*x+c)^3/sin(d*x+c)^3*2^(1/2)","C"
607,1,969,124,0.841000," ","int(cot(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","-\frac{B \left(i \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(d x +c \right) \sqrt{2}\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"-1/2*B/d*(I*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(d*x+c)*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)^2*2^(1/2)","C"
608,1,324,110,0.831000," ","int(cot(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","-\frac{B \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(i \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"-1/2*B/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(I*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))/sin(d*x+c)^2/cos(d*x+c)*(1+cos(d*x+c))^2*2^(1/2)","C"
609,1,284,110,0.924000," ","int((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x)","-\frac{B \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(i \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{2}}{2 d \sin \left(d x +c \right)^{3} \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"-1/2*B/d*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))/sin(d*x+c)^3/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
610,1,658,124,0.929000," ","int((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x)","\frac{B \left(i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(d x +c \right) \sqrt{2}-2 \sqrt{2}\right) \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{2 d \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{5}}"," ",0,"1/2*B/d*(I*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)+((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+2*cos(d*x+c)*2^(1/2)-2*2^(1/2))*(-1+cos(d*x+c))*cos(d*x+c)*(1+cos(d*x+c))^2/(cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^5*2^(1/2)","C"
611,1,546,124,0.934000," ","int((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x)","-\frac{B \left(-1+\cos \left(d x +c \right)\right) \left(3 i \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \cos \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{6 d \sin \left(d x +c \right)^{5} \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/6*B/d*(-1+cos(d*x+c))*(3*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi((-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*cos(d*x+c)*2^(1/2)+2*2^(1/2))*cos(d*x+c)*(1+cos(d*x+c))^2/sin(d*x+c)^5/(cos(d*x+c)/sin(d*x+c))^(5/2)*2^(1/2)","C"
612,1,44451,300,3.277000," ","int(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
613,1,43089,242,2.753000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
614,1,21822,197,2.316000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
615,1,21114,160,2.013000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
616,1,8318,187,1.757000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
617,1,23897,215,1.977000," ","int((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
618,1,28562,268,2.513000," ","int((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
619,1,74366,362,4.082000," ","int(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
620,1,50449,297,3.311000," ","int(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
621,1,48921,250,2.851000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
622,1,24840,194,2.384000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
623,1,42434,222,2.337000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
624,1,27726,218,2.370000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
625,1,31090,271,2.699000," ","int((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
626,1,34780,321,5.207000," ","int((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
627,1,103764,434,7.007000," ","int(cot(d*x+c)^(13/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
628,1,101072,358,6.241000," ","int(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
629,1,68491,295,3.773000," ","int(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
630,1,66711,239,3.188000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
631,1,47330,248,2.979000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
632,1,57707,251,4.263000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
633,1,32893,264,4.844000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
634,1,36015,314,5.467000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
635,1,39803,389,6.778000," ","int((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
636,1,29155,248,2.610000," ","int(cot(d*x+c)^(7/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
637,1,14814,201,2.231000," ","int(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
638,1,14192,165,2.005000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
639,1,3474,133,3.604000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"1/d*2^(1/2)*(cos(d*x+c)/sin(d*x+c))^(1/2)*(1/cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)))^(1/2)*(-2*I*A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2+I*A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3-I*B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b+I*B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b+2*I*A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b*(a^2+b^2)^(1/2)-I*B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*(a^2+b^2)^(1/2)-I*A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3+I*B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*(a^2+b^2)^(1/2)+2*I*A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2-2*I*A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b*(a^2+b^2)^(1/2)+A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*(a^2+b^2)^(1/2)+A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*(a^2+b^2)^(1/2)-2*A*EllipticF((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*(a^2+b^2)^(1/2)-4*A*EllipticF((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^2*(a^2+b^2)^(1/2)-A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b-A*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b+4*A*EllipticF((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b+4*A*EllipticF((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^3+2*B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b*(a^2+b^2)^(1/2)+2*B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b*(a^2+b^2)^(1/2)-B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3-2*B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2-B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3-2*B*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2)*(a*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(((a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/(a^2+b^2)^(1/2)/sin(d*x+c))^(1/2)*(-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/(a*cos(d*x+c)+b*sin(d*x+c))/a/(I*a+(a^2+b^2)^(1/2)-b)/(I*a-(a^2+b^2)^(1/2)+b)","C"
640,1,6682,186,1.898000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
641,1,21458,220,2.206000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
642,1,19785,268,2.512000," ","int(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
643,1,18966,218,2.011000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
644,1,9692,181,1.957000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
645,1,9696,176,1.893000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
646,1,21769,233,2.168000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
647,1,81959,347,7.016000," ","int(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
648,1,54509,295,5.861000," ","int(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
649,1,40953,245,5.659000," ","int(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
650,1,40861,242,5.252000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
651,1,40873,242,3.441000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
652,1,77807,290,7.098000," ","int((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
653,1,2080,123,1.970000," ","int(cot(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)","-\frac{B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{a \cos \left(d x +c \right)+b \sin \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(2 i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a b \sqrt{a^{2}+b^{2}}-2 i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a b \sqrt{a^{2}+b^{2}}-i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{3}-2 i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a \,b^{2}+i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{3}+2 i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a \,b^{2}+2 \sqrt{a^{2}+b^{2}}\, \EllipticF \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{2}+4 \sqrt{a^{2}+b^{2}}\, \EllipticF \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) b^{2}-\EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{2} \sqrt{a^{2}+b^{2}}-\EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{2} \sqrt{a^{2}+b^{2}}-4 \EllipticF \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{2} b -4 \EllipticF \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) b^{3}+\EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{2} b +\EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{2} b \right) \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}\, \sqrt{\frac{\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}\, \left(\sin^{2}\left(d x +c \right)\right)}{d \left(-1+\cos \left(d x +c \right)\right) \left(a \cos \left(d x +c \right)+b \sin \left(d x +c \right)\right) \left(i a -\sqrt{a^{2}+b^{2}}+b \right) \left(i a +\sqrt{a^{2}+b^{2}}-b \right) a}"," ",0,"-B/d*2^(1/2)*(cos(d*x+c)/sin(d*x+c))^(1/2)*(1/cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)))^(1/2)*(2*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b*(a^2+b^2)^(1/2)-2*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b*(a^2+b^2)^(1/2)-I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3-2*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2+I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3+2*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2+2*(a^2+b^2)^(1/2)*EllipticF((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2+4*(a^2+b^2)^(1/2)*EllipticF((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^2-EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*(a^2+b^2)^(1/2)-EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*(a^2+b^2)^(1/2)-4*EllipticF((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b-4*EllipticF((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^3+EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b+EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b)*(a*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(((a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/(a^2+b^2)^(1/2)/sin(d*x+c))^(1/2)*(-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/(a*cos(d*x+c)+b*sin(d*x+c))/(I*a-(a^2+b^2)^(1/2)+b)/(I*a+(a^2+b^2)^(1/2)-b)/a","C"
654,1,1649,127,1.988000," ","int((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x)","\frac{B \left(i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a \sqrt{a^{2}+b^{2}}-i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a \sqrt{a^{2}+b^{2}}-i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a b +i \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a b +2 \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) b \sqrt{a^{2}+b^{2}}+2 \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) b \sqrt{a^{2}+b^{2}}-\EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{2}-2 \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) b^{2}-\EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{2}-2 \EllipticPi \left(\sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}, \frac{-b +\sqrt{a^{2}+b^{2}}}{-i a +\sqrt{a^{2}+b^{2}}-b}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) b^{2}\right) \cos \left(d x +c \right) \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}\, \sqrt{\frac{\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)}}\, \sqrt{-\frac{-\sqrt{a^{2}+b^{2}}\, \sin \left(d x +c \right)+a \cos \left(d x +c \right)+b \sin \left(d x +c \right)-a}{\sin \left(d x +c \right) \left(-b +\sqrt{a^{2}+b^{2}}\right)}}\, \sin \left(d x +c \right) \sqrt{\frac{a \cos \left(d x +c \right)+b \sin \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{2}}{d \left(a \cos \left(d x +c \right)+b \sin \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(i a -\sqrt{a^{2}+b^{2}}+b \right) \left(i a +\sqrt{a^{2}+b^{2}}-b \right)}"," ",0,"B/d*(I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*(a^2+b^2)^(1/2)-I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*(a^2+b^2)^(1/2)-I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b+I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b+2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b*(a^2+b^2)^(1/2)+2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b*(a^2+b^2)^(1/2)-EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2-2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^2-EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2-2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^2)*cos(d*x+c)*(a*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(((a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/(a^2+b^2)^(1/2)/sin(d*x+c))^(1/2)*(-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2)*sin(d*x+c)*(1/cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)))^(1/2)*2^(1/2)/(a*cos(d*x+c)+b*sin(d*x+c))/(-1+cos(d*x+c))/(cos(d*x+c)/sin(d*x+c))^(1/2)/(I*a-(a^2+b^2)^(1/2)+b)/(I*a+(a^2+b^2)^(1/2)-b)","C"
655,1,4699,175,1.842000," ","int((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"2*B/d*2^(1/2)*(-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2)*(((a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/(a^2+b^2)^(1/2)/sin(d*x+c))^(1/2)*(a*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)+a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^4+4*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)+a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^4-EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^4-4*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^4+3*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b^2-2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2*(a^2+b^2)^(1/2)-3*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)+a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b*(a^2+b^2)^(1/2)-2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)+a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2*(a^2+b^2)^(1/2)-2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2*(a^2+b^2)^(1/2)+3*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b*(a^2+b^2)^(1/2)-2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^2*(a^2+b^2)^(1/2)-5*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b^2+2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^3+4*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^3*(a^2+b^2)^(1/2)+EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3*b+2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^3+EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3*b+2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^3+2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)+a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3*b-4*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^4+4*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^4-EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)+a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3*(a^2+b^2)^(1/2)+5*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)+a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b^2+2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)+a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a*b^3-4*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)+a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^3*(a^2+b^2)^(1/2)+2*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3*b-EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^3*(a^2+b^2)^(1/2)+4*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^3*(a^2+b^2)^(1/2)-3*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b^2-4*I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^3*(a^2+b^2)^(1/2)+I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b*(a^2+b^2)^(1/2)-I*EllipticPi((-(-(a^2+b^2)^(1/2)*sin(d*x+c)+a*cos(d*x+c)+b*sin(d*x+c)-a)/sin(d*x+c)/(-b+(a^2+b^2)^(1/2)))^(1/2),(-b+(a^2+b^2)^(1/2))/(-I*a+(a^2+b^2)^(1/2)-b),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a^2*b*(a^2+b^2)^(1/2))*(1/cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)))^(1/2)*cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))/(-1+cos(d*x+c))/(cos(d*x+c)/sin(d*x+c))^(3/2)/(I*a-(a^2+b^2)^(1/2)+b)/(I*a+(a^2+b^2)^(1/2)-b)/(-b+(a^2+b^2)^(1/2)-a)/(-b+(a^2+b^2)^(1/2)+a)","C"
656,0,0,187,1.472000," ","int(cot(d*x+c)^m*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\cot^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^m*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
657,0,0,153,1.556000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\cot^{\frac{3}{2}}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
658,0,0,151,1.587000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\sqrt{\cot}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
659,0,0,153,1.529000," ","int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\int \frac{\left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\sqrt{\cot \left(d x +c \right)}}\, dx"," ",0,"int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x)","F"
660,0,0,153,1.444000," ","int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x)","\int \frac{\left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\cot \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x)","F"
661,0,0,153,1.336000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
662,0,0,153,1.366000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","\int \left(\sqrt{\tan}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)\, dx"," ",0,"int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x)","F"
663,0,0,151,1.377000," ","int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\int \frac{\left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\sqrt{\tan \left(d x +c \right)}}\, dx"," ",0,"int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x)","F"
664,0,0,153,1.312000," ","int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","\int \frac{\left(a +b \tan \left(d x +c \right)\right)^{n} \left(A +B \tan \left(d x +c \right)\right)}{\tan \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x)","F"
665,1,128,60,3.796000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x)","\frac{i {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)} A a}{f \left(1+n \right)}+\frac{i {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)} a A}{f n \left(1+n \right)}+\frac{{\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)} a B}{f n \left(1+n \right)}+\frac{i a B \tan \left(f x +e \right) {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)}}{f \left(1+n \right)}"," ",0,"I/f/(1+n)*exp(n*ln(c-I*c*tan(f*x+e)))*A*a+I/f/n/(1+n)*exp(n*ln(c-I*c*tan(f*x+e)))*a*A+1/f/n/(1+n)*exp(n*ln(c-I*c*tan(f*x+e)))*a*B+I*a*B/f/(1+n)*tan(f*x+e)*exp(n*ln(c-I*c*tan(f*x+e)))","B"
666,1,99,52,0.022000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x)","\frac{a \,c^{4} \left(\frac{i B \left(\tan^{5}\left(f x +e \right)\right)}{5}+\frac{i A \left(\tan^{4}\left(f x +e \right)\right)}{4}-i B \left(\tan^{3}\left(f x +e \right)\right)-\frac{3 B \left(\tan^{4}\left(f x +e \right)\right)}{4}-\frac{3 i A \left(\tan^{2}\left(f x +e \right)\right)}{2}-A \left(\tan^{3}\left(f x +e \right)\right)+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a*c^4*(1/5*I*B*tan(f*x+e)^5+1/4*I*A*tan(f*x+e)^4-I*B*tan(f*x+e)^3-3/4*B*tan(f*x+e)^4-3/2*I*A*tan(f*x+e)^2-A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
667,1,75,52,0.020000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x)","\frac{a \,c^{3} \left(-\frac{2 i B \left(\tan^{3}\left(f x +e \right)\right)}{3}-\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{4}-i A \left(\tan^{2}\left(f x +e \right)\right)-\frac{A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a*c^3*(-2/3*I*B*tan(f*x+e)^3-1/4*B*tan(f*x+e)^4-I*A*tan(f*x+e)^2-1/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
668,1,53,60,0.021000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x)","\frac{a \,c^{2} \left(-\frac{i B \left(\tan^{3}\left(f x +e \right)\right)}{3}-\frac{i A \left(\tan^{2}\left(f x +e \right)\right)}{2}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a*c^2*(-1/3*I*B*tan(f*x+e)^3-1/2*I*A*tan(f*x+e)^2+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
669,1,27,30,0.022000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x)","\frac{c a \left(\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*c*a*(1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
670,1,81,43,0.023000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e)),x)","\frac{i a B \tan \left(f x +e \right)}{f}+\frac{i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) A}{2 f}+\frac{a \ln \left(1+\tan^{2}\left(f x +e \right)\right) B}{2 f}-\frac{i a B \arctan \left(\tan \left(f x +e \right)\right)}{f}+\frac{a A \arctan \left(\tan \left(f x +e \right)\right)}{f}"," ",0,"I*a*B*tan(f*x+e)/f+1/2*I/f*a*ln(1+tan(f*x+e)^2)*A+1/2/f*a*ln(1+tan(f*x+e)^2)*B-I/f*a*B*arctan(tan(f*x+e))+1/f*a*A*arctan(tan(f*x+e))","A"
671,1,64,51,0.251000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","-\frac{i a B}{f c \left(\tan \left(f x +e \right)+i\right)}+\frac{a A}{f c \left(\tan \left(f x +e \right)+i\right)}-\frac{a B \ln \left(\tan \left(f x +e \right)+i\right)}{f c}"," ",0,"-I/f*a/c/(tan(f*x+e)+I)*B+1/f*a/c/(tan(f*x+e)+I)*A-1/f*a/c*B*ln(tan(f*x+e)+I)","A"
672,1,46,42,0.234000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x)","\frac{a \left(\frac{i B}{\tan \left(f x +e \right)+i}-\frac{-i A -B}{2 \left(\tan \left(f x +e \right)+i\right)^{2}}\right)}{f \,c^{2}}"," ",0,"1/f*a/c^2*(I*B/(tan(f*x+e)+I)-1/2*(-I*A-B)/(tan(f*x+e)+I)^2)","A"
673,1,43,48,0.228000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x)","\frac{a \left(-\frac{B}{2 \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{-i B +A}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}\right)}{f \,c^{3}}"," ",0,"1/f*a/c^3*(-1/2*B/(tan(f*x+e)+I)^2-1/3*(A-I*B)/(tan(f*x+e)+I)^3)","A"
674,1,44,49,0.228000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x)","\frac{a \left(-\frac{i A +B}{4 \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{i B}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}\right)}{f \,c^{4}}"," ",0,"1/f*a/c^4*(-1/4*(I*A+B)/(tan(f*x+e)+I)^4-1/3*I*B/(tan(f*x+e)+I)^3)","A"
675,1,45,48,0.229000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^5,x)","\frac{a \left(-\frac{i B -A}{5 \left(\tan \left(f x +e \right)+i\right)^{5}}+\frac{B}{4 \left(\tan \left(f x +e \right)+i\right)^{4}}\right)}{f \,c^{5}}"," ",0,"1/f*a/c^5*(-1/5*(-A+I*B)/(tan(f*x+e)+I)^5+1/4*B/(tan(f*x+e)+I)^4)","A"
676,1,280,104,3.832000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x)","\frac{i n \,{\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)} A \,a^{2}}{f \left(1+n \right) \left(2+n \right)}+\frac{4 i {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)} A \,a^{2}}{f \left(1+n \right) \left(2+n \right)}+\frac{4 i {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)} A \,a^{2}}{f n \left(1+n \right) \left(2+n \right)}+\frac{{\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)} a^{2} B}{f \left(1+n \right) \left(2+n \right)}+\frac{4 \,{\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)} a^{2} B}{f n \left(1+n \right) \left(2+n \right)}-\frac{a^{2} B \left(\tan^{2}\left(f x +e \right)\right) {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)}}{f \left(2+n \right)}-\frac{a^{2} \left(-i B n +A n -4 i B +2 A \right) \tan \left(f x +e \right) {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)}}{f \left(1+n \right) \left(2+n \right)}"," ",0,"I/f*n/(1+n)/(2+n)*exp(n*ln(c-I*c*tan(f*x+e)))*A*a^2+4*I/f/(1+n)/(2+n)*exp(n*ln(c-I*c*tan(f*x+e)))*A*a^2+4*I/f/n/(1+n)/(2+n)*exp(n*ln(c-I*c*tan(f*x+e)))*A*a^2+1/f/(1+n)/(2+n)*exp(n*ln(c-I*c*tan(f*x+e)))*a^2*B+4/f/n/(1+n)/(2+n)*exp(n*ln(c-I*c*tan(f*x+e)))*a^2*B-a^2*B/f/(2+n)*tan(f*x+e)^2*exp(n*ln(c-I*c*tan(f*x+e)))-a^2*(-I*B*n+A*n-4*I*B+2*A)/f/(1+n)/(2+n)*tan(f*x+e)*exp(n*ln(c-I*c*tan(f*x+e)))","B"
677,1,147,88,0.024000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5,x)","\frac{c^{5} a^{2} \left(\frac{i B \left(\tan^{7}\left(f x +e \right)\right)}{7}+\frac{i A \left(\tan^{6}\left(f x +e \right)\right)}{6}-\frac{2 i B \left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{B \left(\tan^{6}\left(f x +e \right)\right)}{2}-\frac{i A \left(\tan^{4}\left(f x +e \right)\right)}{2}-\frac{3 A \left(\tan^{5}\left(f x +e \right)\right)}{5}-i B \left(\tan^{3}\left(f x +e \right)\right)-\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{2}-\frac{3 i A \left(\tan^{2}\left(f x +e \right)\right)}{2}-\frac{2 A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*c^5*a^2*(1/7*I*B*tan(f*x+e)^7+1/6*I*A*tan(f*x+e)^6-2/5*I*B*tan(f*x+e)^5-1/2*B*tan(f*x+e)^6-1/2*I*A*tan(f*x+e)^4-3/5*A*tan(f*x+e)^5-I*B*tan(f*x+e)^3-1/2*B*tan(f*x+e)^4-3/2*I*A*tan(f*x+e)^2-2/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
678,1,101,88,0.022000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x)","\frac{c^{4} a^{2} \left(-\frac{2 i B \left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{B \left(\tan^{6}\left(f x +e \right)\right)}{6}-\frac{i A \left(\tan^{4}\left(f x +e \right)\right)}{2}-\frac{A \left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{2 i B \left(\tan^{3}\left(f x +e \right)\right)}{3}-i A \left(\tan^{2}\left(f x +e \right)\right)+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*c^4*a^2*(-2/5*I*B*tan(f*x+e)^5-1/6*B*tan(f*x+e)^6-1/2*I*A*tan(f*x+e)^4-1/5*A*tan(f*x+e)^5-2/3*I*B*tan(f*x+e)^3-I*A*tan(f*x+e)^2+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
679,1,101,88,0.021000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x)","\frac{c^{3} a^{2} \left(-\frac{i B \left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{i A \left(\tan^{4}\left(f x +e \right)\right)}{4}-\frac{i B \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{4}-\frac{i A \left(\tan^{2}\left(f x +e \right)\right)}{2}+\frac{A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*c^3*a^2*(-1/5*I*B*tan(f*x+e)^5-1/4*I*A*tan(f*x+e)^4-1/3*I*B*tan(f*x+e)^3+1/4*B*tan(f*x+e)^4-1/2*I*A*tan(f*x+e)^2+1/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
680,1,53,58,0.023000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x)","\frac{a^{2} c^{2} \left(\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{4}+\frac{A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a^2*c^2*(1/4*B*tan(f*x+e)^4+1/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
681,1,53,58,0.022000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x)","\frac{a^{2} c \left(\frac{i B \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{i A \left(\tan^{2}\left(f x +e \right)\right)}{2}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a^2*c*(1/3*I*B*tan(f*x+e)^3+1/2*I*A*tan(f*x+e)^2+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
682,1,123,74,0.023000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e)),x)","-\frac{a^{2} B \left(\tan^{2}\left(f x +e \right)\right)}{2 f}-\frac{a^{2} A \tan \left(f x +e \right)}{f}+\frac{2 i a^{2} B \tan \left(f x +e \right)}{f}+\frac{i a^{2} A \ln \left(1+\tan^{2}\left(f x +e \right)\right)}{f}+\frac{a^{2} B \ln \left(1+\tan^{2}\left(f x +e \right)\right)}{f}-\frac{2 i a^{2} B \arctan \left(\tan \left(f x +e \right)\right)}{f}+\frac{2 a^{2} A \arctan \left(\tan \left(f x +e \right)\right)}{f}"," ",0,"-1/2/f*a^2*B*tan(f*x+e)^2-1/f*a^2*A*tan(f*x+e)+2*I/f*a^2*B*tan(f*x+e)+I/f*a^2*A*ln(1+tan(f*x+e)^2)+1/f*a^2*B*ln(1+tan(f*x+e)^2)-2*I/f*a^2*B*arctan(tan(f*x+e))+2/f*a^2*A*arctan(tan(f*x+e))","A"
683,1,113,88,0.252000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","-\frac{i a^{2} B \tan \left(f x +e \right)}{c f}-\frac{2 i a^{2} B}{f c \left(\tan \left(f x +e \right)+i\right)}+\frac{2 a^{2} A}{f c \left(\tan \left(f x +e \right)+i\right)}-\frac{i a^{2} A \ln \left(\tan \left(f x +e \right)+i\right)}{f c}-\frac{3 a^{2} B \ln \left(\tan \left(f x +e \right)+i\right)}{f c}"," ",0,"-I*a^2*B*tan(f*x+e)/c/f-2*I/f*a^2/c/(tan(f*x+e)+I)*B+2/f*a^2/c/(tan(f*x+e)+I)*A-I/f*a^2/c*A*ln(tan(f*x+e)+I)-3/f*a^2/c*B*ln(tan(f*x+e)+I)","A"
684,1,116,86,0.250000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x)","\frac{3 i a^{2} B}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)}-\frac{a^{2} A}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)}+\frac{a^{2} B \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{2}}+\frac{i a^{2} A}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{a^{2} B}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"3*I/f*a^2/c^2/(tan(f*x+e)+I)*B-1/f*a^2/c^2/(tan(f*x+e)+I)*A+1/f*a^2/c^2*B*ln(tan(f*x+e)+I)+I/f*a^2/c^2/(tan(f*x+e)+I)^2*A+1/f*a^2/c^2/(tan(f*x+e)+I)^2*B","A"
685,1,69,83,0.237000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x)","\frac{a^{2} \left(-\frac{i B}{\tan \left(f x +e \right)+i}-\frac{i A +3 B}{2 \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{-2 i B +2 A}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}\right)}{f \,c^{3}}"," ",0,"1/f*a^2/c^3*(-I*B/(tan(f*x+e)+I)-1/2*(I*A+3*B)/(tan(f*x+e)+I)^2-1/3*(2*A-2*I*B)/(tan(f*x+e)+I)^3)","A"
686,1,68,80,0.236000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x)","\frac{a^{2} \left(\frac{B}{2 \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{3 i B -A}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{2 i A +2 B}{4 \left(\tan \left(f x +e \right)+i\right)^{4}}\right)}{f \,c^{4}}"," ",0,"1/f*a^2/c^4*(1/2*B/(tan(f*x+e)+I)^2-1/3*(-A+3*I*B)/(tan(f*x+e)+I)^3-1/4*(2*I*A+2*B)/(tan(f*x+e)+I)^4)","A"
687,1,69,83,0.253000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^5,x)","\frac{a^{2} \left(-\frac{2 i B -2 A}{5 \left(\tan \left(f x +e \right)+i\right)^{5}}+\frac{i B}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{-i A -3 B}{4 \left(\tan \left(f x +e \right)+i\right)^{4}}\right)}{f \,c^{5}}"," ",0,"1/f*a^2/c^5*(-1/5*(-2*A+2*I*B)/(tan(f*x+e)+I)^5+1/3*I*B/(tan(f*x+e)+I)^3-1/4*(-I*A-3*B)/(tan(f*x+e)+I)^4)","A"
688,1,66,80,0.257000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^6,x)","\frac{a^{2} \left(-\frac{B}{4 \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{-3 i B +A}{5 \left(\tan \left(f x +e \right)+i\right)^{5}}-\frac{-2 i A -2 B}{6 \left(\tan \left(f x +e \right)+i\right)^{6}}\right)}{f \,c^{6}}"," ",0,"1/f*a^2/c^6*(-1/4*B/(tan(f*x+e)+I)^4-1/5*(A-3*I*B)/(tan(f*x+e)+I)^5-1/6*(-2*I*A-2*B)/(tan(f*x+e)+I)^6)","A"
689,1,4339,144,4.615000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x)","\text{output too large to display}"," ",0,"4*a^3/(3+n)/f/(exp(2*I*(f*x+e))+1)^3/(1+n)/(2+n)/n*(12*I*n*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(2*I*f*x)*exp(2*I*e)+2*I*n^2*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(2*I*f*x)*exp(2*I*e)+8*I*n^2*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(4*I*f*x)*exp(4*I*e)+I*n^3*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(4*I*f*x)*exp(4*I*e)+11*I*n*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(6*I*f*x)*exp(6*I*e)+6*I*n^2*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(6*I*f*x)*exp(6*I*e)+21*I*n*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(4*I*f*x)*exp(4*I*e)+I*n^3*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(6*I*f*x)*exp(6*I*e)+6*I*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*Pi*n*(csgn(I*c/(exp(2*I*(f*x+e))+1))-csgn(I/(exp(2*I*(f*x+e))+1)))*(-csgn(I*c/(exp(2*I*(f*x+e))+1))+csgn(I*c)))-2*n*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*Pi*n*(csgn(I*c/(exp(2*I*(f*x+e))+1))-csgn(I/(exp(2*I*(f*x+e))+1)))*(-csgn(I*c/(exp(2*I*(f*x+e))+1))+csgn(I*c)))+6*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*Pi*n*(csgn(I*c/(exp(2*I*(f*x+e))+1))-csgn(I/(exp(2*I*(f*x+e))+1)))*(-csgn(I*c/(exp(2*I*(f*x+e))+1))+csgn(I*c)))+2*I*n*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*Pi*n*(csgn(I*c/(exp(2*I*(f*x+e))+1))-csgn(I/(exp(2*I*(f*x+e))+1)))*(-csgn(I*c/(exp(2*I*(f*x+e))+1))+csgn(I*c)))-2*n^2*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(2*I*f*x)*exp(2*I*e)-n^3*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(4*I*f*x)*exp(4*I*e)+18*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(4*I*f*x)*exp(4*I*e)+18*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(2*I*f*x)*exp(2*I*e)+6*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(6*I*f*x)*exp(6*I*e)-2*n^2*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(4*I*f*x)*exp(4*I*e)+9*n*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(4*I*f*x)*exp(4*I*e)+11*n*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(6*I*f*x)*exp(6*I*e)+n^3*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(6*I*f*x)*exp(6*I*e)+6*n^2*B*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(6*I*f*x)*exp(6*I*e)+18*I*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(2*I*f*x)*exp(2*I*e)+18*I*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(4*I*f*x)*exp(4*I*e)+6*I*A*c^n/((exp(2*I*(f*x+e))+1)^n)*2^n*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*Pi*n)*exp(1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(-1/2*I*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*Pi*n)*exp(6*I*f*x)*exp(6*I*e))","C"
690,1,193,120,0.023000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^6,x)","\frac{c^{6} a^{3} \left(-i B \left(\tan^{3}\left(f x +e \right)\right)-\frac{i B \left(\tan^{7}\left(f x +e \right)\right)}{7}+\frac{i A \left(\tan^{8}\left(f x +e \right)\right)}{8}-\frac{3 B \left(\tan^{8}\left(f x +e \right)\right)}{8}-\frac{i A \left(\tan^{6}\left(f x +e \right)\right)}{6}-\frac{3 A \left(\tan^{7}\left(f x +e \right)\right)}{7}+\frac{i B \left(\tan^{9}\left(f x +e \right)\right)}{9}-\frac{5 B \left(\tan^{6}\left(f x +e \right)\right)}{6}-i B \left(\tan^{5}\left(f x +e \right)\right)-A \left(\tan^{5}\left(f x +e \right)\right)-\frac{3 i A \left(\tan^{2}\left(f x +e \right)\right)}{2}-\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{4}-\frac{5 i A \left(\tan^{4}\left(f x +e \right)\right)}{4}-\frac{A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*c^6*a^3*(-I*B*tan(f*x+e)^3-1/7*I*B*tan(f*x+e)^7+1/8*I*A*tan(f*x+e)^8-3/8*B*tan(f*x+e)^8-1/6*I*A*tan(f*x+e)^6-3/7*A*tan(f*x+e)^7+1/9*I*B*tan(f*x+e)^9-5/6*B*tan(f*x+e)^6-I*B*tan(f*x+e)^5-A*tan(f*x+e)^5-3/2*I*A*tan(f*x+e)^2-1/4*B*tan(f*x+e)^4-5/4*I*A*tan(f*x+e)^4-1/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
691,1,169,120,0.026000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5,x)","\frac{c^{5} a^{3} \left(-\frac{2 i B \left(\tan^{7}\left(f x +e \right)\right)}{7}-\frac{B \left(\tan^{8}\left(f x +e \right)\right)}{8}-\frac{i A \left(\tan^{6}\left(f x +e \right)\right)}{3}-\frac{A \left(\tan^{7}\left(f x +e \right)\right)}{7}-\frac{4 i B \left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{B \left(\tan^{6}\left(f x +e \right)\right)}{6}-i A \left(\tan^{4}\left(f x +e \right)\right)-\frac{A \left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{2 i B \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{4}-i A \left(\tan^{2}\left(f x +e \right)\right)+\frac{A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*c^5*a^3*(-2/7*I*B*tan(f*x+e)^7-1/8*B*tan(f*x+e)^8-1/3*I*A*tan(f*x+e)^6-1/7*A*tan(f*x+e)^7-4/5*I*B*tan(f*x+e)^5-1/6*B*tan(f*x+e)^6-I*A*tan(f*x+e)^4-1/5*A*tan(f*x+e)^5-2/3*I*B*tan(f*x+e)^3+1/4*B*tan(f*x+e)^4-I*A*tan(f*x+e)^2+1/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
692,1,147,119,0.022000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x)","\frac{c^{4} a^{3} \left(-\frac{i B \left(\tan^{7}\left(f x +e \right)\right)}{7}-\frac{i A \left(\tan^{6}\left(f x +e \right)\right)}{6}-\frac{2 i B \left(\tan^{5}\left(f x +e \right)\right)}{5}+\frac{B \left(\tan^{6}\left(f x +e \right)\right)}{6}-\frac{i A \left(\tan^{4}\left(f x +e \right)\right)}{2}+\frac{A \left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{i B \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{2}-\frac{i A \left(\tan^{2}\left(f x +e \right)\right)}{2}+\frac{2 A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*c^4*a^3*(-1/7*I*B*tan(f*x+e)^7-1/6*I*A*tan(f*x+e)^6-2/5*I*B*tan(f*x+e)^5+1/6*B*tan(f*x+e)^6-1/2*I*A*tan(f*x+e)^4+1/5*A*tan(f*x+e)^5-1/3*I*B*tan(f*x+e)^3+1/2*B*tan(f*x+e)^4-1/2*I*A*tan(f*x+e)^2+2/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
693,1,75,78,0.021000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x)","\frac{a^{3} c^{3} \left(\frac{B \left(\tan^{6}\left(f x +e \right)\right)}{6}+\frac{A \left(\tan^{5}\left(f x +e \right)\right)}{5}+\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{2}+\frac{2 A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a^3*c^3*(1/6*B*tan(f*x+e)^6+1/5*A*tan(f*x+e)^5+1/2*B*tan(f*x+e)^4+2/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
694,1,101,90,0.021000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x)","\frac{c^{2} a^{3} \left(\frac{i B \left(\tan^{5}\left(f x +e \right)\right)}{5}+\frac{i A \left(\tan^{4}\left(f x +e \right)\right)}{4}+\frac{i B \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{4}+\frac{i A \left(\tan^{2}\left(f x +e \right)\right)}{2}+\frac{A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*c^2*a^3*(1/5*I*B*tan(f*x+e)^5+1/4*I*A*tan(f*x+e)^4+1/3*I*B*tan(f*x+e)^3+1/4*B*tan(f*x+e)^4+1/2*I*A*tan(f*x+e)^2+1/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
695,1,75,54,0.023000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x)","\frac{a^{3} c \left(\frac{2 i B \left(\tan^{3}\left(f x +e \right)\right)}{3}-\frac{B \left(\tan^{4}\left(f x +e \right)\right)}{4}+i A \left(\tan^{2}\left(f x +e \right)\right)-\frac{A \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{B \left(\tan^{2}\left(f x +e \right)\right)}{2}+A \tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a^3*c*(2/3*I*B*tan(f*x+e)^3-1/4*B*tan(f*x+e)^4+I*A*tan(f*x+e)^2-1/3*A*tan(f*x+e)^3+1/2*B*tan(f*x+e)^2+A*tan(f*x+e))","A"
696,1,160,100,0.025000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e)),x)","-\frac{i a^{3} B \left(\tan^{3}\left(f x +e \right)\right)}{3 f}-\frac{i a^{3} A \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{4 i a^{3} B \tan \left(f x +e \right)}{f}-\frac{3 a^{3} B \left(\tan^{2}\left(f x +e \right)\right)}{2 f}-\frac{3 a^{3} A \tan \left(f x +e \right)}{f}+\frac{2 i a^{3} A \ln \left(1+\tan^{2}\left(f x +e \right)\right)}{f}+\frac{2 a^{3} B \ln \left(1+\tan^{2}\left(f x +e \right)\right)}{f}-\frac{4 i a^{3} B \arctan \left(\tan \left(f x +e \right)\right)}{f}+\frac{4 a^{3} A \arctan \left(\tan \left(f x +e \right)\right)}{f}"," ",0,"-1/3*I/f*a^3*B*tan(f*x+e)^3-1/2*I/f*a^3*A*tan(f*x+e)^2+4*I/f*a^3*B*tan(f*x+e)-3/2/f*a^3*B*tan(f*x+e)^2-3/f*a^3*A*tan(f*x+e)+2*I/f*a^3*A*ln(1+tan(f*x+e)^2)+2/f*a^3*B*ln(1+tan(f*x+e)^2)-4*I/f*a^3*B*arctan(tan(f*x+e))+4/f*a^3*A*arctan(tan(f*x+e))","A"
697,1,150,112,0.221000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","\frac{a^{3} A \tan \left(f x +e \right)}{f c}-\frac{4 i a^{3} B \tan \left(f x +e \right)}{f c}+\frac{a^{3} B \left(\tan^{2}\left(f x +e \right)\right)}{2 c f}-\frac{4 i a^{3} B}{f c \left(\tan \left(f x +e \right)+i\right)}+\frac{4 a^{3} A}{f c \left(\tan \left(f x +e \right)+i\right)}-\frac{4 i a^{3} A \ln \left(\tan \left(f x +e \right)+i\right)}{f c}-\frac{8 a^{3} B \ln \left(\tan \left(f x +e \right)+i\right)}{f c}"," ",0,"1/f*a^3/c*A*tan(f*x+e)-4*I/f*a^3/c*B*tan(f*x+e)+1/2*a^3*B*tan(f*x+e)^2/c/f-4*I/f*a^3/c/(tan(f*x+e)+I)*B+4/f*a^3/c/(tan(f*x+e)+I)*A-4*I/f*a^3/c*A*ln(tan(f*x+e)+I)-8/f*a^3/c*B*ln(tan(f*x+e)+I)","A"
698,1,160,116,0.187000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x)","\frac{i a^{3} B \tan \left(f x +e \right)}{c^{2} f}+\frac{8 i a^{3} B}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)}-\frac{4 a^{3} A}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)}+\frac{i a^{3} A \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{2}}+\frac{5 a^{3} B \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{2}}+\frac{2 i a^{3} A}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{2 a^{3} B}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"I*a^3*B*tan(f*x+e)/c^2/f+8*I/f*a^3/c^2/(tan(f*x+e)+I)*B-4/f*a^3/c^2/(tan(f*x+e)+I)*A+I/f*a^3/c^2*A*ln(tan(f*x+e)+I)+5/f*a^3/c^2*B*ln(tan(f*x+e)+I)+2*I/f*a^3/c^2/(tan(f*x+e)+I)^2*A+2/f*a^3/c^2/(tan(f*x+e)+I)^2*B","A"
699,1,164,120,0.236000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x)","-\frac{5 i a^{3} B}{f \,c^{3} \left(\tan \left(f x +e \right)+i\right)}+\frac{a^{3} A}{f \,c^{3} \left(\tan \left(f x +e \right)+i\right)}-\frac{a^{3} B \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{3}}-\frac{2 i a^{3} A}{f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{4 a^{3} B}{c^{3} f \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{4 i a^{3} B}{3 f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{4 a^{3} A}{3 f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"-5*I/f*a^3/c^3/(tan(f*x+e)+I)*B+1/f*a^3/c^3/(tan(f*x+e)+I)*A-1/f*a^3/c^3*B*ln(tan(f*x+e)+I)-2*I/f*a^3/c^3/(tan(f*x+e)+I)^2*A-4*a^3*B/c^3/f/(tan(f*x+e)+I)^2+4/3*I/f*a^3/c^3/(tan(f*x+e)+I)^3*B-4/3/f*a^3/c^3/(tan(f*x+e)+I)^3*A","A"
700,1,90,89,0.241000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x)","\frac{a^{3} \left(\frac{i B}{\tan \left(f x +e \right)+i}-\frac{-i A -5 B}{2 \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{4 i A +4 B}{4 \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{8 i B -4 A}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}\right)}{f \,c^{4}}"," ",0,"1/f*a^3/c^4*(I*B/(tan(f*x+e)+I)-1/2*(-5*B-I*A)/(tan(f*x+e)+I)^2-1/4*(4*I*A+4*B)/(tan(f*x+e)+I)^4-1/3*(8*I*B-4*A)/(tan(f*x+e)+I)^3)","A"
701,1,87,109,0.247000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^5,x)","\frac{a^{3} \left(-\frac{B}{2 \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{-4 i A -8 B}{4 \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{-5 i B +A}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{4 i B -4 A}{5 \left(\tan \left(f x +e \right)+i\right)^{5}}\right)}{f \,c^{5}}"," ",0,"1/f*a^3/c^5*(-1/2*B/(tan(f*x+e)+I)^2-1/4*(-4*I*A-8*B)/(tan(f*x+e)+I)^4-1/3*(A-5*I*B)/(tan(f*x+e)+I)^3-1/5*(4*I*B-4*A)/(tan(f*x+e)+I)^5)","A"
702,1,90,111,0.237000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^6,x)","\frac{a^{3} \left(-\frac{i A +5 B}{4 \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{-4 i A -4 B}{6 \left(\tan \left(f x +e \right)+i\right)^{6}}-\frac{i B}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{-8 i B +4 A}{5 \left(\tan \left(f x +e \right)+i\right)^{5}}\right)}{f \,c^{6}}"," ",0,"1/f*a^3/c^6*(-1/4*(I*A+5*B)/(tan(f*x+e)+I)^4-1/6*(-4*B-4*I*A)/(tan(f*x+e)+I)^6-1/3*I*B/(tan(f*x+e)+I)^3-1/5*(-8*I*B+4*A)/(tan(f*x+e)+I)^5)","A"
703,1,89,110,0.244000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^7,x)","\frac{a^{3} \left(-\frac{5 i B -A}{5 \left(\tan \left(f x +e \right)+i\right)^{5}}-\frac{-4 i B +4 A}{7 \left(\tan \left(f x +e \right)+i\right)^{7}}-\frac{4 i A +8 B}{6 \left(\tan \left(f x +e \right)+i\right)^{6}}+\frac{B}{4 \left(\tan \left(f x +e \right)+i\right)^{4}}\right)}{f \,c^{7}}"," ",0,"1/f*a^3/c^7*(-1/5*(-A+5*I*B)/(tan(f*x+e)+I)^5-1/7*(-4*I*B+4*A)/(tan(f*x+e)+I)^7-1/6*(4*I*A+8*B)/(tan(f*x+e)+I)^6+1/4*B/(tan(f*x+e)+I)^4)","A"
704,1,90,111,0.244000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^8,x)","\frac{a^{3} \left(-\frac{4 i A +4 B}{8 \left(\tan \left(f x +e \right)+i\right)^{8}}-\frac{8 i B -4 A}{7 \left(\tan \left(f x +e \right)+i\right)^{7}}-\frac{-i A -5 B}{6 \left(\tan \left(f x +e \right)+i\right)^{6}}+\frac{i B}{5 \left(\tan \left(f x +e \right)+i\right)^{5}}\right)}{f \,c^{8}}"," ",0,"1/f*a^3/c^8*(-1/8*(4*I*A+4*B)/(tan(f*x+e)+I)^8-1/7*(8*I*B-4*A)/(tan(f*x+e)+I)^7-1/6*(-5*B-I*A)/(tan(f*x+e)+I)^6+1/5*I*B/(tan(f*x+e)+I)^5)","A"
705,0,0,103,5.298000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","\int \frac{\left(A +B \tan \left(f x +e \right)\right) \left(c -i c \tan \left(f x +e \right)\right)^{n}}{a +i a \tan \left(f x +e \right)}\, dx"," ",0,"int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","F"
706,1,193,146,0.192000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e)),x)","\frac{5 c^{4} B \left(\tan^{2}\left(f x +e \right)\right)}{2 f a}-\frac{i B \,c^{4} \left(\tan^{3}\left(f x +e \right)\right)}{3 a f}+\frac{5 c^{4} A \tan \left(f x +e \right)}{f a}-\frac{i c^{4} A \left(\tan^{2}\left(f x +e \right)\right)}{2 f a}+\frac{12 i c^{4} B \tan \left(f x +e \right)}{f a}+\frac{8 i c^{4} B}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{8 c^{4} A}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{12 i c^{4} A \ln \left(\tan \left(f x +e \right)-i\right)}{f a}-\frac{20 c^{4} B \ln \left(\tan \left(f x +e \right)-i\right)}{f a}"," ",0,"5/2/f*c^4/a*B*tan(f*x+e)^2-1/3*I*B*c^4*tan(f*x+e)^3/a/f+5/f*c^4/a*A*tan(f*x+e)-1/2*I/f*c^4/a*A*tan(f*x+e)^2+12*I/f*c^4/a*B*tan(f*x+e)+8*I/f*c^4/a/(tan(f*x+e)-I)*B+8/f*c^4/a/(tan(f*x+e)-I)*A+12*I/f*c^4/a*A*ln(tan(f*x+e)-I)-20/f*c^4/a*B*ln(tan(f*x+e)-I)","A"
707,1,150,114,0.190000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x)","\frac{c^{3} A \tan \left(f x +e \right)}{f a}+\frac{4 i c^{3} B \tan \left(f x +e \right)}{f a}+\frac{B \,c^{3} \left(\tan^{2}\left(f x +e \right)\right)}{2 a f}+\frac{4 i c^{3} B}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{4 c^{3} A}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{4 i c^{3} A \ln \left(\tan \left(f x +e \right)-i\right)}{f a}-\frac{8 c^{3} B \ln \left(\tan \left(f x +e \right)-i\right)}{f a}"," ",0,"1/f*c^3/a*A*tan(f*x+e)+4*I/f*c^3/a*B*tan(f*x+e)+1/2*B*c^3*tan(f*x+e)^2/a/f+4*I/f*c^3/a/(tan(f*x+e)-I)*B+4/f*c^3/a/(tan(f*x+e)-I)*A+4*I/f*c^3/a*A*ln(tan(f*x+e)-I)-8/f*c^3/a*B*ln(tan(f*x+e)-I)","A"
708,1,113,91,0.190000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x)","\frac{i B \,c^{2} \tan \left(f x +e \right)}{a f}+\frac{2 i c^{2} B}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{2 c^{2} A}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{i c^{2} A \ln \left(\tan \left(f x +e \right)-i\right)}{f a}-\frac{3 c^{2} B \ln \left(\tan \left(f x +e \right)-i\right)}{f a}"," ",0,"I*B*c^2*tan(f*x+e)/a/f+2*I/f*c^2/a/(tan(f*x+e)-I)*B+2/f*c^2/a/(tan(f*x+e)-I)*A+I/f*c^2/a*A*ln(tan(f*x+e)-I)-3/f*c^2/a*B*ln(tan(f*x+e)-I)","A"
709,1,64,54,0.224000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","\frac{i c B}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{c A}{f a \left(\tan \left(f x +e \right)-i\right)}-\frac{c B \ln \left(\tan \left(f x +e \right)-i\right)}{f a}"," ",0,"I/f*c/a/(tan(f*x+e)-I)*B+1/f*c/a/(tan(f*x+e)-I)*A-1/f*c/a*B*ln(tan(f*x+e)-I)","A"
710,1,121,40,0.224000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","\frac{B \ln \left(\tan \left(f x +e \right)+i\right)}{4 f a}+\frac{i A \ln \left(\tan \left(f x +e \right)+i\right)}{4 f a}+\frac{A}{2 f a \left(\tan \left(f x +e \right)-i\right)}+\frac{i B}{2 f a \left(\tan \left(f x +e \right)-i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) A}{4 f a}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) B}{4 f a}"," ",0,"1/4/f/a*B*ln(tan(f*x+e)+I)+1/4*I/f/a*A*ln(tan(f*x+e)+I)+1/2/f/a/(tan(f*x+e)-I)*A+1/2*I/f/a/(tan(f*x+e)-I)*B-1/4*I/f/a*ln(tan(f*x+e)-I)*A-1/4/f/a*ln(tan(f*x+e)-I)*B","B"
711,1,142,41,0.307000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","\frac{i A \ln \left(\tan \left(f x +e \right)+i\right)}{4 f c a}+\frac{A}{4 f c a \left(\tan \left(f x +e \right)+i\right)}-\frac{i B}{4 f c a \left(\tan \left(f x +e \right)+i\right)}-\frac{i A \ln \left(\tan \left(f x +e \right)-i\right)}{4 f c a}+\frac{A}{4 f c a \left(\tan \left(f x +e \right)-i\right)}+\frac{i B}{4 f c a \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/4*I/f/c/a*A*ln(tan(f*x+e)+I)+1/4/f/c/a/(tan(f*x+e)+I)*A-1/4*I/f/c/a/(tan(f*x+e)+I)*B-1/4*I/f/c/a*A*ln(tan(f*x+e)-I)+1/4/f/c/a/(tan(f*x+e)-I)*A+1/4*I/f/c/a/(tan(f*x+e)-I)*B","C"
712,1,209,101,0.370000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x)","\frac{A}{4 a \,c^{2} f \left(\tan \left(f x +e \right)+i\right)}+\frac{3 i \ln \left(\tan \left(f x +e \right)+i\right) A}{16 f a \,c^{2}}-\frac{\ln \left(\tan \left(f x +e \right)+i\right) B}{16 f a \,c^{2}}+\frac{i A}{8 f a \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{B}{8 f a \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{A}{8 f a \,c^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{i B}{8 f a \,c^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{3 i \ln \left(\tan \left(f x +e \right)-i\right) A}{16 f a \,c^{2}}+\frac{\ln \left(\tan \left(f x +e \right)-i\right) B}{16 f a \,c^{2}}"," ",0,"1/4*A/a/c^2/f/(tan(f*x+e)+I)+3/16*I/f/a/c^2*ln(tan(f*x+e)+I)*A-1/16/f/a/c^2*ln(tan(f*x+e)+I)*B+1/8*I/f/a/c^2/(tan(f*x+e)+I)^2*A+1/8/f/a/c^2/(tan(f*x+e)+I)^2*B+1/8/f/a/c^2/(tan(f*x+e)-I)*A+1/8*I/f/a/c^2/(tan(f*x+e)-I)*B-3/16*I/f/a/c^2*ln(tan(f*x+e)-I)*A+1/16/f/a/c^2*ln(tan(f*x+e)-I)*B","B"
713,1,257,134,0.459000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x)","\frac{i A}{8 a \,c^{3} f \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{A}{12 f a \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{i B}{12 f a \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{3 A}{16 f a \,c^{3} \left(\tan \left(f x +e \right)+i\right)}+\frac{i B}{16 f a \,c^{3} \left(\tan \left(f x +e \right)+i\right)}-\frac{\ln \left(\tan \left(f x +e \right)+i\right) B}{16 f a \,c^{3}}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) A}{8 f a \,c^{3}}+\frac{A}{16 f a \,c^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{i B}{16 f a \,c^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{\ln \left(\tan \left(f x +e \right)-i\right) B}{16 f a \,c^{3}}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) A}{8 f a \,c^{3}}"," ",0,"1/8*I*A/a/c^3/f/(tan(f*x+e)+I)^2-1/12/f/a/c^3/(tan(f*x+e)+I)^3*A+1/12*I/f/a/c^3/(tan(f*x+e)+I)^3*B+3/16/f/a/c^3/(tan(f*x+e)+I)*A+1/16*I/f/a/c^3/(tan(f*x+e)+I)*B-1/16/f/a/c^3*ln(tan(f*x+e)+I)*B+1/8*I/f/a/c^3*ln(tan(f*x+e)+I)*A+1/16/f/a/c^3/(tan(f*x+e)-I)*A+1/16*I/f/a/c^3/(tan(f*x+e)-I)*B+1/16/f/a/c^3*ln(tan(f*x+e)-I)*B-1/8*I/f/a/c^3*ln(tan(f*x+e)-I)*A","A"
714,1,303,163,0.410000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x)","\frac{A}{8 f a \,c^{4} \left(\tan \left(f x +e \right)+i\right)}+\frac{i B}{16 f a \,c^{4} \left(\tan \left(f x +e \right)+i\right)}+\frac{5 i \ln \left(\tan \left(f x +e \right)+i\right) A}{64 f a \,c^{4}}-\frac{3 \ln \left(\tan \left(f x +e \right)+i\right) B}{64 f a \,c^{4}}+\frac{3 i A}{32 f a \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{B}{32 f a \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{B}{16 f a \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{i A}{16 f a \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{A}{12 a \,c^{4} f \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{A}{32 f a \,c^{4} \left(\tan \left(f x +e \right)-i\right)}+\frac{i B}{32 f a \,c^{4} \left(\tan \left(f x +e \right)-i\right)}-\frac{5 i \ln \left(\tan \left(f x +e \right)-i\right) A}{64 f a \,c^{4}}+\frac{3 \ln \left(\tan \left(f x +e \right)-i\right) B}{64 f a \,c^{4}}"," ",0,"1/8/f/a/c^4/(tan(f*x+e)+I)*A+1/16*I/f/a/c^4/(tan(f*x+e)+I)*B+5/64*I/f/a/c^4*ln(tan(f*x+e)+I)*A-3/64/f/a/c^4*ln(tan(f*x+e)+I)*B+3/32*I/f/a/c^4/(tan(f*x+e)+I)^2*A-1/32/f/a/c^4/(tan(f*x+e)+I)^2*B-1/16/f/a/c^4/(tan(f*x+e)+I)^4*B-1/16*I/f/a/c^4/(tan(f*x+e)+I)^4*A-1/12*A/a/c^4/f/(tan(f*x+e)+I)^3+1/32/f/a/c^4/(tan(f*x+e)-I)*A+1/32*I/f/a/c^4/(tan(f*x+e)-I)*B-5/64*I/f/a/c^4*ln(tan(f*x+e)-I)*A+3/64/f/a/c^4*ln(tan(f*x+e)-I)*B","A"
715,0,0,103,8.166000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","\int \frac{\left(A +B \tan \left(f x +e \right)\right) \left(c -i c \tan \left(f x +e \right)\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","F"
716,1,240,181,0.240000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5/(a+I*a*tan(f*x+e))^2,x)","\frac{i B \,c^{5} \left(\tan^{3}\left(f x +e \right)\right)}{3 a^{2} f}+\frac{i c^{5} A \left(\tan^{2}\left(f x +e \right)\right)}{2 f \,a^{2}}-\frac{24 i c^{5} B \tan \left(f x +e \right)}{f \,a^{2}}-\frac{7 c^{5} B \left(\tan^{2}\left(f x +e \right)\right)}{2 f \,a^{2}}-\frac{7 c^{5} A \tan \left(f x +e \right)}{f \,a^{2}}-\frac{8 i c^{5} A}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{8 c^{5} B}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{48 i c^{5} B}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{32 c^{5} A}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{24 i c^{5} A \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{2}}+\frac{56 c^{5} B \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{2}}"," ",0,"1/3*I*B*c^5*tan(f*x+e)^3/a^2/f+1/2*I/f*c^5/a^2*A*tan(f*x+e)^2-24*I/f*c^5/a^2*B*tan(f*x+e)-7/2/f*c^5/a^2*B*tan(f*x+e)^2-7/f*c^5/a^2*A*tan(f*x+e)-8*I/f*c^5/a^2/(tan(f*x+e)-I)^2*A+8/f*c^5/a^2/(tan(f*x+e)-I)^2*B-48*I/f*c^5/a^2/(tan(f*x+e)-I)*B-32/f*c^5/a^2/(tan(f*x+e)-I)*A-24*I/f*c^5/a^2*A*ln(tan(f*x+e)-I)+56/f*c^5/a^2*B*ln(tan(f*x+e)-I)","A"
717,1,198,149,0.226000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^2,x)","-\frac{B \,c^{4} \left(\tan^{2}\left(f x +e \right)\right)}{2 a^{2} f}-\frac{c^{4} A \tan \left(f x +e \right)}{f \,a^{2}}-\frac{6 i c^{4} B \tan \left(f x +e \right)}{f \,a^{2}}-\frac{20 i c^{4} B}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{12 c^{4} A}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{4 i c^{4} A}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{4 c^{4} B}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{6 i c^{4} A \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{2}}+\frac{18 c^{4} B \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{2}}"," ",0,"-1/2*B*c^4*tan(f*x+e)^2/a^2/f-1/f*c^4/a^2*A*tan(f*x+e)-6*I/f*c^4/a^2*B*tan(f*x+e)-20*I/f*c^4/a^2/(tan(f*x+e)-I)*B-12/f*c^4/a^2/(tan(f*x+e)-I)*A-4*I/f*c^4/a^2/(tan(f*x+e)-I)^2*A+4/f*c^4/a^2/(tan(f*x+e)-I)^2*B-6*I/f*c^4/a^2*A*ln(tan(f*x+e)-I)+18/f*c^4/a^2*B*ln(tan(f*x+e)-I)","A"
718,1,160,121,0.202000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x)","-\frac{i B \,c^{3} \tan \left(f x +e \right)}{a^{2} f}-\frac{2 i c^{3} A}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{2 c^{3} B}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{8 i c^{3} B}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{4 c^{3} A}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{i c^{3} A \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{2}}+\frac{5 c^{3} B \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{2}}"," ",0,"-I*B*c^3*tan(f*x+e)/a^2/f-2*I/f*c^3/a^2/(tan(f*x+e)-I)^2*A+2/f*c^3/a^2/(tan(f*x+e)-I)^2*B-8*I/f*c^3/a^2/(tan(f*x+e)-I)*B-4/f*c^3/a^2/(tan(f*x+e)-I)*A-I/f*c^3/a^2*A*ln(tan(f*x+e)-I)+5/f*c^3/a^2*B*ln(tan(f*x+e)-I)","A"
719,1,116,92,0.280000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x)","-\frac{i c^{2} A}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{c^{2} B}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{3 i c^{2} B}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{c^{2} A}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{c^{2} B \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{2}}"," ",0,"-I/f*c^2/a^2/(tan(f*x+e)-I)^2*A+1/f*c^2/a^2/(tan(f*x+e)-I)^2*B-3*I/f*c^2/a^2/(tan(f*x+e)-I)*B-1/f*c^2/a^2/(tan(f*x+e)-I)*A+1/f*c^2/a^2*B*ln(tan(f*x+e)-I)","A"
720,1,46,44,0.261000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x)","\frac{c \left(-\frac{i B}{\tan \left(f x +e \right)-i}-\frac{i A -B}{2 \left(\tan \left(f x +e \right)-i\right)^{2}}\right)}{f \,a^{2}}"," ",0,"1/f*c/a^2*(-I*B/(tan(f*x+e)-I)-1/2*(I*A-B)/(tan(f*x+e)-I)^2)","A"
721,1,162,69,0.250000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x)","\frac{B \ln \left(\tan \left(f x +e \right)+i\right)}{8 f \,a^{2}}+\frac{i A \ln \left(\tan \left(f x +e \right)+i\right)}{8 f \,a^{2}}-\frac{i A}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{B}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{A}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{i B}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) A}{8 f \,a^{2}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) B}{8 f \,a^{2}}"," ",0,"1/8/f/a^2*B*ln(tan(f*x+e)+I)+1/8*I/f/a^2*A*ln(tan(f*x+e)+I)-1/4*I/f/a^2/(tan(f*x+e)-I)^2*A+1/4/f/a^2/(tan(f*x+e)-I)^2*B+1/4/f/a^2/(tan(f*x+e)-I)*A-1/4*I/f/a^2/(tan(f*x+e)-I)*B-1/8*I/f/a^2*ln(tan(f*x+e)-I)*A-1/8/f/a^2*ln(tan(f*x+e)-I)*B","B"
722,1,209,101,0.428000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x)","\frac{A}{8 f \,a^{2} c \left(\tan \left(f x +e \right)+i\right)}-\frac{i B}{8 f \,a^{2} c \left(\tan \left(f x +e \right)+i\right)}+\frac{3 i \ln \left(\tan \left(f x +e \right)+i\right) A}{16 f \,a^{2} c}+\frac{\ln \left(\tan \left(f x +e \right)+i\right) B}{16 f \,a^{2} c}+\frac{B}{8 f \,a^{2} c \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i A}{8 f \,a^{2} c \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{A}{4 f \,a^{2} c \left(\tan \left(f x +e \right)-i\right)}-\frac{3 i \ln \left(\tan \left(f x +e \right)-i\right) A}{16 f \,a^{2} c}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) B}{16 f \,a^{2} c}"," ",0,"1/8/f/a^2/c/(tan(f*x+e)+I)*A-1/8*I/f/a^2/c/(tan(f*x+e)+I)*B+3/16*I/f/a^2/c*ln(tan(f*x+e)+I)*A+1/16/f/a^2/c*ln(tan(f*x+e)+I)*B+1/8/f/a^2/c/(tan(f*x+e)-I)^2*B-1/8*I/f/a^2/c/(tan(f*x+e)-I)^2*A+1/4/f/a^2/c*A/(tan(f*x+e)-I)-3/16*I/f/a^2/c*ln(tan(f*x+e)-I)*A-1/16/f/a^2/c*ln(tan(f*x+e)-I)*B","B"
723,1,236,65,0.353000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x)","\frac{3 A}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)+i\right)}-\frac{i B}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)+i\right)}+\frac{3 i A \ln \left(\tan \left(f x +e \right)+i\right)}{16 f \,a^{2} c^{2}}+\frac{i A}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{B}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{3 A}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{i B}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{3 i A \ln \left(\tan \left(f x +e \right)-i\right)}{16 f \,a^{2} c^{2}}-\frac{i A}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{B}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}"," ",0,"3/16/f/a^2/c^2/(tan(f*x+e)+I)*A-1/16*I/f/a^2/c^2/(tan(f*x+e)+I)*B+3/16*I/f/a^2/c^2*A*ln(tan(f*x+e)+I)+1/16*I/f/a^2/c^2/(tan(f*x+e)+I)^2*A+1/16/f/a^2/c^2/(tan(f*x+e)+I)^2*B+3/16/f/a^2/c^2/(tan(f*x+e)-I)*A+1/16*I/f/a^2/c^2/(tan(f*x+e)-I)*B-3/16*I/f/a^2/c^2*A*ln(tan(f*x+e)-I)-1/16*I/f/a^2/c^2/(tan(f*x+e)-I)^2*A+1/16/f/a^2/c^2/(tan(f*x+e)-I)^2*B","C"
724,1,303,161,0.427000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x)","\frac{3 A}{16 a^{2} c^{3} f \left(\tan \left(f x +e \right)+i\right)}+\frac{5 i \ln \left(\tan \left(f x +e \right)+i\right) A}{32 f \,a^{2} c^{3}}-\frac{\ln \left(\tan \left(f x +e \right)+i\right) B}{32 f \,a^{2} c^{3}}+\frac{3 i A}{32 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{B}{32 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{A}{24 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{i B}{24 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{B}{32 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i A}{32 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{A}{8 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{i B}{16 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{5 i \ln \left(\tan \left(f x +e \right)-i\right) A}{32 f \,a^{2} c^{3}}+\frac{\ln \left(\tan \left(f x +e \right)-i\right) B}{32 f \,a^{2} c^{3}}"," ",0,"3/16*A/a^2/c^3/f/(tan(f*x+e)+I)+5/32*I/f/a^2/c^3*ln(tan(f*x+e)+I)*A-1/32/f/a^2/c^3*ln(tan(f*x+e)+I)*B+3/32*I/f/a^2/c^3/(tan(f*x+e)+I)^2*A+1/32/f/a^2/c^3/(tan(f*x+e)+I)^2*B-1/24/f/a^2/c^3/(tan(f*x+e)+I)^3*A+1/24*I/f/a^2/c^3/(tan(f*x+e)+I)^3*B+1/32/f/a^2/c^3/(tan(f*x+e)-I)^2*B-1/32*I/f/a^2/c^3/(tan(f*x+e)-I)^2*A+1/8/f/a^2/c^3/(tan(f*x+e)-I)*A+1/16*I/f/a^2/c^3/(tan(f*x+e)-I)*B-5/32*I/f/a^2/c^3*ln(tan(f*x+e)-I)*A+1/32/f/a^2/c^3*ln(tan(f*x+e)-I)*B","A"
725,1,351,194,0.444000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x)","\frac{5 A}{32 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)}+\frac{i B}{32 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)}-\frac{5 \ln \left(\tan \left(f x +e \right)+i\right) B}{128 f \,a^{2} c^{4}}+\frac{15 i \ln \left(\tan \left(f x +e \right)+i\right) A}{128 f \,a^{2} c^{4}}-\frac{i A}{32 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{B}{32 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{A}{16 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{i B}{48 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{3 i A}{32 a^{2} c^{4} f \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{i A}{64 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{B}{64 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{5 A}{64 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)-i\right)}+\frac{3 i B}{64 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)-i\right)}+\frac{5 \ln \left(\tan \left(f x +e \right)-i\right) B}{128 f \,a^{2} c^{4}}-\frac{15 i \ln \left(\tan \left(f x +e \right)-i\right) A}{128 f \,a^{2} c^{4}}"," ",0,"5/32/f/a^2/c^4/(tan(f*x+e)+I)*A+1/32*I/f/a^2/c^4/(tan(f*x+e)+I)*B-5/128/f/a^2/c^4*ln(tan(f*x+e)+I)*B+15/128*I/f/a^2/c^4*ln(tan(f*x+e)+I)*A-1/32*I/f/a^2/c^4/(tan(f*x+e)+I)^4*A-1/32/f/a^2/c^4/(tan(f*x+e)+I)^4*B-1/16/f/a^2/c^4/(tan(f*x+e)+I)^3*A+1/48*I/f/a^2/c^4/(tan(f*x+e)+I)^3*B+3/32*I*A/a^2/c^4/f/(tan(f*x+e)+I)^2-1/64*I/f/a^2/c^4/(tan(f*x+e)-I)^2*A+1/64/f/a^2/c^4/(tan(f*x+e)-I)^2*B+5/64/f/a^2/c^4/(tan(f*x+e)-I)*A+3/64*I/f/a^2/c^4/(tan(f*x+e)-I)*B+5/128/f/a^2/c^4*ln(tan(f*x+e)-I)*B-15/128*I/f/a^2/c^4*ln(tan(f*x+e)-I)*A","A"
726,1,397,221,0.451000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^5,x)","\frac{15 A}{128 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)+i\right)}+\frac{i B}{32 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)-i\right)}-\frac{21 i \ln \left(\tan \left(f x +e \right)-i\right) A}{256 f \,a^{2} c^{5}}-\frac{9 \ln \left(\tan \left(f x +e \right)+i\right) B}{256 f \,a^{2} c^{5}}+\frac{5 i A}{64 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{B}{64 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{i A}{128 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{B}{64 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{A}{40 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)+i\right)^{5}}-\frac{3 i A}{64 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{A}{16 a^{2} c^{5} f \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{B}{128 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i B}{40 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)+i\right)^{5}}+\frac{21 i \ln \left(\tan \left(f x +e \right)+i\right) A}{256 f \,a^{2} c^{5}}+\frac{3 A}{64 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)-i\right)}+\frac{5 i B}{128 f \,a^{2} c^{5} \left(\tan \left(f x +e \right)+i\right)}+\frac{9 \ln \left(\tan \left(f x +e \right)-i\right) B}{256 f \,a^{2} c^{5}}"," ",0,"15/128/f/a^2/c^5/(tan(f*x+e)+I)*A+1/32*I/f/a^2/c^5/(tan(f*x+e)-I)*B-21/256*I/f/a^2/c^5*ln(tan(f*x+e)-I)*A-9/256/f/a^2/c^5*ln(tan(f*x+e)+I)*B+5/64*I/f/a^2/c^5/(tan(f*x+e)+I)^2*A-1/64/f/a^2/c^5/(tan(f*x+e)+I)^4*B-1/128*I/f/a^2/c^5/(tan(f*x+e)-I)^2*A-1/64/f/a^2/c^5/(tan(f*x+e)+I)^2*B+1/40/f/a^2/c^5/(tan(f*x+e)+I)^5*A-3/64*I/f/a^2/c^5/(tan(f*x+e)+I)^4*A-1/16*A/a^2/c^5/f/(tan(f*x+e)+I)^3+1/128/f/a^2/c^5/(tan(f*x+e)-I)^2*B-1/40*I/f/a^2/c^5/(tan(f*x+e)+I)^5*B+21/256*I/f/a^2/c^5*ln(tan(f*x+e)+I)*A+3/64/f/a^2/c^5/(tan(f*x+e)-I)*A+5/128*I/f/a^2/c^5/(tan(f*x+e)+I)*B+9/256/f/a^2/c^5*ln(tan(f*x+e)-I)*B","A"
727,0,0,103,10.260000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x)","\int \frac{\left(A +B \tan \left(f x +e \right)\right) \left(c -i c \tan \left(f x +e \right)\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x)","F"
728,1,244,178,0.246000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5/(a+I*a*tan(f*x+e))^3,x)","\frac{c^{5} A \tan \left(f x +e \right)}{f \,a^{3}}+\frac{8 i c^{5} B \tan \left(f x +e \right)}{f \,a^{3}}+\frac{B \,c^{5} \left(\tan^{2}\left(f x +e \right)\right)}{2 a^{3} f}+\frac{16 i c^{5} A}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{24 c^{5} B}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{56 i c^{5} B}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{24 c^{5} A}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{16 c^{5} A}{3 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{16 i c^{5} B}{3 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{8 i c^{5} A \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{3}}-\frac{32 c^{5} B \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{3}}"," ",0,"1/f*c^5/a^3*A*tan(f*x+e)+8*I/f*c^5/a^3*B*tan(f*x+e)+1/2*B*c^5*tan(f*x+e)^2/a^3/f+16*I/f*c^5/a^3/(tan(f*x+e)-I)^2*A-24/f*c^5/a^3/(tan(f*x+e)-I)^2*B+56*I/f*c^5/a^3/(tan(f*x+e)-I)*B+24/f*c^5/a^3/(tan(f*x+e)-I)*A-16/3/f*c^5/a^3/(tan(f*x+e)-I)^3*A-16/3*I/f*c^5/a^3/(tan(f*x+e)-I)^3*B+8*I/f*c^5/a^3*A*ln(tan(f*x+e)-I)-32/f*c^5/a^3*B*ln(tan(f*x+e)-I)","A"
729,1,207,153,0.232000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^3,x)","\frac{i B \,c^{4} \tan \left(f x +e \right)}{a^{3} f}-\frac{8 c^{4} A}{3 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{8 i c^{4} B}{3 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{18 i c^{4} B}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{6 c^{4} A}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{i c^{4} A \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{3}}-\frac{7 c^{4} B \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{3}}+\frac{6 i c^{4} A}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{10 c^{4} B}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}"," ",0,"I*B*c^4*tan(f*x+e)/a^3/f-8/3/f*c^4/a^3/(tan(f*x+e)-I)^3*A-8/3*I/f*c^4/a^3/(tan(f*x+e)-I)^3*B+18*I/f*c^4/a^3/(tan(f*x+e)-I)*B+6/f*c^4/a^3/(tan(f*x+e)-I)*A+I/f*c^4/a^3*A*ln(tan(f*x+e)-I)-7/f*c^4/a^3*B*ln(tan(f*x+e)-I)+6*I/f*c^4/a^3/(tan(f*x+e)-I)^2*A-10/f*c^4/a^3/(tan(f*x+e)-I)^2*B","A"
730,1,164,126,0.245000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{3} A}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{4 c^{3} B}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{5 i c^{3} B}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{c^{3} A}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{4 i c^{3} B}{3 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{4 c^{3} A}{3 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{c^{3} B \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{3}}"," ",0,"2*I/f*c^3/a^3/(tan(f*x+e)-I)^2*A-4/f*c^3/a^3/(tan(f*x+e)-I)^2*B+5*I/f*c^3/a^3/(tan(f*x+e)-I)*B+1/f*c^3/a^3/(tan(f*x+e)-I)*A-4/3*I/f*c^3/a^3/(tan(f*x+e)-I)^3*B-4/3/f*c^3/a^3/(tan(f*x+e)-I)^3*A-1/f*c^3/a^3*B*ln(tan(f*x+e)-I)","A"
731,1,69,89,0.278000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x)","\frac{c^{2} \left(-\frac{-i A +3 B}{2 \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{i B}{\tan \left(f x +e \right)-i}-\frac{2 i B +2 A}{3 \left(\tan \left(f x +e \right)-i\right)^{3}}\right)}{f \,a^{3}}"," ",0,"1/f*c^2/a^3*(-1/2*(-I*A+3*B)/(tan(f*x+e)-I)^2+I*B/(tan(f*x+e)-I)-1/3*(2*I*B+2*A)/(tan(f*x+e)-I)^3)","A"
732,1,43,52,0.264000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x)","\frac{c \left(-\frac{B}{2 \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i B +A}{3 \left(\tan \left(f x +e \right)-i\right)^{3}}\right)}{f \,a^{3}}"," ",0,"1/f*c/a^3*(-1/2*B/(tan(f*x+e)-I)^2-1/3*(A+I*B)/(tan(f*x+e)-I)^3)","A"
733,1,203,97,0.253000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x)","\frac{B \ln \left(\tan \left(f x +e \right)+i\right)}{16 f \,a^{3}}+\frac{i A \ln \left(\tan \left(f x +e \right)+i\right)}{16 f \,a^{3}}-\frac{A}{6 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i B}{6 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{A}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{i B}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{i A}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{B}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) A}{16 f \,a^{3}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) B}{16 f \,a^{3}}"," ",0,"1/16/f/a^3*B*ln(tan(f*x+e)+I)+1/16*I/f/a^3*A*ln(tan(f*x+e)+I)-1/6/f/a^3/(tan(f*x+e)-I)^3*A-1/6*I/f/a^3/(tan(f*x+e)-I)^3*B+1/8/f/a^3/(tan(f*x+e)-I)*A-1/8*I/f/a^3/(tan(f*x+e)-I)*B-1/8*I/f/a^3/(tan(f*x+e)-I)^2*A-1/8/f/a^3/(tan(f*x+e)-I)^2*B-1/16*I/f/a^3*ln(tan(f*x+e)-I)*A-1/16/f/a^3*ln(tan(f*x+e)-I)*B","B"
734,1,257,134,0.465000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x)","\frac{A}{16 f \,a^{3} c \left(\tan \left(f x +e \right)+i\right)}-\frac{i B}{16 f \,a^{3} c \left(\tan \left(f x +e \right)+i\right)}+\frac{\ln \left(\tan \left(f x +e \right)+i\right) B}{16 f \,a^{3} c}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) A}{8 f \,a^{3} c}-\frac{i A}{8 f \,a^{3} c \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{3 A}{16 f \,a^{3} c \left(\tan \left(f x +e \right)-i\right)}-\frac{i B}{16 f \,a^{3} c \left(\tan \left(f x +e \right)-i\right)}-\frac{A}{12 f \,a^{3} c \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i B}{12 f \,a^{3} c \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) B}{16 f \,a^{3} c}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) A}{8 f \,a^{3} c}"," ",0,"1/16/f/a^3/c/(tan(f*x+e)+I)*A-1/16*I/f/a^3/c/(tan(f*x+e)+I)*B+1/16/f/a^3/c*ln(tan(f*x+e)+I)*B+1/8*I/f/a^3/c*ln(tan(f*x+e)+I)*A-1/8*I/f/a^3/c*A/(tan(f*x+e)-I)^2+3/16/f/a^3/c/(tan(f*x+e)-I)*A-1/16*I/f/a^3/c/(tan(f*x+e)-I)*B-1/12/f/a^3/c/(tan(f*x+e)-I)^3*A-1/12*I/f/a^3/c/(tan(f*x+e)-I)^3*B-1/16/f/a^3/c*ln(tan(f*x+e)-I)*B-1/8*I/f/a^3/c*ln(tan(f*x+e)-I)*A","A"
735,1,303,161,0.456000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x)","-\frac{i B}{16 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)+i\right)}+\frac{A}{8 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)+i\right)}+\frac{5 i \ln \left(\tan \left(f x +e \right)+i\right) A}{32 f \,a^{3} c^{2}}+\frac{\ln \left(\tan \left(f x +e \right)+i\right) B}{32 f \,a^{3} c^{2}}+\frac{i A}{32 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{B}{32 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{3 i A}{32 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{B}{32 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{3 A}{16 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{5 i \ln \left(\tan \left(f x +e \right)-i\right) A}{32 f \,a^{3} c^{2}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) B}{32 f \,a^{3} c^{2}}-\frac{A}{24 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i B}{24 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)-i\right)^{3}}"," ",0,"-1/16*I/f/a^3/c^2/(tan(f*x+e)+I)*B+1/8/f/a^3/c^2/(tan(f*x+e)+I)*A+5/32*I/f/a^3/c^2*ln(tan(f*x+e)+I)*A+1/32/f/a^3/c^2*ln(tan(f*x+e)+I)*B+1/32*I/f/a^3/c^2/(tan(f*x+e)+I)^2*A+1/32/f/a^3/c^2/(tan(f*x+e)+I)^2*B-3/32*I/f/a^3/c^2/(tan(f*x+e)-I)^2*A+1/32/f/a^3/c^2/(tan(f*x+e)-I)^2*B+3/16/f/a^3/c^2*A/(tan(f*x+e)-I)-5/32*I/f/a^3/c^2*ln(tan(f*x+e)-I)*A-1/32/f/a^3/c^2*ln(tan(f*x+e)-I)*B-1/24/f/a^3/c^2/(tan(f*x+e)-I)^3*A-1/24*I/f/a^3/c^2/(tan(f*x+e)-I)^3*B","A"
736,1,330,91,0.332000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x)","\frac{5 i A \ln \left(\tan \left(f x +e \right)+i\right)}{32 f \,a^{3} c^{3}}+\frac{5 A}{32 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)+i\right)}-\frac{i B}{32 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)+i\right)}-\frac{A}{48 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{i B}{48 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{B}{32 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{i A}{16 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{5 i A \ln \left(\tan \left(f x +e \right)-i\right)}{32 f \,a^{3} c^{3}}+\frac{5 A}{32 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{i B}{32 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{A}{48 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i B}{48 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{B}{32 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i A}{16 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}"," ",0,"5/32*I/f/a^3/c^3*A*ln(tan(f*x+e)+I)+5/32/f/a^3/c^3/(tan(f*x+e)+I)*A-1/32*I/f/a^3/c^3/(tan(f*x+e)+I)*B-1/48/f/a^3/c^3/(tan(f*x+e)+I)^3*A+1/48*I/f/a^3/c^3/(tan(f*x+e)+I)^3*B+1/32/f/a^3/c^3/(tan(f*x+e)+I)^2*B+1/16*I/f/a^3/c^3/(tan(f*x+e)+I)^2*A-5/32*I/f/a^3/c^3*A*ln(tan(f*x+e)-I)+5/32/f/a^3/c^3/(tan(f*x+e)-I)*A+1/32*I/f/a^3/c^3/(tan(f*x+e)-I)*B-1/48/f/a^3/c^3/(tan(f*x+e)-I)^3*A-1/48*I/f/a^3/c^3/(tan(f*x+e)-I)^3*B+1/32/f/a^3/c^3/(tan(f*x+e)-I)^2*B-1/16*I/f/a^3/c^3/(tan(f*x+e)-I)^2*A","C"
737,1,397,223,0.480000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x)","\frac{5 A}{32 a^{3} c^{4} f \left(\tan \left(f x +e \right)+i\right)}+\frac{5 i A}{64 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{5 \ln \left(\tan \left(f x +e \right)+i\right) B}{256 f \,a^{3} c^{4}}-\frac{B}{64 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}+\frac{i B}{48 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{5 i B}{128 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)-i\right)}+\frac{B}{64 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{A}{24 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{i A}{64 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{5 i A}{128 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{3 B}{128 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{15 A}{128 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)-i\right)}+\frac{35 i \ln \left(\tan \left(f x +e \right)+i\right) A}{256 f \,a^{3} c^{4}}-\frac{A}{96 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i B}{96 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{35 i \ln \left(\tan \left(f x +e \right)-i\right) A}{256 f \,a^{3} c^{4}}+\frac{5 \ln \left(\tan \left(f x +e \right)-i\right) B}{256 f \,a^{3} c^{4}}"," ",0,"5/32*A/a^3/c^4/f/(tan(f*x+e)+I)+5/64*I/f/a^3/c^4/(tan(f*x+e)+I)^2*A-5/256/f/a^3/c^4*ln(tan(f*x+e)+I)*B-1/64/f/a^3/c^4/(tan(f*x+e)+I)^4*B+1/48*I/f/a^3/c^4/(tan(f*x+e)+I)^3*B+5/128*I/f/a^3/c^4/(tan(f*x+e)-I)*B+1/64/f/a^3/c^4/(tan(f*x+e)+I)^2*B-1/24/f/a^3/c^4/(tan(f*x+e)+I)^3*A-1/64*I/f/a^3/c^4/(tan(f*x+e)+I)^4*A-5/128*I/f/a^3/c^4/(tan(f*x+e)-I)^2*A+3/128/f/a^3/c^4/(tan(f*x+e)-I)^2*B+15/128/f/a^3/c^4/(tan(f*x+e)-I)*A+35/256*I/f/a^3/c^4*ln(tan(f*x+e)+I)*A-1/96/f/a^3/c^4/(tan(f*x+e)-I)^3*A-1/96*I/f/a^3/c^4/(tan(f*x+e)-I)^3*B-35/256*I/f/a^3/c^4*ln(tan(f*x+e)-I)*A+5/256/f/a^3/c^4*ln(tan(f*x+e)-I)*B","A"
738,1,445,254,0.467000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^5,x)","-\frac{i B}{80 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)+i\right)^{5}}+\frac{A}{80 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)+i\right)^{5}}+\frac{i B}{96 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{5 A}{96 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{9 i B}{256 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)-i\right)}+\frac{35 A}{256 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)+i\right)}-\frac{7 i \ln \left(\tan \left(f x +e \right)-i\right) A}{64 f \,a^{3} c^{5}}-\frac{B}{64 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{3 i A}{128 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{7 \ln \left(\tan \left(f x +e \right)+i\right) B}{256 f \,a^{3} c^{5}}+\frac{5 i A}{64 a^{3} c^{5} f \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{A}{192 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{7 i \ln \left(\tan \left(f x +e \right)+i\right) A}{64 f \,a^{3} c^{5}}+\frac{7 \ln \left(\tan \left(f x +e \right)-i\right) B}{256 f \,a^{3} c^{5}}-\frac{i A}{32 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)+i\right)^{4}}+\frac{21 A}{256 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)-i\right)}+\frac{5 i B}{256 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)+i\right)}+\frac{B}{64 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i B}{192 f \,a^{3} c^{5} \left(\tan \left(f x +e \right)-i\right)^{3}}"," ",0,"-1/80*I/f/a^3/c^5/(tan(f*x+e)+I)^5*B+1/80/f/a^3/c^5/(tan(f*x+e)+I)^5*A+1/96*I/f/a^3/c^5/(tan(f*x+e)+I)^3*B-5/96/f/a^3/c^5/(tan(f*x+e)+I)^3*A+9/256*I/f/a^3/c^5/(tan(f*x+e)-I)*B+35/256/f/a^3/c^5/(tan(f*x+e)+I)*A-7/64*I/f/a^3/c^5*ln(tan(f*x+e)-I)*A-1/64/f/a^3/c^5/(tan(f*x+e)+I)^4*B-3/128*I/f/a^3/c^5/(tan(f*x+e)-I)^2*A-7/256/f/a^3/c^5*ln(tan(f*x+e)+I)*B+5/64*I*A/a^3/c^5/f/(tan(f*x+e)+I)^2-1/192/f/a^3/c^5/(tan(f*x+e)-I)^3*A+7/64*I/f/a^3/c^5*ln(tan(f*x+e)+I)*A+7/256/f/a^3/c^5*ln(tan(f*x+e)-I)*B-1/32*I/f/a^3/c^5/(tan(f*x+e)+I)^4*A+21/256/f/a^3/c^5/(tan(f*x+e)-I)*A+5/256*I/f/a^3/c^5/(tan(f*x+e)+I)*B+1/64/f/a^3/c^5/(tan(f*x+e)-I)^2*B-1/192*I/f/a^3/c^5/(tan(f*x+e)-I)^3*B","A"
739,1,491,283,0.408000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^6,x)","-\frac{21 i \ln \left(\tan \left(f x +e \right)-i\right) A}{256 f \,a^{3} c^{6}}+\frac{7 A}{64 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)}+\frac{i A}{96 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)^{6}}-\frac{7 \ln \left(\tan \left(f x +e \right)+i\right) B}{256 f \,a^{3} c^{6}}+\frac{35 i A}{512 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{A}{40 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)^{5}}+\frac{7 i B}{256 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)}-\frac{5 B}{512 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{5 A}{96 a^{3} c^{6} f \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{7 i B}{256 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)-i\right)}-\frac{B}{128 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)^{4}}-\frac{7 i A}{512 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{B}{96 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)^{6}}+\frac{5 B}{512 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i B}{384 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{A}{384 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i B}{80 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)^{5}}-\frac{5 i A}{128 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)+i\right)^{4}}+\frac{7 A}{128 f \,a^{3} c^{6} \left(\tan \left(f x +e \right)-i\right)}+\frac{21 i \ln \left(\tan \left(f x +e \right)+i\right) A}{256 f \,a^{3} c^{6}}+\frac{7 \ln \left(\tan \left(f x +e \right)-i\right) B}{256 f \,a^{3} c^{6}}"," ",0,"-21/256*I/f/a^3/c^6*ln(tan(f*x+e)-I)*A+7/64/f/a^3/c^6/(tan(f*x+e)+I)*A+1/96*I/f/a^3/c^6/(tan(f*x+e)+I)^6*A-7/256/f/a^3/c^6*ln(tan(f*x+e)+I)*B+35/512*I/f/a^3/c^6/(tan(f*x+e)+I)^2*A+1/40/f/a^3/c^6/(tan(f*x+e)+I)^5*A+7/256*I/f/a^3/c^6/(tan(f*x+e)+I)*B-5/512/f/a^3/c^6/(tan(f*x+e)+I)^2*B-5/96*A/a^3/c^6/f/(tan(f*x+e)+I)^3+7/256*I/f/a^3/c^6/(tan(f*x+e)-I)*B-1/128/f/a^3/c^6/(tan(f*x+e)+I)^4*B-7/512*I/f/a^3/c^6/(tan(f*x+e)-I)^2*A+1/96/f/a^3/c^6/(tan(f*x+e)+I)^6*B+5/512/f/a^3/c^6/(tan(f*x+e)-I)^2*B-1/384*I/f/a^3/c^6/(tan(f*x+e)-I)^3*B-1/384/f/a^3/c^6/(tan(f*x+e)-I)^3*A-1/80*I/f/a^3/c^6/(tan(f*x+e)+I)^5*B-5/128*I/f/a^3/c^6/(tan(f*x+e)+I)^4*A+7/128/f/a^3/c^6/(tan(f*x+e)-I)*A+21/256*I/f/a^3/c^6*ln(tan(f*x+e)+I)*A+7/256/f/a^3/c^6*ln(tan(f*x+e)-I)*B","A"
740,1,55,51,0.400000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x)","\frac{2 i a \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9}+\frac{\left(-i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}\right)}{f c}"," ",0,"2*I/f*a/c*(1/9*I*B*(c-I*c*tan(f*x+e))^(9/2)+1/7*(-I*B*c+c*A)*(c-I*c*tan(f*x+e))^(7/2))","A"
741,1,55,51,0.394000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i a \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}+\frac{\left(-i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}\right)}{f c}"," ",0,"2*I/f*a/c*(1/7*I*B*(c-I*c*tan(f*x+e))^(7/2)+1/5*(-I*B*c+c*A)*(c-I*c*tan(f*x+e))^(5/2))","A"
742,1,55,51,0.368000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i a \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}+\frac{\left(-i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}\right)}{f c}"," ",0,"2*I/f*a/c*(1/5*I*B*(c-I*c*tan(f*x+e))^(5/2)+1/3*(-I*B*c+c*A)*(c-I*c*tan(f*x+e))^(3/2))","A"
743,1,66,51,0.460000," ","int((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))*(A+B*tan(f*x+e)),x)","\frac{2 i a \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}-i B c \sqrt{c -i c \tan \left(f x +e \right)}+c A \sqrt{c -i c \tan \left(f x +e \right)}\right)}{f c}"," ",0,"2*I/f*a/c*(1/3*I*B*(c-I*c*tan(f*x+e))^(3/2)-I*B*c*(c-I*c*tan(f*x+e))^(1/2)+c*A*(c-I*c*tan(f*x+e))^(1/2))","A"
744,1,53,51,0.299000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x)","\frac{2 i a \left(i B \sqrt{c -i c \tan \left(f x +e \right)}-\frac{c \left(-i B +A \right)}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f c}"," ",0,"2*I/f*a/c*(I*B*(c-I*c*tan(f*x+e))^(1/2)-c*(A-I*B)/(c-I*c*tan(f*x+e))^(1/2))","A"
745,1,53,51,0.250000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i a \left(-\frac{c \left(-i B +A \right)}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{i B}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f c}"," ",0,"2*I/f*a/c*(-1/3*c*(A-I*B)/(c-I*c*tan(f*x+e))^(3/2)-I*B/(c-I*c*tan(f*x+e))^(1/2))","A"
746,1,53,51,0.283000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i a \left(-\frac{i B}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{c \left(-i B +A \right)}{5 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\right)}{f c}"," ",0,"2*I/f*a/c*(-1/3*I*B/(c-I*c*tan(f*x+e))^(3/2)-1/5*c*(A-I*B)/(c-I*c*tan(f*x+e))^(5/2))","A"
747,1,53,51,0.261000," ","int((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x)","\frac{2 i a \left(-\frac{c \left(-i B +A \right)}{7 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}-\frac{i B}{5 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\right)}{f c}"," ",0,"2*I/f*a/c*(-1/7*c*(A-I*B)/(c-I*c*tan(f*x+e))^(7/2)-1/5*I*B/(c-I*c*tan(f*x+e))^(5/2))","A"
748,1,83,88,0.262000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x)","-\frac{2 i a^{2} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{11}{2}}}{11}+\frac{\left(-3 i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9}-\frac{2 \left(-i B c +c A \right) c \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}\right)}{f \,c^{2}}"," ",0,"-2*I/f*a^2/c^2*(1/11*I*B*(c-I*c*tan(f*x+e))^(11/2)+1/9*(-3*I*B*c+c*A)*(c-I*c*tan(f*x+e))^(9/2)-2/7*(-I*B*c+c*A)*c*(c-I*c*tan(f*x+e))^(7/2))","A"
749,1,83,88,0.299000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{2 i a^{2} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9}+\frac{\left(-3 i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}-\frac{2 \left(-i B c +c A \right) c \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}\right)}{f \,c^{2}}"," ",0,"-2*I/f*a^2/c^2*(1/9*I*B*(c-I*c*tan(f*x+e))^(9/2)+1/7*(-3*I*B*c+c*A)*(c-I*c*tan(f*x+e))^(7/2)-2/5*(-I*B*c+c*A)*c*(c-I*c*tan(f*x+e))^(5/2))","A"
750,1,83,88,0.297000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{2 i a^{2} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}+\frac{\left(-3 i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}-\frac{2 \left(-i B c +c A \right) c \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}\right)}{f \,c^{2}}"," ",0,"-2*I/f*a^2/c^2*(1/7*I*B*(c-I*c*tan(f*x+e))^(7/2)+1/5*(-3*I*B*c+c*A)*(c-I*c*tan(f*x+e))^(5/2)-2/3*(-I*B*c+c*A)*c*(c-I*c*tan(f*x+e))^(3/2))","A"
751,1,83,88,0.274000," ","int((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e)),x)","-\frac{2 i a^{2} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}+\frac{\left(-3 i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}-2 \left(-i B c +c A \right) c \sqrt{c -i c \tan \left(f x +e \right)}\right)}{f \,c^{2}}"," ",0,"-2*I/f*a^2/c^2*(1/5*I*B*(c-I*c*tan(f*x+e))^(5/2)+1/3*(-3*I*B*c+c*A)*(c-I*c*tan(f*x+e))^(3/2)-2*(-I*B*c+c*A)*c*(c-I*c*tan(f*x+e))^(1/2))","A"
752,1,93,88,0.346000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x)","-\frac{2 i a^{2} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}-3 i B c \sqrt{c -i c \tan \left(f x +e \right)}+c A \sqrt{c -i c \tan \left(f x +e \right)}+\frac{2 c^{2} \left(-i B +A \right)}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{2}}"," ",0,"-2*I/f*a^2/c^2*(1/3*I*B*(c-I*c*tan(f*x+e))^(3/2)-3*I*B*c*(c-I*c*tan(f*x+e))^(1/2)+c*A*(c-I*c*tan(f*x+e))^(1/2)+2*c^2*(A-I*B)/(c-I*c*tan(f*x+e))^(1/2))","A"
753,1,80,88,0.284000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{2 i a^{2} \left(i B \sqrt{c -i c \tan \left(f x +e \right)}+\frac{2 c^{2} \left(-i B +A \right)}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{c \left(-3 i B +A \right)}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{2}}"," ",0,"-2*I/f*a^2/c^2*(I*B*(c-I*c*tan(f*x+e))^(1/2)+2/3*c^2*(A-I*B)/(c-I*c*tan(f*x+e))^(3/2)-c*(A-3*I*B)/(c-I*c*tan(f*x+e))^(1/2))","A"
754,1,80,88,0.257000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{2 i a^{2} \left(-\frac{c \left(-3 i B +A \right)}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{2 c^{2} \left(-i B +A \right)}{5 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}-\frac{i B}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{2}}"," ",0,"-2*I/f*a^2/c^2*(-1/3*c*(A-3*I*B)/(c-I*c*tan(f*x+e))^(3/2)+2/5*c^2*(A-I*B)/(c-I*c*tan(f*x+e))^(5/2)-I*B/(c-I*c*tan(f*x+e))^(1/2))","A"
755,1,80,88,0.301000," ","int((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x)","-\frac{2 i a^{2} \left(\frac{2 c^{2} \left(-i B +A \right)}{7 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}-\frac{i B}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{c \left(-3 i B +A \right)}{5 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\right)}{f \,c^{2}}"," ",0,"-2*I/f*a^2/c^2*(2/7*c^2*(A-I*B)/(c-I*c*tan(f*x+e))^(7/2)-1/3*I*B/(c-I*c*tan(f*x+e))^(3/2)-1/5*c*(A-3*I*B)/(c-I*c*tan(f*x+e))^(5/2))","A"
756,1,121,121,0.396000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x)","\frac{2 i a^{3} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{13}{2}}}{13}+\frac{\left(-5 i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{11}{2}}}{11}+\frac{\left(-4 \left(-i B c +c A \right) c +4 i B \,c^{2}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9}+\frac{4 \left(-i B c +c A \right) c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}\right)}{f \,c^{3}}"," ",0,"2*I/f*a^3/c^3*(1/13*I*B*(c-I*c*tan(f*x+e))^(13/2)+1/11*(-5*I*B*c+c*A)*(c-I*c*tan(f*x+e))^(11/2)+1/9*(-4*(-I*B*c+c*A)*c+4*I*B*c^2)*(c-I*c*tan(f*x+e))^(9/2)+4/7*(-I*B*c+c*A)*c^2*(c-I*c*tan(f*x+e))^(7/2))","A"
757,1,121,121,0.370000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i a^{3} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{11}{2}}}{11}+\frac{\left(-5 i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9}+\frac{\left(-4 \left(-i B c +c A \right) c +4 i B \,c^{2}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}+\frac{4 \left(-i B c +c A \right) c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}\right)}{f \,c^{3}}"," ",0,"2*I/f*a^3/c^3*(1/11*I*B*(c-I*c*tan(f*x+e))^(11/2)+1/9*(-5*I*B*c+c*A)*(c-I*c*tan(f*x+e))^(9/2)+1/7*(-4*(-I*B*c+c*A)*c+4*I*B*c^2)*(c-I*c*tan(f*x+e))^(7/2)+4/5*(-I*B*c+c*A)*c^2*(c-I*c*tan(f*x+e))^(5/2))","A"
758,1,121,121,0.419000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i a^{3} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9}+\frac{\left(-5 i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}+\frac{\left(-4 \left(-i B c +c A \right) c +4 i B \,c^{2}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}+\frac{4 \left(-i B c +c A \right) c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}\right)}{f \,c^{3}}"," ",0,"2*I/f*a^3/c^3*(1/9*I*B*(c-I*c*tan(f*x+e))^(9/2)+1/7*(-5*I*B*c+c*A)*(c-I*c*tan(f*x+e))^(7/2)+1/5*(-4*(-I*B*c+c*A)*c+4*I*B*c^2)*(c-I*c*tan(f*x+e))^(5/2)+4/3*(-I*B*c+c*A)*c^2*(c-I*c*tan(f*x+e))^(3/2))","A"
759,1,121,121,0.410000," ","int((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e)),x)","\frac{2 i a^{3} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}+\frac{\left(-5 i B c +c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}+\frac{\left(-4 \left(-i B c +c A \right) c +4 i B \,c^{2}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}+4 \left(-i B c +c A \right) c^{2} \sqrt{c -i c \tan \left(f x +e \right)}\right)}{f \,c^{3}}"," ",0,"2*I/f*a^3/c^3*(1/7*I*B*(c-I*c*tan(f*x+e))^(7/2)+1/5*(-5*I*B*c+c*A)*(c-I*c*tan(f*x+e))^(5/2)+1/3*(-4*(-I*B*c+c*A)*c+4*I*B*c^2)*(c-I*c*tan(f*x+e))^(3/2)+4*(-I*B*c+c*A)*c^2*(c-I*c*tan(f*x+e))^(1/2))","A"
760,1,135,121,0.305000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x)","\frac{2 i a^{3} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}-\frac{5 i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3}+\frac{A \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3}+8 i B \,c^{2} \sqrt{c -i c \tan \left(f x +e \right)}-4 A \,c^{2} \sqrt{c -i c \tan \left(f x +e \right)}-\frac{4 c^{3} \left(-i B +A \right)}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{3}}"," ",0,"2*I/f*a^3/c^3*(1/5*I*B*(c-I*c*tan(f*x+e))^(5/2)-5/3*I*B*(c-I*c*tan(f*x+e))^(3/2)*c+1/3*A*(c-I*c*tan(f*x+e))^(3/2)*c+8*I*B*c^2*(c-I*c*tan(f*x+e))^(1/2)-4*A*c^2*(c-I*c*tan(f*x+e))^(1/2)-4*c^3*(A-I*B)/(c-I*c*tan(f*x+e))^(1/2))","A"
761,1,118,121,0.309000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i a^{3} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}-5 i B c \sqrt{c -i c \tan \left(f x +e \right)}+c A \sqrt{c -i c \tan \left(f x +e \right)}-\frac{4 c^{3} \left(-i B +A \right)}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{4 c^{2} \left(-2 i B +A \right)}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{3}}"," ",0,"2*I/f*a^3/c^3*(1/3*I*B*(c-I*c*tan(f*x+e))^(3/2)-5*I*B*c*(c-I*c*tan(f*x+e))^(1/2)+c*A*(c-I*c*tan(f*x+e))^(1/2)-4/3*c^3*(A-I*B)/(c-I*c*tan(f*x+e))^(3/2)+4*c^2*(A-2*I*B)/(c-I*c*tan(f*x+e))^(1/2))","A"
762,1,105,121,0.310000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i a^{3} \left(i B \sqrt{c -i c \tan \left(f x +e \right)}+\frac{4 c^{2} \left(-2 i B +A \right)}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{4 c^{3} \left(-i B +A \right)}{5 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}-\frac{c \left(-5 i B +A \right)}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{3}}"," ",0,"2*I/f*a^3/c^3*(I*B*(c-I*c*tan(f*x+e))^(1/2)+4/3*c^2*(A-2*I*B)/(c-I*c*tan(f*x+e))^(3/2)-4/5*c^3*(A-I*B)/(c-I*c*tan(f*x+e))^(5/2)-c*(A-5*I*B)/(c-I*c*tan(f*x+e))^(1/2))","A"
763,1,105,121,0.294000," ","int((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x)","\frac{2 i a^{3} \left(-\frac{4 c^{3} \left(-i B +A \right)}{7 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}-\frac{c \left(-5 i B +A \right)}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{4 c^{2} \left(-2 i B +A \right)}{5 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}-\frac{i B}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{3}}"," ",0,"2*I/f*a^3/c^3*(-4/7*c^3*(A-I*B)/(c-I*c*tan(f*x+e))^(7/2)-1/3*c*(A-5*I*B)/(c-I*c*tan(f*x+e))^(3/2)+4/5*c^2*(A-2*I*B)/(c-I*c*tan(f*x+e))^(5/2)-I*B/(c-I*c*tan(f*x+e))^(1/2))","A"
764,1,192,186,0.671000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e)),x)","\frac{2 i c \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}+i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c +\frac{A \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3}+8 i B \,c^{2} \sqrt{c -i c \tan \left(f x +e \right)}+4 A \,c^{2} \sqrt{c -i c \tan \left(f x +e \right)}+4 c^{3} \left(\frac{\left(-\frac{A}{2}-\frac{i B}{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{-c -i c \tan \left(f x +e \right)}-\frac{\left(9 i B +5 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{4 \sqrt{c}}\right)\right)}{f a}"," ",0,"2*I/f/a*c*(1/5*I*B*(c-I*c*tan(f*x+e))^(5/2)+I*B*(c-I*c*tan(f*x+e))^(3/2)*c+1/3*A*(c-I*c*tan(f*x+e))^(3/2)*c+8*I*B*c^2*(c-I*c*tan(f*x+e))^(1/2)+4*A*c^2*(c-I*c*tan(f*x+e))^(1/2)+4*c^3*((-1/2*A-1/2*I*B)*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-1/4*(5*A+9*I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2))))","A"
765,1,150,152,0.626000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x)","\frac{2 i c \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}+3 i B c \sqrt{c -i c \tan \left(f x +e \right)}+c A \sqrt{c -i c \tan \left(f x +e \right)}+4 c^{2} \left(\frac{\left(-\frac{A}{4}-\frac{i B}{4}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{-c -i c \tan \left(f x +e \right)}-\frac{\left(7 i B +3 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{8 \sqrt{c}}\right)\right)}{f a}"," ",0,"2*I/f/a*c*(1/3*I*B*(c-I*c*tan(f*x+e))^(3/2)+3*I*B*c*(c-I*c*tan(f*x+e))^(1/2)+c*A*(c-I*c*tan(f*x+e))^(1/2)+4*c^2*((-1/4*A-1/4*I*B)*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-1/8*(3*A+7*I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2))))","A"
766,1,109,120,0.549000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x)","\frac{2 i c \left(i B \sqrt{c -i c \tan \left(f x +e \right)}+c \left(\frac{\left(-\frac{A}{2}-\frac{i B}{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{-c -i c \tan \left(f x +e \right)}-\frac{\left(5 i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{4 \sqrt{c}}\right)\right)}{f a}"," ",0,"2*I/f/a*c*(I*B*(c-I*c*tan(f*x+e))^(1/2)+c*((-1/2*A-1/2*I*B)*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-1/4*(A+5*I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2))))","A"
767,1,88,89,0.704000," ","int((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","\frac{2 i c \left(\frac{\left(-\frac{A}{4}-\frac{i B}{4}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{-c -i c \tan \left(f x +e \right)}+\frac{\left(-3 i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{8 \sqrt{c}}\right)}{f a}"," ",0,"2*I/f/a*c*((-1/4*A-1/4*I*B)*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))+1/8*(A-3*I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
768,1,121,117,0.548000," ","int((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x)","\frac{2 i c \left(-\frac{\frac{\left(\frac{A}{2}+\frac{i B}{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{-c -i c \tan \left(f x +e \right)}-\frac{\left(-i B +3 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{4 \sqrt{c}}}{4 c}-\frac{-i B +A}{4 c \sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f a}"," ",0,"2*I/f/a*c*(-1/4/c*((1/2*A+1/2*I*B)*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-1/4*(3*A-I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))-1/4/c*(A-I*B)/(c-I*c*tan(f*x+e))^(1/2))","A"
769,1,141,148,0.448000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i c \left(-\frac{\frac{\left(\frac{A}{4}+\frac{i B}{4}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{-c -i c \tan \left(f x +e \right)}-\frac{\left(i B +5 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{8 \sqrt{c}}}{4 c^{2}}-\frac{A}{4 c^{2} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{-i B +A}{12 c \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\right)}{f a}"," ",0,"2*I/f/a*c*(-1/4/c^2*((1/4*A+1/4*I*B)*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-1/8*(5*A+I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))-1/4/c^2*A/(c-I*c*tan(f*x+e))^(1/2)-1/12/c*(A-I*B)/(c-I*c*tan(f*x+e))^(3/2))","A"
770,1,168,185,0.527000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i c \left(-\frac{\frac{\left(\frac{A}{2}+\frac{i B}{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{-c -i c \tan \left(f x +e \right)}-\frac{\left(3 i B +7 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{4 \sqrt{c}}}{16 c^{3}}-\frac{i B +3 A}{16 c^{3} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{A}{12 c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{-i B +A}{20 c \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\right)}{f a}"," ",0,"2*I/f/a*c*(-1/16/c^3*((1/2*A+1/2*I*B)*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-1/4*(7*A+3*I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))-1/16/c^3*(3*A+I*B)/(c-I*c*tan(f*x+e))^(1/2)-1/12/c^2*A/(c-I*c*tan(f*x+e))^(3/2)-1/20/c*(A-I*B)/(c-I*c*tan(f*x+e))^(5/2))","A"
771,1,221,232,0.644000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{2} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}+\frac{5 i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3}+\frac{A \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3}+18 i B \,c^{2} \sqrt{c -i c \tan \left(f x +e \right)}+6 A \,c^{2} \sqrt{c -i c \tan \left(f x +e \right)}+8 c^{3} \left(\frac{\left(-\frac{21 i B}{16}-\frac{13 A}{16}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(\frac{19}{8} i B c +\frac{11}{8} c A \right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{7 \left(13 i B +5 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{32 \sqrt{c}}\right)\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^2*(1/5*I*B*(c-I*c*tan(f*x+e))^(5/2)+5/3*I*B*(c-I*c*tan(f*x+e))^(3/2)*c+1/3*A*(c-I*c*tan(f*x+e))^(3/2)*c+18*I*B*c^2*(c-I*c*tan(f*x+e))^(1/2)+6*A*c^2*(c-I*c*tan(f*x+e))^(1/2)+8*c^3*(((-21/16*I*B-13/16*A)*(c-I*c*tan(f*x+e))^(3/2)+(19/8*I*B*c+11/8*c*A)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^2-7/32*(13*I*B+5*A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2))))","A"
772,1,179,199,0.569000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{2} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}+5 i B c \sqrt{c -i c \tan \left(f x +e \right)}+c A \sqrt{c -i c \tan \left(f x +e \right)}+2 c^{2} \left(\frac{\left(-\frac{17 i B}{8}-\frac{9 A}{8}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(\frac{15}{4} i B c +\frac{7}{4} c A \right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{5 \left(11 i B +3 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{16 \sqrt{c}}\right)\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^2*(1/3*I*B*(c-I*c*tan(f*x+e))^(3/2)+5*I*B*c*(c-I*c*tan(f*x+e))^(1/2)+c*A*(c-I*c*tan(f*x+e))^(1/2)+2*c^2*(((-17/8*I*B-9/8*A)*(c-I*c*tan(f*x+e))^(3/2)+(15/4*I*B*c+7/4*c*A)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^2-5/16*(11*I*B+3*A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2))))","A"
773,1,138,166,0.687000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{2} \left(i B \sqrt{c -i c \tan \left(f x +e \right)}+c \left(\frac{\left(-\frac{13 i B}{8}-\frac{5 A}{8}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(\frac{11}{4} i B c +\frac{3}{4} c A \right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{3 \left(9 i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{16 \sqrt{c}}\right)\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^2*(I*B*(c-I*c*tan(f*x+e))^(1/2)+c*(((-13/8*I*B-5/8*A)*(c-I*c*tan(f*x+e))^(3/2)+(11/4*I*B*c+3/4*c*A)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^2-3/16*(9*I*B+A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2))))","A"
774,1,117,133,0.635000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{2} \left(\frac{\left(-\frac{9 i B}{16}-\frac{A}{16}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(\frac{7}{8} i B c -\frac{1}{8} c A \right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}+\frac{\left(-7 i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{32 \sqrt{c}}\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^2*(((-9/16*I*B-1/16*A)*(c-I*c*tan(f*x+e))^(3/2)+(7/8*I*B*c-1/8*c*A)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^2+1/32*(-7*I*B+A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
775,1,121,132,0.597000," ","int((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{2} \left(\frac{\frac{\left(-5 i B +3 A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{32 c}+\left(-\frac{5 A}{16}+\frac{3 i B}{16}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{\left(-5 i B +3 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{64 c^{\frac{3}{2}}}\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^2*((1/32/c*(3*A-5*I*B)*(c-I*c*tan(f*x+e))^(3/2)+(-5/16*A+3/16*I*B)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^2-1/64/c^(3/2)*(3*A-5*I*B)*2^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
776,1,152,162,0.590000," ","int((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{2} \left(\frac{\frac{\left(-\frac{i B}{8}+\frac{7 A}{8}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(-\frac{9}{4} c A -\frac{1}{4} i B c \right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{3 \left(-3 i B +5 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{16 \sqrt{c}}}{8 c^{2}}-\frac{i B -A}{8 c^{2} \sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^2*(1/8/c^2*(((-1/8*I*B+7/8*A)*(c-I*c*tan(f*x+e))^(3/2)+(-9/4*c*A-1/4*I*B*c)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^2-3/16*(-3*I*B+5*A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))-1/8/c^2*(-A+I*B)/(c-I*c*tan(f*x+e))^(1/2))","A"
777,1,179,187,0.493000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{2 i c^{2} \left(\frac{\frac{\left(\frac{3 i B}{8}+\frac{11 A}{8}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(-\frac{13}{4} c A -\frac{5}{4} i B c \right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{5 \left(-i B +7 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{16 \sqrt{c}}}{16 c^{3}}-\frac{i B -3 A}{16 c^{3} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{i B -A}{24 c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^2*(1/16/c^3*(((3/8*I*B+11/8*A)*(c-I*c*tan(f*x+e))^(3/2)+(-13/4*c*A-5/4*I*B*c)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^2-5/16*(7*A-I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))-1/16/c^3*(-3*A+I*B)/(c-I*c*tan(f*x+e))^(1/2)-1/24/c^2*(-A+I*B)/(c-I*c*tan(f*x+e))^(3/2))","A"
778,1,199,228,0.444000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{2 i c^{2} \left(\frac{\frac{\left(\frac{7 i B}{16}+\frac{15 A}{16}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(-\frac{9}{8} i B c -\frac{17}{8} c A \right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{7 \left(i B +9 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{32 \sqrt{c}}}{16 c^{4}}+\frac{3 A}{16 c^{4} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{i B -3 A}{48 c^{3} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{i B -A}{40 c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^2*(1/16/c^4*(((7/16*I*B+15/16*A)*(c-I*c*tan(f*x+e))^(3/2)+(-9/8*I*B*c-17/8*c*A)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^2-7/32*(I*B+9*A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))+3/16/c^4*A/(c-I*c*tan(f*x+e))^(1/2)-1/48/c^3*(-3*A+I*B)/(c-I*c*tan(f*x+e))^(3/2)-1/40/c^2*(-A+I*B)/(c-I*c*tan(f*x+e))^(5/2))","A"
779,1,206,245,0.648000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{3} \left(\frac{i B \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}+7 i B c \sqrt{c -i c \tan \left(f x +e \right)}+c A \sqrt{c -i c \tan \left(f x +e \right)}+8 c^{2} \left(\frac{\left(-\frac{81 i B}{64}-\frac{29 A}{64}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}+\left(\frac{53}{12} i B c +\frac{17}{12} c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(-\frac{63}{16} i B \,c^{2}-\frac{19}{16} A \,c^{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{35 \left(5 i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{128 \sqrt{c}}\right)\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^3*(1/3*I*B*(c-I*c*tan(f*x+e))^(3/2)+7*I*B*c*(c-I*c*tan(f*x+e))^(1/2)+c*A*(c-I*c*tan(f*x+e))^(1/2)+8*c^2*(((-81/64*I*B-29/64*A)*(c-I*c*tan(f*x+e))^(5/2)+(53/12*I*B*c+17/12*c*A)*(c-I*c*tan(f*x+e))^(3/2)+(-63/16*I*B*c^2-19/16*A*c^2)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-35/128*(A+5*I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2))))","A"
780,1,167,212,0.656000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{3} \left(i B \sqrt{c -i c \tan \left(f x +e \right)}+c \left(\frac{\left(-\frac{47 i B}{16}-\frac{11 A}{16}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}+\left(\frac{29}{3} i B c +\frac{5}{3} c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(-\frac{33}{4} i B \,c^{2}-\frac{5}{4} A \,c^{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{5 \left(13 i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{32 \sqrt{c}}\right)\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^3*(I*B*(c-I*c*tan(f*x+e))^(1/2)+c*(((-47/16*I*B-11/16*A)*(c-I*c*tan(f*x+e))^(5/2)+(29/3*I*B*c+5/3*c*A)*(c-I*c*tan(f*x+e))^(3/2)+(-33/4*I*B*c^2-5/4*A*c^2)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-5/32*(13*I*B+A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2))))","A"
781,1,146,179,0.550000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{3} \left(\frac{\left(-\frac{21 i B}{32}-\frac{A}{32}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}+\left(\frac{11}{6} i B c -\frac{1}{6} c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(-\frac{11}{8} i B \,c^{2}+\frac{1}{8} A \,c^{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}+\frac{\left(-11 i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{64 \sqrt{c}}\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^3*(((-21/32*I*B-1/32*A)*(c-I*c*tan(f*x+e))^(5/2)+(11/6*I*B*c-1/6*c*A)*(c-I*c*tan(f*x+e))^(3/2)+(-11/8*I*B*c^2+1/8*A*c^2)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3+1/64*(-11*I*B+A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
782,1,140,177,0.656000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{3} \left(\frac{\frac{\left(-3 i B +A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{64 c}+\left(-\frac{A}{12}-\frac{i B}{12}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}-\frac{c \left(-3 i B +A \right) \sqrt{c -i c \tan \left(f x +e \right)}}{16}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{\left(-3 i B +A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{128 c^{\frac{3}{2}}}\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^3*((1/64/c*(A-3*I*B)*(c-I*c*tan(f*x+e))^(5/2)+(-1/12*A-1/12*I*B)*(c-I*c*tan(f*x+e))^(3/2)-1/16*c*(A-3*I*B)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-1/128/c^(3/2)*(A-3*I*B)*2^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
783,1,148,175,0.667000," ","int((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{3} \left(\frac{-\frac{\left(-7 i B +5 A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{128 c^{2}}+\frac{\left(-7 i B +5 A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{24 c}+\left(-\frac{11 A}{32}+\frac{9 i B}{32}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}+\frac{\left(-7 i B +5 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{256 c^{\frac{5}{2}}}\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^3*((-1/128/c^2*(5*A-7*I*B)*(c-I*c*tan(f*x+e))^(5/2)+1/24/c*(5*A-7*I*B)*(c-I*c*tan(f*x+e))^(3/2)+(-11/32*A+9/32*I*B)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3+1/256/c^(5/2)*(5*A-7*I*B)*2^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
784,1,179,205,0.567000," ","int((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{3} \left(-\frac{\frac{\left(-\frac{9 i B}{16}+\frac{19 A}{16}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}+\left(\frac{7}{3} i B c -\frac{17}{3} c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(-\frac{7}{4} i B \,c^{2}+\frac{29}{4} A \,c^{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{5 \left(-5 i B +7 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{32 \sqrt{c}}}{16 c^{3}}-\frac{-i B +A}{16 c^{3} \sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^3*(-1/16/c^3*(((-9/16*I*B+19/16*A)*(c-I*c*tan(f*x+e))^(5/2)+(7/3*I*B*c-17/3*c*A)*(c-I*c*tan(f*x+e))^(3/2)+(-7/4*I*B*c^2+29/4*A*c^2)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-5/32*(-5*I*B+7*A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))-1/16/c^3*(A-I*B)/(c-I*c*tan(f*x+e))^(1/2))","A"
785,1,206,228,0.583000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i c^{3} \left(-\frac{\frac{\left(-\frac{3 i B}{32}+\frac{41 A}{32}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}+\left(\frac{1}{6} i B c -\frac{35}{6} c A \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(\frac{55}{8} A \,c^{2}+\frac{3}{8} i B \,c^{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{35 \left(-i B +3 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{64 \sqrt{c}}}{16 c^{4}}-\frac{-i B +2 A}{16 c^{4} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{-i B +A}{48 c^{3} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^3*(-1/16/c^4*(((-3/32*I*B+41/32*A)*(c-I*c*tan(f*x+e))^(5/2)+(1/6*I*B*c-35/6*c*A)*(c-I*c*tan(f*x+e))^(3/2)+(55/8*A*c^2+3/8*I*B*c^2)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-35/64*(3*A-I*B)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))-1/16/c^4*(2*A-I*B)/(c-I*c*tan(f*x+e))^(1/2)-1/48/c^3*(A-I*B)/(c-I*c*tan(f*x+e))^(3/2))","A"
786,1,233,259,0.582000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i c^{3} \left(-\frac{\frac{\left(\frac{11 i B}{32}+\frac{71 A}{32}\right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}+\left(-\frac{59}{6} c A -\frac{11}{6} i B c \right) \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}+\left(\frac{21}{8} i B \,c^{2}+\frac{89}{8} A \,c^{2}\right) \sqrt{c -i c \tan \left(f x +e \right)}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{21 \left(-i B +11 A \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{64 \sqrt{c}}}{32 c^{5}}-\frac{-i B +5 A}{32 c^{5} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{-i B +2 A}{48 c^{4} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{-i B +A}{80 c^{3} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^3*(-1/32/c^5*(((11/32*I*B+71/32*A)*(c-I*c*tan(f*x+e))^(5/2)+(-59/6*c*A-11/6*I*B*c)*(c-I*c*tan(f*x+e))^(3/2)+(21/8*I*B*c^2+89/8*A*c^2)*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-21/64*(-I*B+11*A)*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))-1/32/c^5*(5*A-I*B)/(c-I*c*tan(f*x+e))^(1/2)-1/48/c^4*(2*A-I*B)/(c-I*c*tan(f*x+e))^(3/2)-1/80/c^3*(A-I*B)/(c-I*c*tan(f*x+e))^(5/2))","A"
787,1,349,220,0.559000," ","int((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, c^{3} \left(6 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+8 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+45 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -45 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-24 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-88 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+60 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -36 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+72 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{24 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/24/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*c^3*(6*I*B*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+8*I*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+45*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-45*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-24*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-88*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+60*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-36*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+72*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
788,1,285,176,0.680000," ","int((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, c^{2} \left(-6 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +6 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+2 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+12 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-9 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +3 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-10 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{6 f \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}}"," ",0,"-1/6/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*c^2*(-6*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+6*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)+2*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+12*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)-9*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+3*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-10*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2)/(c*a*(1+tan(f*x+e)^2))^(1/2)","A"
789,1,223,132,0.627000," ","int((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, c \left(i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +2 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-2 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -2 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{2 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"-1/2/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*c*(I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*c*a+2*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-2*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-2*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
790,1,121,83,0.555000," ","int((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*(A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
791,1,321,88,0.612000," ","int((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x)","-\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(-2 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{f c \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan \left(f x +e \right)+i\right)^{2} \sqrt{c a}}"," ",0,"-I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c*(-2*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(tan(f*x+e)+I)^2/(c*a)^(1/2)","B"
792,1,100,84,0.496000," ","int((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(2 i B \left(\tan^{2}\left(f x +e \right)\right)+3 i A \tan \left(f x +e \right)+A \left(\tan^{2}\left(f x +e \right)\right)-i B -3 B \tan \left(f x +e \right)-2 A \right)}{3 f \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"1/3/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^2*(2*I*B*tan(f*x+e)^2+3*I*A*tan(f*x+e)+A*tan(f*x+e)^2-I*B-3*B*tan(f*x+e)-2*A)/(tan(f*x+e)+I)^3","A"
793,1,125,128,0.438000," ","int((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(2 i A \left(\tan^{3}\left(f x +e \right)\right)-12 i B \left(\tan^{2}\left(f x +e \right)\right)-3 B \left(\tan^{3}\left(f x +e \right)\right)-13 i A \tan \left(f x +e \right)-8 A \left(\tan^{2}\left(f x +e \right)\right)+3 i B +12 B \tan \left(f x +e \right)+7 A \right)}{15 f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"-1/15*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^3*(2*I*A*tan(f*x+e)^3-12*I*B*tan(f*x+e)^2-3*B*tan(f*x+e)^3-13*I*A*tan(f*x+e)-8*A*tan(f*x+e)^2+3*I*B+12*B*tan(f*x+e)+7*A)/(tan(f*x+e)+I)^4","A"
794,1,147,172,0.524000," ","int((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(8 i B \left(\tan^{4}\left(f x +e \right)\right)+30 i A \left(\tan^{3}\left(f x +e \right)\right)+6 A \left(\tan^{4}\left(f x +e \right)\right)-84 i B \left(\tan^{2}\left(f x +e \right)\right)-40 B \left(\tan^{3}\left(f x +e \right)\right)-75 i A \tan \left(f x +e \right)-63 A \left(\tan^{2}\left(f x +e \right)\right)+13 i B +65 B \tan \left(f x +e \right)+36 A \right)}{105 f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{5}}"," ",0,"1/105/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^4*(8*I*B*tan(f*x+e)^4+30*I*A*tan(f*x+e)^3+6*A*tan(f*x+e)^4-84*I*B*tan(f*x+e)^2-40*B*tan(f*x+e)^3-75*I*A*tan(f*x+e)-63*A*tan(f*x+e)^2+13*I*B+65*B*tan(f*x+e)+36*A)/(tan(f*x+e)+I)^5","A"
795,1,412,227,0.622000," ","int((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, c^{3} a \left(60 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+24 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+80 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+30 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-30 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +30 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-32 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+80 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-75 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -45 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-56 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{120 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"-1/120/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*c^3*a*(60*I*B*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+24*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+80*I*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+30*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-30*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+30*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-32*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+80*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)-75*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-45*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-56*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
796,1,350,183,0.534000," ","int((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, c^{2} a \left(6 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+8 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-3 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +3 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-8 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+8 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-12 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -12 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-8 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{24 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"-1/24/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*c^2*a*(6*I*B*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+8*I*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-3*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+3*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-8*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+8*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-12*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-12*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-8*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
797,1,186,126,0.639000," ","int((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, c a \left(2 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+3 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +3 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+2 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{6 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/6/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*c*a*(2*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+3*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+2*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
798,1,223,128,0.607000," ","int((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, a \left(-i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+2 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+2 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +2 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{2 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/2/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*a*(-I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*c*a+I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+2*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+2*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+2*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
799,1,497,140,0.512000," ","int((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x)","\frac{\left(2 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -2 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -2 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -4 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-4 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+2 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +2 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+3 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right) \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a}{f c \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan \left(f x +e \right)+i\right)^{2} \sqrt{c a}}"," ",0,"1/f*(2*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-2*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-2*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-4*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-4*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+2*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+2*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+3*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c*a/(c*a*(1+tan(f*x+e)^2))^(1/2)/(tan(f*x+e)+I)^2/(c*a)^(1/2)","B"
800,1,406,126,0.511000," ","int((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a \left(3 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c -9 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -7 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{2}\left(f x +e \right)\right)-9 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+5 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+3 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +12 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{3 f \,c^{2} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan \left(f x +e \right)+i\right)^{3} \sqrt{c a}}"," ",0,"-1/3/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^2*a*(3*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c-9*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-7*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-9*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+5*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+12*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(tan(f*x+e)+I)^3/(c*a)^(1/2)","B"
801,1,90,84,0.483000," ","int((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a \left(1+\tan^{2}\left(f x +e \right)\right) \left(-4 A +i A \tan \left(f x +e \right)-i B -4 B \tan \left(f x +e \right)\right)}{15 f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"1/15*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^3*a*(1+tan(f*x+e)^2)*(-4*A+I*A*tan(f*x+e)-I*B-4*B*tan(f*x+e))/(tan(f*x+e)+I)^4","A"
802,1,113,128,0.434000," ","int((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x)","\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a \left(1+\tan^{2}\left(f x +e \right)\right) \left(5 B -25 i B \tan \left(f x +e \right)-5 B \left(\tan^{2}\left(f x +e \right)\right)-23 i A -10 A \tan \left(f x +e \right)+2 i A \left(\tan^{2}\left(f x +e \right)\right)\right)}{105 f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{5}}"," ",0,"1/105*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^4*a*(1+tan(f*x+e)^2)*(5*B-25*I*B*tan(f*x+e)-5*B*tan(f*x+e)^2-23*I*A-10*A*tan(f*x+e)+2*I*A*tan(f*x+e)^2)/(tan(f*x+e)+I)^5","A"
803,1,136,172,0.503000," ","int((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(9/2),x)","\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a \left(1+\tan^{2}\left(f x +e \right)\right) \left(2 i A \left(\tan^{3}\left(f x +e \right)\right)-24 i B \left(\tan^{2}\left(f x +e \right)\right)-4 B \left(\tan^{3}\left(f x +e \right)\right)-33 i A \tan \left(f x +e \right)-12 A \left(\tan^{2}\left(f x +e \right)\right)+11 i B +66 B \tan \left(f x +e \right)+58 A \right)}{315 f \,c^{5} \left(\tan \left(f x +e \right)+i\right)^{6}}"," ",0,"1/315*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^5*a*(1+tan(f*x+e)^2)*(2*I*A*tan(f*x+e)^3-24*I*B*tan(f*x+e)^2-4*B*tan(f*x+e)^3-33*I*A*tan(f*x+e)-12*A*tan(f*x+e)^2+11*I*B+66*B*tan(f*x+e)+58*A)/(tan(f*x+e)+I)^6","A"
804,1,158,216,0.498000," ","int((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(11/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a \left(1+\tan^{2}\left(f x +e \right)\right) \left(14 i B \left(\tan^{4}\left(f x +e \right)\right)+56 i A \left(\tan^{3}\left(f x +e \right)\right)+8 A \left(\tan^{4}\left(f x +e \right)\right)-315 i B \left(\tan^{2}\left(f x +e \right)\right)-98 B \left(\tan^{3}\left(f x +e \right)\right)-364 i A \tan \left(f x +e \right)-180 A \left(\tan^{2}\left(f x +e \right)\right)+91 i B +637 B \tan \left(f x +e \right)+547 A \right)}{3465 f \,c^{6} \left(\tan \left(f x +e \right)+i\right)^{7}}"," ",0,"-1/3465/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^6*a*(1+tan(f*x+e)^2)*(14*I*B*tan(f*x+e)^4+56*I*A*tan(f*x+e)^3+8*A*tan(f*x+e)^4-315*I*B*tan(f*x+e)^2-98*B*tan(f*x+e)^3-364*I*A*tan(f*x+e)-180*A*tan(f*x+e)^2+91*I*B+637*B*tan(f*x+e)+547*A)/(tan(f*x+e)+I)^7","A"
805,1,478,236,0.533000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} c^{3} \left(40 i B \left(\tan^{5}\left(f x +e \right)\right) \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}+48 i A \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}+70 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-48 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+96 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-60 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-15 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +15 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-96 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+48 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-90 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -150 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-48 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{240 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"-1/240/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2*c^3*(40*I*B*tan(f*x+e)^5*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+48*I*A*tan(f*x+e)^4*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+70*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^3-48*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+96*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^2-60*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-15*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+15*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-96*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+48*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)-90*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-150*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-48*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","B"
806,1,252,172,0.638000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} c^{2} \left(8 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+10 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+16 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+15 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +25 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+8 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{40 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/40/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2*c^2*(8*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+10*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+16*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+15*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+25*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+8*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
807,1,350,179,0.599000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} c \left(6 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+8 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-3 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +3 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+8 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+8 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+12 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +12 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+8 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{24 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/24/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2*c*(6*I*B*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+8*I*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-3*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+3*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+8*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+8*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+12*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+12*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+8*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
808,1,285,176,0.545000," ","int((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, a^{2} \left(-6 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +6 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-2 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+12 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+9 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -3 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+10 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{6 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/6/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*a^2*(-6*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+6*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-2*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+12*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+9*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-3*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+10*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
809,1,565,187,0.567000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x)","\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} \left(6 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +18 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +4 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{2}\left(f x +e \right)\right)+9 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)-6 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -12 i A \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)-12 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -2 A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-14 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-9 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -19 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+10 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{2 f c \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan \left(f x +e \right)+i\right)^{2} \sqrt{c a}}"," ",0,"1/2*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2/c*(6*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+18*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+4*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^2+9*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-6*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-12*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-12*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-2*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-14*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-9*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-19*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+10*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(tan(f*x+e)+I)^2/(c*a)^(1/2)","B"
810,1,667,186,0.497000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} \left(-12 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +9 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +3 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +36 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +29 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{2}\left(f x +e \right)\right)+36 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +3 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)-3 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -12 i A \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)-9 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -8 A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-19 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-12 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -45 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+4 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{3 f \,c^{2} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan \left(f x +e \right)+i\right)^{3} \sqrt{c a}}"," ",0,"1/3/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2/c^2*(-12*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+9*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+3*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+36*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+29*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^2+36*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+3*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-3*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-12*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-9*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-8*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-19*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-12*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-45*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+4*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(tan(f*x+e)+I)^3/(c*a)^(1/2)","B"
811,1,555,166,0.438000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} \left(-15 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{4}\left(f x +e \right)\right) a c +90 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +43 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+60 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +3 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-3 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-15 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -77 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-60 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -97 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+3 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-3 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+23 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{15 f \,c^{3} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan \left(f x +e \right)+i\right)^{4} \sqrt{c a}}"," ",0,"-1/15/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2/c^3*(-15*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^4*a*c+90*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+43*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3+60*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+3*I*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-3*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-15*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-77*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-60*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-97*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-3*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+23*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(tan(f*x+e)+I)^4/(c*a)^(1/2)","B"
812,1,115,84,0.502000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x)","-\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} \left(1+\tan^{2}\left(f x +e \right)\right) \left(i A \left(\tan^{2}\left(f x +e \right)\right)+5 i B \tan \left(f x +e \right)-6 B \left(\tan^{2}\left(f x +e \right)\right)+6 i A -5 A \tan \left(f x +e \right)-B \right)}{35 f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{5}}"," ",0,"-1/35*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2/c^4*(1+tan(f*x+e)^2)*(I*A*tan(f*x+e)^2+5*I*B*tan(f*x+e)-6*B*tan(f*x+e)^2+6*I*A-5*A*tan(f*x+e)-B)/(tan(f*x+e)+I)^5","A"
813,1,138,128,0.487000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(9/2),x)","-\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} \left(1+\tan^{2}\left(f x +e \right)\right) \left(-47 A -42 i B \left(\tan^{2}\left(f x +e \right)\right)-12 A \left(\tan^{2}\left(f x +e \right)\right)-33 i A \tan \left(f x +e \right)+2 i A \left(\tan^{3}\left(f x +e \right)\right)-42 B \tan \left(f x +e \right)-7 i B -7 B \left(\tan^{3}\left(f x +e \right)\right)\right)}{315 f \,c^{5} \left(\tan \left(f x +e \right)+i\right)^{6}}"," ",0,"-1/315*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2/c^5*(1+tan(f*x+e)^2)*(-47*A-42*I*B*tan(f*x+e)^2-12*A*tan(f*x+e)^2-33*I*A*tan(f*x+e)+2*I*A*tan(f*x+e)^3-42*B*tan(f*x+e)-7*I*B-7*B*tan(f*x+e)^3)/(tan(f*x+e)+I)^6","A"
814,1,161,172,0.424000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(11/2),x)","-\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} \left(1+\tan^{2}\left(f x +e \right)\right) \left(6 i A \left(\tan^{4}\left(f x +e \right)\right)-112 i B \left(\tan^{3}\left(f x +e \right)\right)-16 B \left(\tan^{4}\left(f x +e \right)\right)-135 i A \left(\tan^{2}\left(f x +e \right)\right)-42 A \left(\tan^{3}\left(f x +e \right)\right)-427 i B \tan \left(f x +e \right)+360 B \left(\tan^{2}\left(f x +e \right)\right)-456 i A +273 A \tan \left(f x +e \right)+61 B \right)}{3465 f \,c^{6} \left(\tan \left(f x +e \right)+i\right)^{7}}"," ",0,"-1/3465*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2/c^6*(1+tan(f*x+e)^2)*(6*I*A*tan(f*x+e)^4-112*I*B*tan(f*x+e)^3-16*B*tan(f*x+e)^4-135*I*A*tan(f*x+e)^2-42*A*tan(f*x+e)^3-427*I*B*tan(f*x+e)+360*B*tan(f*x+e)^2-456*I*A+273*A*tan(f*x+e)+61*B)/(tan(f*x+e)+I)^7","A"
815,1,183,216,0.513000," ","int((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(13/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{2} \left(1+\tan^{2}\left(f x +e \right)\right) \left(18 i B \left(\tan^{5}\left(f x +e \right)\right)+64 i A \left(\tan^{4}\left(f x +e \right)\right)+8 A \left(\tan^{5}\left(f x +e \right)\right)-531 i B \left(\tan^{3}\left(f x +e \right)\right)-144 B \left(\tan^{4}\left(f x +e \right)\right)-544 i A \left(\tan^{2}\left(f x +e \right)\right)-236 A \left(\tan^{3}\left(f x +e \right)\right)-1704 i B \tan \left(f x +e \right)+1224 B \left(\tan^{2}\left(f x +e \right)\right)-1763 i A +911 A \tan \left(f x +e \right)+213 B \right)}{15015 f \,c^{7} \left(\tan \left(f x +e \right)+i\right)^{8}}"," ",0,"1/15015/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2/c^7*(1+tan(f*x+e)^2)*(18*I*B*tan(f*x+e)^5+64*I*A*tan(f*x+e)^4+8*A*tan(f*x+e)^5-531*I*B*tan(f*x+e)^3-144*B*tan(f*x+e)^4-544*I*A*tan(f*x+e)^2-236*A*tan(f*x+e)^3-1704*I*B*tan(f*x+e)+1224*B*tan(f*x+e)^2-1763*I*A+911*A*tan(f*x+e)+213*B)/(tan(f*x+e)+I)^8","A"
816,1,604,289,0.607000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} c^{4} \left(1152 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{4}\left(f x +e \right)\right)+952 i B \left(\tan^{5}\left(f x +e \right)\right) \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}+384 i A \left(\tan^{6}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-384 B \left(\tan^{6}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+826 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-448 A \left(\tan^{5}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-105 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -1152 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+1152 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-1456 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+105 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+336 i B \left(\tan^{7}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-1152 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+384 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-840 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -1848 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-384 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{2688 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"-1/2688/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3*c^4*(1152*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^4+952*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^5+384*I*A*tan(f*x+e)^6*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-384*B*tan(f*x+e)^6*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+826*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-448*A*tan(f*x+e)^5*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-105*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-1152*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+1152*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-1456*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+105*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+336*I*B*tan(f*x+e)^7*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-1152*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+384*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-840*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-1848*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-384*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","B"
817,1,314,218,0.538000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} c^{3} \left(48 B \left(\tan^{6}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+56 A \left(\tan^{5}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+144 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+182 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+144 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+105 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +231 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+48 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{336 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/336/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3*c^3*(48*B*tan(f*x+e)^6*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+56*A*tan(f*x+e)^5*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+144*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+182*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+144*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+105*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+231*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+48*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
818,1,478,232,0.633000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} c^{2} \left(40 i B \left(\tan^{5}\left(f x +e \right)\right) \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}+48 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{4}\left(f x +e \right)\right)+70 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+48 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+96 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+60 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-15 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +15 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+96 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+48 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+90 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +150 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+48 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{240 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/240/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3*c^2*(40*I*B*tan(f*x+e)^5*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+48*I*A*tan(f*x+e)^4*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+70*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^3+48*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+96*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^2+60*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-15*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+15*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)+96*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+48*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+90*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+150*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+48*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","B"
819,1,412,227,0.596000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} c \left(60 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-24 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+80 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-30 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-30 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +30 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+32 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+80 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+75 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +45 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+56 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{120 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/120/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3*c*(60*I*B*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-24*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+80*I*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-30*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-30*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+30*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)+32*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+80*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+75*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+45*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+56*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
820,1,349,220,0.529000," ","int((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e)),x)","-\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(6 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+8 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+45 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -45 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+24 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-88 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-60 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +36 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-72 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{24 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"-1/24/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*a^3*(6*I*B*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+8*I*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+45*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-45*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+24*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-88*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-60*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+36*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-72*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
821,1,627,234,0.571000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(-60 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +8 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-2 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+90 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +18 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+45 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -3 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+60 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +128 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+120 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +24 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-72 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-45 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -93 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-94 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{6 f c \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan \left(f x +e \right)+i\right)^{2} \sqrt{c a}}"," ",0,"-1/6/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c*(-60*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+8*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-2*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+90*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+18*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2+45*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-3*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+60*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+128*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+120*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+24*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-72*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-45*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-93*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-94*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(tan(f*x+e)+I)^2/(c*a)^(1/2)","B"
822,1,731,234,0.510000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(-75 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +6 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)+185 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{2}\left(f x +e \right)\right)+225 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +30 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +3 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{4}\left(f x +e \right)\right)-30 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +225 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +21 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)-114 i A \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)+90 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -90 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -74 A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-118 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-75 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -279 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+46 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{6 f \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{3} \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}}"," ",0,"1/6/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c^2*(-75*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+6*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3+185*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2+225*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+30*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+3*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^4-30*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+225*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+21*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-114*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+90*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-90*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-74*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-118*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-75*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-279*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+46*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(tan(f*x+e)+I)^3/(c*a)^(1/2)/(c*a*(1+tan(f*x+e)^2))^(1/2)","B"
823,1,833,234,0.484000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(-60 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +60 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +15 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{4}\left(f x +e \right)\right) a c +246 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-90 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{4}\left(f x +e \right)\right) a c +360 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +15 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-90 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -94 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-90 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -46 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-474 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+540 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -360 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -564 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+26 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+15 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +74 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+141 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{15 f \,c^{3} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan \left(f x +e \right)+i\right)^{4} \sqrt{c a}}"," ",0,"-1/15/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c^3*(-60*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+60*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+15*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^4*a*c+246*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-90*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^4*a*c+360*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+15*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-90*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-94*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-90*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-46*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-474*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+540*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-360*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-564*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+26*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+15*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+74*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+141*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(tan(f*x+e)+I)^4/(c*a)^(1/2)","B"
824,1,638,206,0.536000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(-105 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{5}\left(f x +e \right)\right) a c +1050 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +337 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{4}\left(f x +e \right)\right)+525 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{4}\left(f x +e \right)\right) a c +30 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)-15 A \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-525 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -1176 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{2}\left(f x +e \right)\right)-1050 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -950 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)+30 i A \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)+167 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+105 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +730 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+15 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{105 f \,c^{4} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan \left(f x +e \right)+i\right)^{5} \sqrt{c a}}"," ",0,"1/105/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c^4*(-105*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^5*a*c+1050*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+337*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^4+525*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^4*a*c+30*I*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-15*A*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-525*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-1176*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^2-1050*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-950*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3+30*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)+167*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+105*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+730*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+15*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(tan(f*x+e)+I)^5/(c*a)^(1/2)","B"
825,1,134,84,0.511000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(9/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(1+\tan^{2}\left(f x +e \right)\right) \left(8 i B \left(\tan^{3}\left(f x +e \right)\right)+6 i A \left(\tan^{2}\left(f x +e \right)\right)+A \left(\tan^{3}\left(f x +e \right)\right)-6 i B \tan \left(f x +e \right)+15 B \left(\tan^{2}\left(f x +e \right)\right)-8 i A +15 A \tan \left(f x +e \right)+B \right)}{63 f \,c^{5} \left(\tan \left(f x +e \right)+i\right)^{6}}"," ",0,"-1/63/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c^5*(1+tan(f*x+e)^2)*(8*I*B*tan(f*x+e)^3+6*I*A*tan(f*x+e)^2+A*tan(f*x+e)^3-6*I*B*tan(f*x+e)+15*B*tan(f*x+e)^2-8*I*A+15*A*tan(f*x+e)+B)/(tan(f*x+e)+I)^6","A"
826,1,161,128,0.428000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(11/2),x)","\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(1+\tan^{2}\left(f x +e \right)\right) \left(2 i A \left(\tan^{4}\left(f x +e \right)\right)-63 i B \left(\tan^{3}\left(f x +e \right)\right)-9 B \left(\tan^{4}\left(f x +e \right)\right)-45 i A \left(\tan^{2}\left(f x +e \right)\right)-14 A \left(\tan^{3}\left(f x +e \right)\right)+63 i B \tan \left(f x +e \right)-144 B \left(\tan^{2}\left(f x +e \right)\right)+79 i A -140 A \tan \left(f x +e \right)-9 B \right)}{693 f \,c^{6} \left(\tan \left(f x +e \right)+i\right)^{7}}"," ",0,"1/693*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c^6*(1+tan(f*x+e)^2)*(2*I*A*tan(f*x+e)^4-63*I*B*tan(f*x+e)^3-9*B*tan(f*x+e)^4-45*I*A*tan(f*x+e)^2-14*A*tan(f*x+e)^3+63*I*B*tan(f*x+e)-144*B*tan(f*x+e)^2+79*I*A-140*A*tan(f*x+e)-9*B)/(tan(f*x+e)+I)^7","A"
827,1,184,172,0.529000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(13/2),x)","\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(1+\tan^{2}\left(f x +e \right)\right) \left(6 i A \left(\tan^{5}\left(f x +e \right)\right)-160 i B \left(\tan^{4}\left(f x +e \right)\right)-20 B \left(\tan^{5}\left(f x +e \right)\right)-177 i A \left(\tan^{3}\left(f x +e \right)\right)-48 A \left(\tan^{4}\left(f x +e \right)\right)-1643 i B \left(\tan^{2}\left(f x +e \right)\right)+590 B \left(\tan^{3}\left(f x +e \right)\right)-1569 i A \tan \left(f x +e \right)+408 A \left(\tan^{2}\left(f x +e \right)\right)-97 i B -776 B \tan \left(f x +e \right)-930 A \right)}{9009 f \,c^{7} \left(\tan \left(f x +e \right)+i\right)^{8}}"," ",0,"1/9009*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c^7*(1+tan(f*x+e)^2)*(6*I*A*tan(f*x+e)^5-160*I*B*tan(f*x+e)^4-20*B*tan(f*x+e)^5-177*I*A*tan(f*x+e)^3-48*A*tan(f*x+e)^4-1643*I*B*tan(f*x+e)^2+590*B*tan(f*x+e)^3-1569*I*A*tan(f*x+e)+408*A*tan(f*x+e)^2-97*I*B-776*B*tan(f*x+e)-930*A)/(tan(f*x+e)+I)^8","A"
828,1,206,216,0.470000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(15/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(1+\tan^{2}\left(f x +e \right)\right) \left(22 i B \left(\tan^{6}\left(f x +e \right)\right)+72 i A \left(\tan^{5}\left(f x +e \right)\right)+8 A \left(\tan^{6}\left(f x +e \right)\right)-825 i B \left(\tan^{4}\left(f x +e \right)\right)-198 B \left(\tan^{5}\left(f x +e \right)\right)-780 i A \left(\tan^{3}\left(f x +e \right)\right)-300 A \left(\tan^{4}\left(f x +e \right)\right)-7260 i B \left(\tan^{2}\left(f x +e \right)\right)+2145 B \left(\tan^{3}\left(f x +e \right)\right)-6858 i A \tan \left(f x +e \right)+1455 A \left(\tan^{2}\left(f x +e \right)\right)-407 i B -3663 B \tan \left(f x +e \right)-4243 A \right)}{45045 f \,c^{8} \left(\tan \left(f x +e \right)+i\right)^{9}}"," ",0,"-1/45045/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c^8*(1+tan(f*x+e)^2)*(22*I*B*tan(f*x+e)^6+72*I*A*tan(f*x+e)^5+8*A*tan(f*x+e)^6-825*I*B*tan(f*x+e)^4-198*B*tan(f*x+e)^5-780*I*A*tan(f*x+e)^3-300*A*tan(f*x+e)^4-7260*I*B*tan(f*x+e)^2+2145*B*tan(f*x+e)^3-6858*I*A*tan(f*x+e)+1455*A*tan(f*x+e)^2-407*I*B-3663*B*tan(f*x+e)-4243*A)/(tan(f*x+e)+I)^9","A"
829,1,230,260,0.438000," ","int((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(17/2),x)","\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, a^{3} \left(1+\tan^{2}\left(f x +e \right)\right) \left(109881 i B \left(\tan^{2}\left(f x +e \right)\right)+11175 i A \left(\tan^{3}\left(f x +e \right)\right)-96 B \left(\tan^{7}\left(f x +e \right)\right)+40 i A \left(\tan^{7}\left(f x +e \right)\right)-400 A \left(\tan^{6}\left(f x +e \right)\right)-960 i B \left(\tan^{6}\left(f x +e \right)\right)+4464 B \left(\tan^{5}\left(f x +e \right)\right)+103165 i A \tan \left(f x +e \right)+5400 A \left(\tan^{4}\left(f x +e \right)\right)+12960 i B \left(\tan^{4}\left(f x +e \right)\right)-26820 B \left(\tan^{3}\left(f x +e \right)\right)-1860 i A \left(\tan^{5}\left(f x +e \right)\right)-18030 A \left(\tan^{2}\left(f x +e \right)\right)+5871 i B +58710 B \tan \left(f x +e \right)+66260 A \right)}{765765 f \,c^{9} \left(\tan \left(f x +e \right)+i\right)^{10}}"," ",0,"1/765765*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c^9*(1+tan(f*x+e)^2)*(109881*I*B*tan(f*x+e)^2+11175*I*A*tan(f*x+e)^3-96*B*tan(f*x+e)^7+40*I*A*tan(f*x+e)^7-400*A*tan(f*x+e)^6-960*I*B*tan(f*x+e)^6+4464*B*tan(f*x+e)^5+103165*I*A*tan(f*x+e)+5400*A*tan(f*x+e)^4+12960*I*B*tan(f*x+e)^4-26820*B*tan(f*x+e)^3-1860*I*A*tan(f*x+e)^5-18030*A*tan(f*x+e)^2+5871*I*B+58710*B*tan(f*x+e)+66260*A)/(tan(f*x+e)+I)^10","A"
830,1,566,188,0.609000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(1/2),x)","\frac{i \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, c^{2} \left(6 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +18 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +4 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{2}\left(f x +e \right)\right)-9 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)-6 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -12 i A \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)+12 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +2 A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-14 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+9 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +19 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-10 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{2 f a \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(-\tan \left(f x +e \right)+i\right)^{2} \sqrt{c a}}"," ",0,"1/2*I/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^2/a*(6*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+18*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+4*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^2-9*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-6*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-12*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)+12*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+2*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-14*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+9*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+19*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-10*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(-tan(f*x+e)+I)^2/(c*a)^(1/2)","B"
831,1,499,140,0.544000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(1/2),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, c \left(-2 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +2 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +2 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +4 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-4 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-2 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +2 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+3 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{f a \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(-\tan \left(f x +e \right)+i\right)^{2} \sqrt{c a}}"," ",0,"1/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c/a*(-2*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+2*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+2*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+4*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-4*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-2*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+2*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+3*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(-tan(f*x+e)+I)^2/(c*a)^(1/2)","B"
832,1,323,89,0.474000," ","int((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2),x)","-\frac{i \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(-2 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +i A \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)-B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{f a \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(-\tan \left(f x +e \right)+i\right)^{2} \sqrt{c a}}"," ",0,"-I/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a*(-2*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(-tan(f*x+e)+I)^2/(c*a)^(1/2)","B"
833,1,99,79,0.424000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(1/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(A \left(\tan^{3}\left(f x +e \right)\right)-B \left(\tan^{2}\left(f x +e \right)\right)+A \tan \left(f x +e \right)-B \right)}{f c a \left(\tan \left(f x +e \right)+i\right)^{2} \left(-\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"1/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c/a*(A*tan(f*x+e)^3-B*tan(f*x+e)^2+A*tan(f*x+e)-B)/(tan(f*x+e)+I)^2/(-tan(f*x+e)+I)^2","A"
834,1,151,132,0.418000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(2 i A \left(\tan^{4}\left(f x +e \right)\right)-i B \left(\tan^{3}\left(f x +e \right)\right)-B \left(\tan^{4}\left(f x +e \right)\right)+3 i A \left(\tan^{2}\left(f x +e \right)\right)-2 A \left(\tan^{3}\left(f x +e \right)\right)-i B \tan \left(f x +e \right)+i A -2 A \tan \left(f x +e \right)+B \right)}{3 f \,c^{2} a \left(\tan \left(f x +e \right)+i\right)^{3} \left(-\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"-1/3*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^2/a*(2*I*A*tan(f*x+e)^4-I*B*tan(f*x+e)^3-B*tan(f*x+e)^4+3*I*A*tan(f*x+e)^2-2*A*tan(f*x+e)^3-I*B*tan(f*x+e)+I*A-2*A*tan(f*x+e)+B)/(tan(f*x+e)+I)^3/(-tan(f*x+e)+I)^2","A"
835,1,184,179,0.386000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(4 i B \left(\tan^{5}\left(f x +e \right)\right)+12 i A \left(\tan^{4}\left(f x +e \right)\right)+6 A \left(\tan^{5}\left(f x +e \right)\right)+2 i B \left(\tan^{3}\left(f x +e \right)\right)-8 B \left(\tan^{4}\left(f x +e \right)\right)+18 i A \left(\tan^{2}\left(f x +e \right)\right)+3 A \left(\tan^{3}\left(f x +e \right)\right)-2 i B \tan \left(f x +e \right)-7 B \left(\tan^{2}\left(f x +e \right)\right)+6 i A -3 A \tan \left(f x +e \right)+B \right)}{15 f \,c^{3} a \left(\tan \left(f x +e \right)+i\right)^{4} \left(-\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"1/15/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^3/a*(4*I*B*tan(f*x+e)^5+12*I*A*tan(f*x+e)^4+6*A*tan(f*x+e)^5+2*I*B*tan(f*x+e)^3-8*B*tan(f*x+e)^4+18*I*A*tan(f*x+e)^2+3*A*tan(f*x+e)^3-2*I*B*tan(f*x+e)-7*B*tan(f*x+e)^2+6*I*A-3*A*tan(f*x+e)+B)/(tan(f*x+e)+I)^4/(-tan(f*x+e)+I)^2","A"
836,1,733,236,0.516000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^(3/2),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, c^{3} \left(-75 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +6 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)+185 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{2}\left(f x +e \right)\right)+225 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c -30 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +3 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{4}\left(f x +e \right)\right)-30 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -225 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -21 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)-114 i A \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)+90 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +90 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +74 A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-118 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+75 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +279 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-46 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{6 f \,a^{2} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(-\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"1/6/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^3/a^2*(-75*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+6*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3+185*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2+225*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c-30*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+3*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^4-30*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-225*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-21*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-114*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+90*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+90*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+74*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-118*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+75*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+279*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-46*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)/(-tan(f*x+e)+I)^3","B"
837,1,669,189,0.492000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(3/2),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, c^{2} \left(-12 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +9 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -3 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +36 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +29 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{2}\left(f x +e \right)\right)-36 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c -3 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{3}\left(f x +e \right)\right)-3 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -12 i A \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)+9 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +8 A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-19 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+12 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +45 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-4 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{3 f \,a^{2} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(-\tan \left(f x +e \right)+i\right)^{3} \sqrt{c a}}"," ",0,"1/3/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^2/a^2*(-12*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+9*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-3*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+36*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+29*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^2-36*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c-3*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-3*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-12*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)+9*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+8*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-19*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+12*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+45*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-4*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(-tan(f*x+e)+I)^3/(c*a)^(1/2)","B"
838,1,408,128,0.431000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, c \left(-3 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +9 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +7 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{2}\left(f x +e \right)\right)-9 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-5 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+3 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c +12 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{3 f \,a^{2} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(-\tan \left(f x +e \right)+i\right)^{3} \sqrt{c a}}"," ",0,"1/3/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c/a^2*(-3*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+9*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+7*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-9*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-5*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c+12*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(-tan(f*x+e)+I)^3/(c*a)^(1/2)","B"
839,1,103,86,0.527000," ","int((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(2 i B \left(\tan^{2}\left(f x +e \right)\right)+3 i A \tan \left(f x +e \right)-A \left(\tan^{2}\left(f x +e \right)\right)-i B +3 B \tan \left(f x +e \right)+2 A \right)}{3 f \,a^{2} \left(-\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"1/3/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a^2*(2*I*B*tan(f*x+e)^2+3*I*A*tan(f*x+e)-A*tan(f*x+e)^2-I*B+3*B*tan(f*x+e)+2*A)/(-tan(f*x+e)+I)^3","A"
840,1,152,128,0.421000," ","int((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x)","\frac{i \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(2 i A \left(\tan^{4}\left(f x +e \right)\right)-i B \left(\tan^{3}\left(f x +e \right)\right)+B \left(\tan^{4}\left(f x +e \right)\right)+3 i A \left(\tan^{2}\left(f x +e \right)\right)+2 A \left(\tan^{3}\left(f x +e \right)\right)-i B \tan \left(f x +e \right)+i A +2 A \tan \left(f x +e \right)-B \right)}{3 f c \,a^{2} \left(\tan \left(f x +e \right)+i\right)^{2} \left(-\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"1/3*I/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/c/a^2*(2*I*A*tan(f*x+e)^4-I*B*tan(f*x+e)^3+B*tan(f*x+e)^4+3*I*A*tan(f*x+e)^2+2*A*tan(f*x+e)^3-I*B*tan(f*x+e)+I*A+2*A*tan(f*x+e)-B)/(tan(f*x+e)+I)^2/(-tan(f*x+e)+I)^3","A"
841,1,113,126,0.332000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(2 A \left(\tan^{5}\left(f x +e \right)\right)+5 A \left(\tan^{3}\left(f x +e \right)\right)-B \left(\tan^{2}\left(f x +e \right)\right)+3 A \tan \left(f x +e \right)-B \right)}{3 f \,c^{2} a^{2} \left(\tan \left(f x +e \right)+i\right)^{3} \left(-\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"-1/3/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^2/a^2*(2*A*tan(f*x+e)^5+5*A*tan(f*x+e)^3-B*tan(f*x+e)^2+3*A*tan(f*x+e)-B)/(tan(f*x+e)+I)^3/(-tan(f*x+e)+I)^3","A"
842,1,199,224,0.410000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(8 i A \left(\tan^{6}\left(f x +e \right)\right)-2 i B \left(\tan^{5}\left(f x +e \right)\right)-2 B \left(\tan^{6}\left(f x +e \right)\right)+20 i A \left(\tan^{4}\left(f x +e \right)\right)-8 A \left(\tan^{5}\left(f x +e \right)\right)-5 i B \left(\tan^{3}\left(f x +e \right)\right)-5 B \left(\tan^{4}\left(f x +e \right)\right)+15 i A \left(\tan^{2}\left(f x +e \right)\right)-20 A \left(\tan^{3}\left(f x +e \right)\right)-3 i B \tan \left(f x +e \right)+3 i A -12 A \tan \left(f x +e \right)+3 B \right)}{15 f \,c^{3} a^{2} \left(\tan \left(f x +e \right)+i\right)^{4} \left(-\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"1/15*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^3/a^2*(8*I*A*tan(f*x+e)^6-2*I*B*tan(f*x+e)^5-2*B*tan(f*x+e)^6+20*I*A*tan(f*x+e)^4-8*A*tan(f*x+e)^5-5*I*B*tan(f*x+e)^3-5*B*tan(f*x+e)^4+15*I*A*tan(f*x+e)^2-20*A*tan(f*x+e)^3-3*I*B*tan(f*x+e)+3*I*A-12*A*tan(f*x+e)+3*B)/(tan(f*x+e)+I)^4/(-tan(f*x+e)+I)^3","A"
843,1,899,283,0.533000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^(5/2),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, c^{4} \left(-840 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +840 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +2014 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-735 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -210 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{4}\left(f x +e \right)\right) a c -1316 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-3881 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-2940 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c -150 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-735 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{4}\left(f x +e \right)\right) a c +4410 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +1260 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +584 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+30 i A \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan^{4}\left(f x +e \right)\right)+334 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+2940 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +4576 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+15 i B \left(\tan^{5}\left(f x +e \right)\right) \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}-210 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -1096 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-1154 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{30 f \,a^{3} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(-\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"1/30/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^4/a^3*(-840*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+840*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+2014*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^3-735*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-210*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^4*a*c-1316*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^2-3881*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-2940*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c-150*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-735*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^4*a*c+4410*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+1260*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+584*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+30*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^4+334*I*A*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)+2940*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+4576*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+15*I*B*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^5-210*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-1096*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-1154*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)/(-tan(f*x+e)+I)^4","B"
844,1,835,235,0.433000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^(5/2),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, c^{3} \left(-60 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +60 i A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c -15 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{4}\left(f x +e \right)\right) a c +246 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-90 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -360 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c -15 B \left(\tan^{4}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-94 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-474 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+90 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +46 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-90 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{4}\left(f x +e \right)\right) a c +540 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +360 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +564 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+26 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-15 A \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -74 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-141 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{15 f \,a^{3} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(-\tan \left(f x +e \right)+i\right)^{4} \sqrt{c a}}"," ",0,"1/15/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^3/a^3*(-60*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+60*I*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c-15*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^4*a*c+246*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-90*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-360*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c-15*B*tan(f*x+e)^4*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-94*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-474*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+90*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+46*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-90*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^4*a*c+540*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+360*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+564*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+26*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-15*A*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-74*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-141*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(-tan(f*x+e)+I)^4/(c*a)^(1/2)","B"
845,1,557,168,0.500000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x)","\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, c^{2} \left(-15 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{4}\left(f x +e \right)\right) a c +90 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a c +43 i B \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-60 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \left(\tan^{3}\left(f x +e \right)\right) a c +3 i A \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+3 A \left(\tan^{3}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-15 i B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) a c -77 i B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+60 B \ln \left(\frac{c a \tan \left(f x +e \right)+\sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}{\sqrt{c a}}\right) \tan \left(f x +e \right) a c +97 B \left(\tan^{2}\left(f x +e \right)\right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+3 i A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+3 A \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-23 B \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{15 f \,a^{3} \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(-\tan \left(f x +e \right)+i\right)^{4} \sqrt{c a}}"," ",0,"1/15/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^2/a^3*(-15*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^4*a*c+90*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^2*a*c+43*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3-60*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)^3*a*c+3*I*A*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*A*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-15*I*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*a*c-77*I*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+60*B*ln((c*a*tan(f*x+e)+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a)^(1/2))*tan(f*x+e)*a*c+97*B*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*I*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*A*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-23*B*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(c*a*(1+tan(f*x+e)^2))^(1/2)/(-tan(f*x+e)+I)^4/(c*a)^(1/2)","B"
846,1,92,86,0.499000," ","int((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x)","\frac{i \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, c \left(1+\tan^{2}\left(f x +e \right)\right) \left(i A \tan \left(f x +e \right)-i B +4 B \tan \left(f x +e \right)+4 A \right)}{15 f \,a^{3} \left(-\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"1/15*I/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c/a^3*(1+tan(f*x+e)^2)*(I*A*tan(f*x+e)-I*B+4*B*tan(f*x+e)+4*A)/(-tan(f*x+e)+I)^4","A"
847,1,127,130,0.430000," ","int((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(5/2),x)","-\frac{i \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(2 i A \left(\tan^{3}\left(f x +e \right)\right)-12 i B \left(\tan^{2}\left(f x +e \right)\right)+3 B \left(\tan^{3}\left(f x +e \right)\right)-13 i A \tan \left(f x +e \right)+8 A \left(\tan^{2}\left(f x +e \right)\right)+3 i B -12 B \tan \left(f x +e \right)-7 A \right)}{15 f \,a^{3} \left(-\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"-1/15*I/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a^3*(2*I*A*tan(f*x+e)^3-12*I*B*tan(f*x+e)^2+3*B*tan(f*x+e)^3-13*I*A*tan(f*x+e)+8*A*tan(f*x+e)^2+3*I*B-12*B*tan(f*x+e)-7*A)/(-tan(f*x+e)+I)^4","A"
848,1,186,179,0.459000," ","int((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x)","-\frac{\sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(4 i B \left(\tan^{5}\left(f x +e \right)\right)+12 i A \left(\tan^{4}\left(f x +e \right)\right)-6 A \left(\tan^{5}\left(f x +e \right)\right)+2 i B \left(\tan^{3}\left(f x +e \right)\right)+8 B \left(\tan^{4}\left(f x +e \right)\right)+18 i A \left(\tan^{2}\left(f x +e \right)\right)-3 A \left(\tan^{3}\left(f x +e \right)\right)-2 i B \tan \left(f x +e \right)+7 B \left(\tan^{2}\left(f x +e \right)\right)+6 i A +3 A \tan \left(f x +e \right)-B \right)}{15 f c \,a^{3} \left(\tan \left(f x +e \right)+i\right)^{2} \left(-\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"-1/15/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/c/a^3*(4*I*B*tan(f*x+e)^5+12*I*A*tan(f*x+e)^4-6*A*tan(f*x+e)^5+2*I*B*tan(f*x+e)^3+8*B*tan(f*x+e)^4+18*I*A*tan(f*x+e)^2-3*A*tan(f*x+e)^3-2*I*B*tan(f*x+e)+7*B*tan(f*x+e)^2+6*I*A+3*A*tan(f*x+e)-B)/(tan(f*x+e)+I)^2/(-tan(f*x+e)+I)^4","A"
849,1,199,182,0.365000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{i \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(8 i A \left(\tan^{6}\left(f x +e \right)\right)-2 i B \left(\tan^{5}\left(f x +e \right)\right)+2 B \left(\tan^{6}\left(f x +e \right)\right)+20 i A \left(\tan^{4}\left(f x +e \right)\right)+8 A \left(\tan^{5}\left(f x +e \right)\right)-5 i B \left(\tan^{3}\left(f x +e \right)\right)+5 B \left(\tan^{4}\left(f x +e \right)\right)+15 i A \left(\tan^{2}\left(f x +e \right)\right)+20 A \left(\tan^{3}\left(f x +e \right)\right)-3 i B \tan \left(f x +e \right)+3 i A +12 A \tan \left(f x +e \right)-3 B \right)}{15 f \,c^{2} a^{3} \left(\tan \left(f x +e \right)+i\right)^{3} \left(-\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"-1/15*I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^2/a^3*(8*I*A*tan(f*x+e)^6-2*I*B*tan(f*x+e)^5+2*B*tan(f*x+e)^6+20*I*A*tan(f*x+e)^4+8*A*tan(f*x+e)^5-5*I*B*tan(f*x+e)^3+5*B*tan(f*x+e)^4+15*I*A*tan(f*x+e)^2+20*A*tan(f*x+e)^3-3*I*B*tan(f*x+e)+3*I*A+12*A*tan(f*x+e)-3*B)/(tan(f*x+e)+I)^3/(-tan(f*x+e)+I)^4","A"
850,1,124,172,0.345000," ","int((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{-c \left(-1+i \tan \left(f x +e \right)\right)}\, \left(8 A \left(\tan^{7}\left(f x +e \right)\right)+28 A \left(\tan^{5}\left(f x +e \right)\right)+35 A \left(\tan^{3}\left(f x +e \right)\right)-3 B \left(\tan^{2}\left(f x +e \right)\right)+15 A \tan \left(f x +e \right)-3 B \right)}{15 f \,c^{3} a^{3} \left(\tan \left(f x +e \right)+i\right)^{4} \left(-\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"1/15/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^3/a^3*(8*A*tan(f*x+e)^7+28*A*tan(f*x+e)^5+35*A*tan(f*x+e)^3-3*B*tan(f*x+e)^2+15*A*tan(f*x+e)-3*B)/(tan(f*x+e)+I)^4/(-tan(f*x+e)+I)^4","A"
851,0,0,138,6.349000," ","int((a+I*a*tan(f*x+e))^m*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \left(A +B \tan \left(f x +e \right)\right) \left(c -i c \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x)","F"
852,0,0,136,12.175000," ","int((a+I*a*tan(f*x+e))^(1+m)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(-1-m),x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{1+m} \left(A +B \tan \left(f x +e \right)\right) \left(c -i c \tan \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^(1+m)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(-1-m),x)","F"
853,0,0,31,4.719000," ","int((c-I*c*tan(f*x+e))^n*(-I*(2+n)+(-2+n)*tan(f*x+e))/(tan(f*x+e)-I)^2,x)","\int \frac{\left(c -i c \tan \left(f x +e \right)\right)^{n} \left(-i \left(2+n \right)+\left(-2+n \right) \tan \left(f x +e \right)\right)}{\left(\tan \left(f x +e \right)-i\right)^{2}}\, dx"," ",0,"int((c-I*c*tan(f*x+e))^n*(-I*(2+n)+(-2+n)*tan(f*x+e))/(tan(f*x+e)-I)^2,x)","F"
854,1,338,90,0.261000," ","int((A+B*tan(f*x+e))*(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x)","\frac{A \ln \left(\tan \left(f x +e \right)+i\right) d}{8 f \,a^{2}}+\frac{B \ln \left(\tan \left(f x +e \right)+i\right) c}{8 f \,a^{2}}-\frac{i B \ln \left(\tan \left(f x +e \right)+i\right) d}{8 f \,a^{2}}-\frac{i A c}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i A d}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{i \ln \left(\tan \left(f x +e \right)-i\right) B d}{8 f \,a^{2}}+\frac{c A}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{3 B d}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{A d}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{B c}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i B c}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{i A \ln \left(\tan \left(f x +e \right)+i\right) c}{8 f \,a^{2}}+\frac{i B d}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) A c}{8 f \,a^{2}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) A d}{8 f \,a^{2}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) B c}{8 f \,a^{2}}"," ",0,"1/8/f/a^2*A*ln(tan(f*x+e)+I)*d+1/8/f/a^2*B*ln(tan(f*x+e)+I)*c-1/8*I/f/a^2*B*ln(tan(f*x+e)+I)*d-1/4*I/f/a^2/(tan(f*x+e)-I)^2*A*c-1/4*I/f/a^2/(tan(f*x+e)-I)*A*d+1/8*I/f/a^2*ln(tan(f*x+e)-I)*B*d+1/4/f/a^2/(tan(f*x+e)-I)*c*A+3/4/f/a^2/(tan(f*x+e)-I)*B*d+1/4/f/a^2/(tan(f*x+e)-I)^2*A*d+1/4/f/a^2/(tan(f*x+e)-I)^2*B*c-1/4*I/f/a^2/(tan(f*x+e)-I)*B*c+1/8*I/f/a^2*A*ln(tan(f*x+e)+I)*c+1/4*I/f/a^2/(tan(f*x+e)-I)^2*B*d-1/8*I/f/a^2*ln(tan(f*x+e)-I)*A*c-1/8/f/a^2*ln(tan(f*x+e)-I)*A*d-1/8/f/a^2*ln(tan(f*x+e)-I)*B*c","B"
855,1,131,119,0.266000," ","int((A+B*tan(f*x+e))*(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2),x)","-\frac{2 i \left(-\frac{\left(\frac{1}{4} i A d +\frac{1}{4} i B c -\frac{1}{4} c A +\frac{1}{4} B d \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{2 \sqrt{a}}-\frac{-\frac{1}{4} i A d -\frac{1}{4} i B c +\frac{1}{4} c A +\frac{3}{4} B d}{\sqrt{a +i a \tan \left(f x +e \right)}}-\frac{a \left(i A d +i B c +c A -B d \right)}{6 \left(a +i a \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\right)}{f a}"," ",0,"-2*I/f/a*(-1/2*(1/4*I*A*d+1/4*I*B*c-1/4*c*A+1/4*B*d)*2^(1/2)/a^(1/2)*arctanh(1/2*(a+I*a*tan(f*x+e))^(1/2)*2^(1/2)/a^(1/2))-(-1/4*I*A*d-1/4*I*B*c+1/4*c*A+3/4*B*d)/(a+I*a*tan(f*x+e))^(1/2)-1/6*a*(-B*d+I*A*d+I*B*c+c*A)/(a+I*a*tan(f*x+e))^(3/2))","A"