1,1,104,90,0.018000," ","int(tan(d*x+c)^5*(a+I*a*tan(d*x+c)),x)","\frac{i a \tan \left(d x +c \right)}{d}+\frac{i a \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{i a \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{i a \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"I*a*tan(d*x+c)/d+1/5*I*a*tan(d*x+c)^5/d+1/4*a*tan(d*x+c)^4/d-1/3*I*a*tan(d*x+c)^3/d-1/2*a*tan(d*x+c)^2/d+1/2/d*a*ln(1+tan(d*x+c)^2)-I/d*a*arctan(tan(d*x+c))","A"
2,1,88,74,0.019000," ","int(tan(d*x+c)^4*(a+I*a*tan(d*x+c)),x)","-\frac{a \tan \left(d x +c \right)}{d}+\frac{i a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{i a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{i a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-a*tan(d*x+c)/d+1/4*I*a*tan(d*x+c)^4/d+1/3*a*tan(d*x+c)^3/d-1/2*I*a*tan(d*x+c)^2/d+1/2*I/d*a*ln(1+tan(d*x+c)^2)+1/d*a*arctan(tan(d*x+c))","A"
3,1,75,60,0.019000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c)),x)","-\frac{i a \tan \left(d x +c \right)}{d}+\frac{i a \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{i a \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-I*a*tan(d*x+c)/d+1/3*I*a*tan(d*x+c)^3/d+1/2*a*tan(d*x+c)^2/d-1/2/d*a*ln(1+tan(d*x+c)^2)+I/d*a*arctan(tan(d*x+c))","A"
4,1,59,45,0.020000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c)),x)","\frac{i a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \tan \left(d x +c \right)}{d}-\frac{i a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2*I*a*tan(d*x+c)^2/d+a*tan(d*x+c)/d-1/2*I/d*a*ln(1+tan(d*x+c)^2)-1/d*a*arctan(tan(d*x+c))","A"
5,1,46,32,0.018000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c)),x)","\frac{i a \tan \left(d x +c \right)}{d}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{i a \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"I*a*tan(d*x+c)/d+1/2/d*a*ln(1+tan(d*x+c)^2)-I/d*a*arctan(tan(d*x+c))","A"
6,1,23,18,0.015000," ","int(a+I*a*tan(d*x+c),x)","a x +\frac{i a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"a*x+1/2*I/d*a*ln(1+tan(d*x+c)^2)","A"
7,1,27,18,0.297000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c)),x)","i a x +\frac{i a c}{d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"I*a*x+I/d*a*c+a*ln(sin(d*x+c))/d","A"
8,1,39,31,0.253000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c)),x)","\frac{i a \ln \left(\sin \left(d x +c \right)\right)}{d}-a x -\frac{a \cot \left(d x +c \right)}{d}-\frac{c a}{d}"," ",0,"I*a*ln(sin(d*x+c))/d-a*x-a*cot(d*x+c)/d-1/d*c*a","A"
9,1,55,46,0.383000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c)),x)","-i a x -\frac{i a \cot \left(d x +c \right)}{d}-\frac{i a c}{d}-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-I*a*x-I*a*cot(d*x+c)/d-I/d*a*c-1/2*a*cot(d*x+c)^2/d-a*ln(sin(d*x+c))/d","A"
10,1,65,58,0.302000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c)),x)","-\frac{i a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{i a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cot \left(d x +c \right)}{d}+a x +\frac{c a}{d}"," ",0,"-1/2*I*a*cot(d*x+c)^2/d-I*a*ln(sin(d*x+c))/d-1/3*a*cot(d*x+c)^3/d+a*cot(d*x+c)/d+a*x+1/d*c*a","A"
11,1,83,74,0.313000," ","int(cot(d*x+c)^5*(a+I*a*tan(d*x+c)),x)","-\frac{i a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{i a \cot \left(d x +c \right)}{d}+i a x +\frac{i a c}{d}-\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/3*I*a*cot(d*x+c)^3/d+I*a*cot(d*x+c)/d+I*a*x+I/d*a*c-1/4*a*cot(d*x+c)^4/d+1/2*a*cot(d*x+c)^2/d+a*ln(sin(d*x+c))/d","A"
12,1,97,89,0.335000," ","int(cot(d*x+c)^6*(a+I*a*tan(d*x+c)),x)","-\frac{i a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{i a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{i a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \cot \left(d x +c \right)}{d}-a x -\frac{c a}{d}"," ",0,"-1/4*I*a*cot(d*x+c)^4/d+1/2*I*a*cot(d*x+c)^2/d+I*a*ln(sin(d*x+c))/d-1/5*a*cot(d*x+c)^5/d+1/3*a*cot(d*x+c)^3/d-a*cot(d*x+c)/d-a*x-1/d*c*a","A"
13,1,117,103,0.016000," ","int(tan(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x)","-\frac{2 a^{2} \tan \left(d x +c \right)}{d}-\frac{a^{2} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{i a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{2 d}+\frac{2 a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{i a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{i a^{2} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{2} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-2*a^2*tan(d*x+c)/d-1/5*a^2*tan(d*x+c)^5/d+1/2*I*a^2*tan(d*x+c)^4/d+2/3*a^2*tan(d*x+c)^3/d-I*a^2*tan(d*x+c)^2/d+I/d*a^2*ln(1+tan(d*x+c)^2)+2/d*a^2*arctan(tan(d*x+c))","A"
14,1,100,86,0.020000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x)","-\frac{2 i a^{2} \tan \left(d x +c \right)}{d}-\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{2 i a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{a^{2} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{2 i a^{2} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-2*I*a^2*tan(d*x+c)/d-1/4*a^2*tan(d*x+c)^4/d+2/3*I*a^2*tan(d*x+c)^3/d+a^2*tan(d*x+c)^2/d-1/d*a^2*ln(1+tan(d*x+c)^2)+2*I/d*a^2*arctan(tan(d*x+c))","A"
15,1,84,59,0.019000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x)","\frac{2 a^{2} \tan \left(d x +c \right)}{d}-\frac{a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{i a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{i a^{2} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"2*a^2*tan(d*x+c)/d-1/3*a^2*tan(d*x+c)^3/d+I/d*a^2*tan(d*x+c)^2-I/d*a^2*ln(1+tan(d*x+c)^2)-2/d*a^2*arctan(tan(d*x+c))","A"
16,1,67,57,0.019000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^2,x)","\frac{2 i a^{2} \tan \left(d x +c \right)}{d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 i a^{2} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"2*I/d*a^2*tan(d*x+c)-1/2*a^2*tan(d*x+c)^2/d+1/d*a^2*ln(1+tan(d*x+c)^2)-2*I/d*a^2*arctan(tan(d*x+c))","A"
17,1,51,37,0.018000," ","int((a+I*a*tan(d*x+c))^2,x)","\frac{i a^{2} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{2} \arctan \left(\tan \left(d x +c \right)\right)}{d}-\frac{a^{2} \tan \left(d x +c \right)}{d}"," ",0,"I/d*a^2*ln(1+tan(d*x+c)^2)+2/d*a^2*arctan(tan(d*x+c))-a^2*tan(d*x+c)/d","A"
18,1,47,36,0.363000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^2,x)","2 i a^{2} x +\frac{2 i a^{2} c}{d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"2*I*a^2*x+2*I/d*a^2*c+a^2*ln(sin(d*x+c))/d+a^2*ln(cos(d*x+c))/d","A"
19,1,47,37,0.268000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x)","\frac{2 i a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-2 a^{2} x -\frac{a^{2} \cot \left(d x +c \right)}{d}-\frac{2 a^{2} c}{d}"," ",0,"2*I*a^2*ln(sin(d*x+c))/d-2*a^2*x-a^2*cot(d*x+c)/d-2/d*a^2*c","A"
20,1,65,54,0.369000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x)","-\frac{2 a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-2 i a^{2} x -\frac{2 i a^{2} \cot \left(d x +c \right)}{d}-\frac{2 i a^{2} c}{d}-\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-2*a^2*ln(sin(d*x+c))/d-2*I*a^2*x-2*I*a^2*cot(d*x+c)/d-2*I/d*a^2*c-1/2*a^2*cot(d*x+c)^2/d","A"
21,1,80,70,0.320000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x)","2 a^{2} x +\frac{2 a^{2} \cot \left(d x +c \right)}{d}+\frac{2 a^{2} c}{d}-\frac{i a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{2 i a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"2*a^2*x+2*a^2*cot(d*x+c)/d+2/d*a^2*c-I*a^2*cot(d*x+c)^2/d-2*I*a^2*ln(sin(d*x+c))/d-1/3*a^2*cot(d*x+c)^3/d","A"
22,1,97,86,0.332000," ","int(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x)","\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 i a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 i a^{2} \cot \left(d x +c \right)}{d}+2 i a^{2} x +\frac{2 i a^{2} c}{d}-\frac{a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}"," ",0,"a^2*cot(d*x+c)^2/d+2*a^2*ln(sin(d*x+c))/d-2/3*I*a^2*cot(d*x+c)^3/d+2*I*a^2*cot(d*x+c)/d+2*I*a^2*x+2*I/d*a^2*c-1/4*a^2*cot(d*x+c)^4/d","A"
23,1,113,103,0.355000," ","int(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x)","\frac{2 a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{2} \cot \left(d x +c \right)}{d}-2 a^{2} x -\frac{2 a^{2} c}{d}-\frac{i a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{2 d}+\frac{i a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{2 i a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}"," ",0,"2/3*a^2*cot(d*x+c)^3/d-2*a^2*cot(d*x+c)/d-2*a^2*x-2/d*a^2*c-1/2*I*a^2*cot(d*x+c)^4/d+I*a^2*cot(d*x+c)^2/d+2*I*a^2*ln(sin(d*x+c))/d-1/5*a^2*cot(d*x+c)^5/d","A"
24,1,118,116,0.020000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x)","-\frac{4 i a^{3} \tan \left(d x +c \right)}{d}-\frac{i a^{3} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{3 a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{4 i a^{3} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 a^{3} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 i a^{3} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-4*I*a^3*tan(d*x+c)/d-1/5*I/d*a^3*tan(d*x+c)^5-3/4*a^3*tan(d*x+c)^4/d+4/3*I*a^3*tan(d*x+c)^3/d+2*a^3*tan(d*x+c)^2/d-2/d*a^3*ln(1+tan(d*x+c)^2)+4*I/d*a^3*arctan(tan(d*x+c))","A"
25,1,101,81,0.019000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x)","\frac{4 a^{3} \tan \left(d x +c \right)}{d}-\frac{i a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} \left(\tan^{3}\left(d x +c \right)\right)}{d}+\frac{2 i a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{4 a^{3} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"4*a^3*tan(d*x+c)/d-1/4*I/d*a^3*tan(d*x+c)^4-1/d*a^3*tan(d*x+c)^3+2*I/d*a^3*tan(d*x+c)^2-2*I/d*a^3*ln(1+tan(d*x+c)^2)-4/d*a^3*arctan(tan(d*x+c))","A"
26,1,85,77,0.020000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^3,x)","\frac{4 i a^{3} \tan \left(d x +c \right)}{d}-\frac{i a^{3} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{3 a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 a^{3} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{4 i a^{3} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"4*I/d*a^3*tan(d*x+c)-1/3*I/d*a^3*tan(d*x+c)^3-3/2*a^3*tan(d*x+c)^2/d+2/d*a^3*ln(1+tan(d*x+c)^2)-4*I/d*a^3*arctan(tan(d*x+c))","A"
27,1,68,58,0.020000," ","int((a+I*a*tan(d*x+c))^3,x)","-\frac{3 a^{3} \tan \left(d x +c \right)}{d}-\frac{i a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 a^{3} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-3*a^3*tan(d*x+c)/d-1/2*I/d*a^3*tan(d*x+c)^2+2*I/d*a^3*ln(1+tan(d*x+c)^2)+4/d*a^3*arctan(tan(d*x+c))","A"
28,1,63,59,0.331000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^3,x)","4 i a^{3} x -\frac{i a^{3} \tan \left(d x +c \right)}{d}+\frac{4 i a^{3} c}{d}+\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"4*I*a^3*x-I/d*tan(d*x+c)*a^3+4*I/d*a^3*c+a^3*ln(sin(d*x+c))/d+3*a^3*ln(cos(d*x+c))/d","A"
29,1,63,66,0.316000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x)","\frac{i a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 i a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-4 a^{3} x -\frac{a^{3} \cot \left(d x +c \right)}{d}-\frac{4 a^{3} c}{d}"," ",0,"I*a^3*ln(cos(d*x+c))/d+3*I*a^3*ln(sin(d*x+c))/d-4*a^3*x-a^3*cot(d*x+c)/d-4/d*a^3*c","A"
30,1,65,66,0.370000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x)","-4 i a^{3} x -\frac{4 i a^{3} c}{d}-\frac{4 a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 i \cot \left(d x +c \right) a^{3}}{d}-\frac{a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-4*I*a^3*x-4*I/d*a^3*c-4*a^3*ln(sin(d*x+c))/d-3*I/d*cot(d*x+c)*a^3-1/2*a^3*cot(d*x+c)^2/d","A"
31,1,80,93,0.325000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x)","-\frac{4 i a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+4 a^{3} x +\frac{4 a^{3} \cot \left(d x +c \right)}{d}+\frac{4 a^{3} c}{d}-\frac{3 i a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"-4*I*a^3*ln(sin(d*x+c))/d+4*a^3*x+4*a^3*cot(d*x+c)/d+4/d*a^3*c-3/2*I/d*a^3*cot(d*x+c)^2-1/3*a^3*cot(d*x+c)^3/d","A"
32,1,98,100,0.326000," ","int(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^3,x)","4 i a^{3} x +\frac{4 i \cot \left(d x +c \right) a^{3}}{d}+\frac{4 i a^{3} c}{d}+\frac{2 a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{4 a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{i a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}"," ",0,"4*I*a^3*x+4*I*a^3*cot(d*x+c)/d+4*I/d*a^3*c+2*a^3*cot(d*x+c)^2/d+4*a^3*ln(sin(d*x+c))/d-I/d*a^3*cot(d*x+c)^3-1/4/d*a^3*cot(d*x+c)^4","A"
33,1,113,116,0.352000," ","int(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x)","\frac{2 i a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{4 i a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-4 a^{3} x -\frac{4 a^{3} \cot \left(d x +c \right)}{d}-\frac{4 a^{3} c}{d}-\frac{3 i a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}"," ",0,"2*I*a^3*cot(d*x+c)^2/d+4*I*a^3*ln(sin(d*x+c))/d+4/3*a^3*cot(d*x+c)^3/d-4*a^3*x-4*a^3*cot(d*x+c)/d-4/d*a^3*c-3/4*I/d*a^3*cot(d*x+c)^4-1/5*a^3*cot(d*x+c)^5/d","A"
34,1,134,147,0.019000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x)","-\frac{8 i a^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}-\frac{4 i a^{4} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{7 a^{4} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{8 i a^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{4 a^{4} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{4 a^{4} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{8 i a^{4} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-8*I*a^4*tan(d*x+c)/d+1/6/d*a^4*tan(d*x+c)^6-4/5*I/d*a^4*tan(d*x+c)^5-7/4*a^4*tan(d*x+c)^4/d+8/3*I*a^4*tan(d*x+c)^3/d+4*a^4*tan(d*x+c)^2/d-4/d*a^4*ln(1+tan(d*x+c)^2)+8*I/d*a^4*arctan(tan(d*x+c))","A"
35,1,117,105,0.017000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x)","\frac{8 a^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{i a^{4} \left(\tan^{4}\left(d x +c \right)\right)}{d}-\frac{7 a^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{4 i a^{4} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{4 i a^{4} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{8 a^{4} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"8*a^4*tan(d*x+c)/d+1/5/d*a^4*tan(d*x+c)^5-I/d*a^4*tan(d*x+c)^4-7/3/d*a^4*tan(d*x+c)^3+4*I/d*a^4*tan(d*x+c)^2-4*I/d*a^4*ln(1+tan(d*x+c)^2)-8/d*a^4*arctan(tan(d*x+c))","A"
36,1,101,99,0.022000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^4,x)","\frac{8 i a^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{4 i a^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{7 a^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{4 a^{4} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{8 i a^{4} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"8*I/d*a^4*tan(d*x+c)+1/4*a^4*tan(d*x+c)^4/d-4/3*I/d*a^4*tan(d*x+c)^3-7/2*a^4*tan(d*x+c)^2/d+4/d*a^4*ln(1+tan(d*x+c)^2)-8*I/d*a^4*arctan(tan(d*x+c))","A"
37,1,84,82,0.018000," ","int((a+I*a*tan(d*x+c))^4,x)","-\frac{7 a^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 i a^{4} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 i a^{4} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{8 a^{4} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-7*a^4*tan(d*x+c)/d+1/3/d*a^4*tan(d*x+c)^3-2*I/d*a^4*tan(d*x+c)^2+4*I/d*a^4*ln(1+tan(d*x+c)^2)+8/d*a^4*arctan(tan(d*x+c))","A"
38,1,79,81,0.350000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^4,x)","\frac{a^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{7 a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}+8 i a^{4} x -\frac{4 i a^{4} \tan \left(d x +c \right)}{d}+\frac{8 i a^{4} c}{d}+\frac{a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^4*tan(d*x+c)^2/d+7*a^4*ln(cos(d*x+c))/d+8*I*a^4*x-4*I/d*tan(d*x+c)*a^4+8*I/d*a^4*c+a^4*ln(sin(d*x+c))/d","A"
39,1,76,68,0.308000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x)","\frac{4 i a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{4 i a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-8 a^{4} x -\frac{a^{4} \cot \left(d x +c \right)}{d}+\frac{a^{4} \tan \left(d x +c \right)}{d}-\frac{8 a^{4} c}{d}"," ",0,"4*I*a^4*ln(cos(d*x+c))/d+4*I*a^4*ln(sin(d*x+c))/d-8*a^4*x-a^4*cot(d*x+c)/d+a^4*tan(d*x+c)/d-8/d*a^4*c","A"
40,1,80,97,0.376000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x)","-\frac{a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}-8 i a^{4} x -\frac{8 i a^{4} c}{d}-\frac{7 a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 i \cot \left(d x +c \right) a^{4}}{d}-\frac{a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-a^4*ln(cos(d*x+c))/d-8*I*a^4*x-8*I/d*a^4*c-7*a^4*ln(sin(d*x+c))/d-4*I/d*cot(d*x+c)*a^4-1/2*a^4*cot(d*x+c)^2/d","A"
41,1,80,97,0.321000," ","int(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^4,x)","8 a^{4} x +\frac{8 a^{4} c}{d}-\frac{8 i a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{7 a^{4} \cot \left(d x +c \right)}{d}-\frac{2 i a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"8*a^4*x+8/d*a^4*c-8*I*a^4*ln(sin(d*x+c))/d+7*a^4*cot(d*x+c)/d-2*I/d*a^4*cot(d*x+c)^2-1/3*a^4*cot(d*x+c)^3/d","A"
42,1,98,124,0.325000," ","int(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^4,x)","\frac{8 a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}+8 i a^{4} x +\frac{8 i \cot \left(d x +c \right) a^{4}}{d}+\frac{8 i a^{4} c}{d}+\frac{7 a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{4 i a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}"," ",0,"8*a^4*ln(sin(d*x+c))/d+8*I*a^4*x+8*I/d*cot(d*x+c)*a^4+8*I/d*a^4*c+7/2*a^4*cot(d*x+c)^2/d-4/3*I/d*a^4*cot(d*x+c)^3-1/4*a^4*cot(d*x+c)^4/d","A"
43,1,113,131,0.357000," ","int(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^4,x)","-8 a^{4} x -\frac{8 a^{4} \cot \left(d x +c \right)}{d}-\frac{8 a^{4} c}{d}+\frac{4 i a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{8 i a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{7 a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{i a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{d}-\frac{a^{4} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}"," ",0,"-8*a^4*x-8*a^4*cot(d*x+c)/d-8/d*a^4*c+4*I*a^4*cot(d*x+c)^2/d+8*I*a^4*ln(sin(d*x+c))/d+7/3*a^4*cot(d*x+c)^3/d-I/d*a^4*cot(d*x+c)^4-1/5*a^4*cot(d*x+c)^5/d","A"
44,1,131,148,0.366000," ","int(cot(d*x+c)^7*(a+I*a*tan(d*x+c))^4,x)","-\frac{4 a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{8 a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{8 i \cot \left(d x +c \right) a^{4}}{d}-8 i a^{4} x +\frac{8 i a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{4 i a^{4} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{7 a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{8 i a^{4} c}{d}-\frac{a^{4} \left(\cot^{6}\left(d x +c \right)\right)}{6 d}"," ",0,"-4*a^4*cot(d*x+c)^2/d-8*a^4*ln(sin(d*x+c))/d-8*I*a^4*cot(d*x+c)/d-8*I*a^4*x+8/3*I*a^4*cot(d*x+c)^3/d-4/5*I/d*a^4*cot(d*x+c)^5+7/4*a^4*cot(d*x+c)^4/d-8*I/d*a^4*c-1/6/d*a^4*cot(d*x+c)^6","A"
45,1,123,114,0.150000," ","int(tan(d*x+c)^6/(a+I*a*tan(d*x+c)),x)","-\frac{2 \tan \left(d x +c \right)}{d a}-\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{4 d a}+\frac{\tan^{3}\left(d x +c \right)}{3 d a}+\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{d a}-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{11 i \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}-\frac{1}{2 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-2*tan(d*x+c)/d/a-1/4*I/d/a*tan(d*x+c)^4+1/3*tan(d*x+c)^3/d/a+I/d/a*tan(d*x+c)^2-1/4*I/d/a*ln(tan(d*x+c)+I)-11/4*I/d/a*ln(tan(d*x+c)-I)-1/2/d/a/(tan(d*x+c)-I)","A"
46,1,106,97,0.122000," ","int(tan(d*x+c)^5/(a+I*a*tan(d*x+c)),x)","\frac{2 i \tan \left(d x +c \right)}{d a}-\frac{i \left(\tan^{3}\left(d x +c \right)\right)}{3 d a}+\frac{\tan^{2}\left(d x +c \right)}{2 d a}+\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{i}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{9 \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}"," ",0,"2*I/d/a*tan(d*x+c)-1/3*I/d/a*tan(d*x+c)^3+1/2*tan(d*x+c)^2/d/a+1/4/d/a*ln(tan(d*x+c)+I)+1/2*I/d/a/(tan(d*x+c)-I)-9/4/d/a*ln(tan(d*x+c)-I)","A"
47,1,89,81,0.129000," ","int(tan(d*x+c)^4/(a+I*a*tan(d*x+c)),x)","\frac{\tan \left(d x +c \right)}{d a}-\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2 d a}+\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{7 i \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}+\frac{1}{2 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"tan(d*x+c)/d/a-1/2*I*tan(d*x+c)^2/d/a+1/4*I/d/a*ln(tan(d*x+c)+I)+7/4*I/d/a*ln(tan(d*x+c)-I)+1/2/d/a/(tan(d*x+c)-I)","A"
48,1,73,65,0.148000," ","int(tan(d*x+c)^3/(a+I*a*tan(d*x+c)),x)","-\frac{i \tan \left(d x +c \right)}{d a}-\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{i}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{5 \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}"," ",0,"-I/d/a*tan(d*x+c)-1/4/d/a*ln(tan(d*x+c)+I)-1/2*I/d/a/(tan(d*x+c)-I)+5/4/d/a*ln(tan(d*x+c)-I)","A"
49,1,59,43,0.120000," ","int(tan(d*x+c)^2/(a+I*a*tan(d*x+c)),x)","-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{3 i \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}-\frac{1}{2 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-1/4*I/d/a*ln(tan(d*x+c)+I)-3/4*I/d/a*ln(tan(d*x+c)-I)-1/2/d/a/(tan(d*x+c)-I)","A"
50,1,58,27,0.122000," ","int(tan(d*x+c)/(a+I*a*tan(d*x+c)),x)","\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{i}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{\ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}"," ",0,"1/4/d/a*ln(tan(d*x+c)+I)+1/2*I/d/a/(tan(d*x+c)-I)-1/4/d/a*ln(tan(d*x+c)-I)","B"
51,1,59,27,0.116000," ","int(1/(a+I*a*tan(d*x+c)),x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}+\frac{1}{2 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/4*I/d/a*ln(tan(d*x+c)+I)-1/4*I/d/a*ln(tan(d*x+c)-I)+1/2/d/a/(tan(d*x+c)-I)","B"
52,1,72,41,0.473000," ","int(cot(d*x+c)/(a+I*a*tan(d*x+c)),x)","-\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}+\frac{\ln \left(\tan \left(d x +c \right)\right)}{d a}-\frac{i}{2 d a \left(\tan \left(d x +c \right)-i\right)}-\frac{3 \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}"," ",0,"-1/4/d/a*ln(tan(d*x+c)+I)+1/d/a*ln(tan(d*x+c))-1/2*I/d/a/(tan(d*x+c)-I)-3/4/d/a*ln(tan(d*x+c)-I)","A"
53,1,91,62,0.397000," ","int(cot(d*x+c)^2/(a+I*a*tan(d*x+c)),x)","-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{1}{d a \tan \left(d x +c \right)}-\frac{i \ln \left(\tan \left(d x +c \right)\right)}{a d}+\frac{5 i \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}-\frac{1}{2 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-1/4*I/d/a*ln(tan(d*x+c)+I)-1/d/a/tan(d*x+c)-I/a/d*ln(tan(d*x+c))+5/4*I/a/d*ln(tan(d*x+c)-I)-1/2/d/a/(tan(d*x+c)-I)","A"
54,1,106,81,0.457000," ","int(cot(d*x+c)^3/(a+I*a*tan(d*x+c)),x)","\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{1}{2 a d \tan \left(d x +c \right)^{2}}+\frac{i}{a d \tan \left(d x +c \right)}-\frac{2 \ln \left(\tan \left(d x +c \right)\right)}{d a}+\frac{i}{2 d a \left(\tan \left(d x +c \right)-i\right)}+\frac{7 \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}"," ",0,"1/4/d/a*ln(tan(d*x+c)+I)-1/2/a/d/tan(d*x+c)^2+I/a/d/tan(d*x+c)-2/d/a*ln(tan(d*x+c))+1/2*I/d/a/(tan(d*x+c)-I)+7/4/d/a*ln(tan(d*x+c)-I)","A"
55,1,124,97,0.447000," ","int(cot(d*x+c)^4/(a+I*a*tan(d*x+c)),x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{1}{3 d a \tan \left(d x +c \right)^{3}}+\frac{i}{2 a d \tan \left(d x +c \right)^{2}}+\frac{2 i \ln \left(\tan \left(d x +c \right)\right)}{a d}+\frac{2}{d a \tan \left(d x +c \right)}-\frac{9 i \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}+\frac{1}{2 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/4*I/d/a*ln(tan(d*x+c)+I)-1/3/d/a/tan(d*x+c)^3+1/2*I/a/d/tan(d*x+c)^2+2*I/a/d*ln(tan(d*x+c))+2/d/a/tan(d*x+c)-9/4*I/a/d*ln(tan(d*x+c)-I)+1/2/d/a/(tan(d*x+c)-I)","A"
56,1,126,127,0.154000," ","int(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^2,x)","\frac{4 \tan \left(d x +c \right)}{a^{2} d}-\frac{\tan^{3}\left(d x +c \right)}{3 a^{2} d}-\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{d \,a^{2}}-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{49 i \ln \left(\tan \left(d x +c \right)-i\right)}{8 d \,a^{2}}+\frac{11}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"4*tan(d*x+c)/a^2/d-1/3*tan(d*x+c)^3/a^2/d-I/d/a^2*tan(d*x+c)^2-1/8*I/d/a^2*ln(tan(d*x+c)+I)+1/4*I/d/a^2/(tan(d*x+c)-I)^2+49/8*I/d/a^2*ln(tan(d*x+c)-I)+11/4/d/a^2/(tan(d*x+c)-I)","A"
57,1,108,111,0.123000," ","int(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 i \tan \left(d x +c \right)}{d \,a^{2}}-\frac{\tan^{2}\left(d x +c \right)}{2 a^{2} d}+\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{9 i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}+\frac{1}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{31 \ln \left(\tan \left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"-2*I/d/a^2*tan(d*x+c)-1/2*tan(d*x+c)^2/a^2/d+1/8/d/a^2*ln(tan(d*x+c)+I)-9/4*I/d/a^2/(tan(d*x+c)-I)+1/4/d/a^2/(tan(d*x+c)-I)^2+31/8/d/a^2*ln(tan(d*x+c)-I)","A"
58,1,93,94,0.128000," ","int(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x)","-\frac{\tan \left(d x +c \right)}{a^{2} d}+\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{17 i \ln \left(\tan \left(d x +c \right)-i\right)}{8 d \,a^{2}}-\frac{i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{7}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-tan(d*x+c)/a^2/d+1/8*I/d/a^2*ln(tan(d*x+c)+I)-17/8*I/d/a^2*ln(tan(d*x+c)-I)-1/4*I/d/a^2/(tan(d*x+c)-I)^2-7/4/d/a^2/(tan(d*x+c)-I)","A"
59,1,77,70,0.123000," ","int(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x)","-\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{5 i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{1}{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)}{8 d \,a^{2}}"," ",0,"-1/8/d/a^2*ln(tan(d*x+c)+I)+5/4*I/d/a^2/(tan(d*x+c)-I)-1/4/d/a^2/(tan(d*x+c)-I)^2-7/8/d/a^2*ln(tan(d*x+c)-I)","A"
60,1,79,49,0.153000," ","int(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x)","-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{8 d \,a^{2}}+\frac{3}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-1/8*I/d/a^2*ln(tan(d*x+c)+I)+1/4*I/d/a^2/(tan(d*x+c)-I)^2+1/8*I/d/a^2*ln(tan(d*x+c)-I)+3/4/d/a^2/(tan(d*x+c)-I)","A"
61,1,77,50,0.118000," ","int(tan(d*x+c)/(a+I*a*tan(d*x+c))^2,x)","\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}+\frac{1}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{\ln \left(\tan \left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"1/8/d/a^2*ln(tan(d*x+c)+I)-1/4*I/d/a^2/(tan(d*x+c)-I)+1/4/d/a^2/(tan(d*x+c)-I)^2-1/8/d/a^2*ln(tan(d*x+c)-I)","A"
62,1,79,51,0.121000," ","int(1/(a+I*a*tan(d*x+c))^2,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{8 d \,a^{2}}-\frac{i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/8*I/d/a^2*ln(tan(d*x+c)+I)-1/8*I/d/a^2*ln(tan(d*x+c)-I)-1/4*I/d/a^2/(tan(d*x+c)-I)^2+1/4/d/a^2/(tan(d*x+c)-I)","A"
63,1,91,62,0.450000," ","int(cot(d*x+c)/(a+I*a*tan(d*x+c))^2,x)","-\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{\ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}-\frac{3 i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}-\frac{1}{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)}{8 d \,a^{2}}"," ",0,"-1/8/d/a^2*ln(tan(d*x+c)+I)+1/a^2/d*ln(tan(d*x+c))-3/4*I/a^2/d/(tan(d*x+c)-I)-1/4/d/a^2/(tan(d*x+c)-I)^2-7/8/d/a^2*ln(tan(d*x+c)-I)","A"
64,1,111,88,0.398000," ","int(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x)","-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{1}{d \,a^{2} \tan \left(d x +c \right)}-\frac{2 i \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}+\frac{i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{17 i \ln \left(\tan \left(d x +c \right)-i\right)}{8 d \,a^{2}}-\frac{5}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-1/8*I/d/a^2*ln(tan(d*x+c)+I)-1/d/a^2/tan(d*x+c)-2*I/a^2/d*ln(tan(d*x+c))+1/4*I/d/a^2/(tan(d*x+c)-I)^2+17/8*I/a^2/d*ln(tan(d*x+c)-I)-5/4/d/a^2/(tan(d*x+c)-I)","A"
65,1,125,110,0.454000," ","int(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x)","\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{1}{2 a^{2} d \tan \left(d x +c \right)^{2}}+\frac{2 i}{a^{2} d \tan \left(d x +c \right)}-\frac{4 \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}+\frac{7 i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}+\frac{1}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{31 \ln \left(\tan \left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"1/8/d/a^2*ln(tan(d*x+c)+I)-1/2/a^2/d/tan(d*x+c)^2+2*I/a^2/d/tan(d*x+c)-4/a^2/d*ln(tan(d*x+c))+7/4*I/a^2/d/(tan(d*x+c)-I)+1/4/d/a^2/(tan(d*x+c)-I)^2+31/8/d/a^2*ln(tan(d*x+c)-I)","A"
66,1,129,143,0.154000," ","int(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^3,x)","-\frac{3 \tan \left(d x +c \right)}{a^{3} d}+\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2 a^{3} d}-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{111 i \ln \left(\tan \left(d x +c \right)-i\right)}{16 a^{3} d}-\frac{11 i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{49}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-3*tan(d*x+c)/a^3/d+1/2*I*tan(d*x+c)^2/a^3/d-1/16*I/d/a^3*ln(tan(d*x+c)+I)-111/16*I/d/a^3*ln(tan(d*x+c)-I)-11/8*I/d/a^3/(tan(d*x+c)-I)^2+1/6/d/a^3/(tan(d*x+c)-I)^3-49/8/d/a^3/(tan(d*x+c)-I)","A"
67,1,112,127,0.123000," ","int(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x)","\frac{i \tan \left(d x +c \right)}{d \,a^{3}}+\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{31 i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{i}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{9}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{49 \ln \left(\tan \left(d x +c \right)-i\right)}{16 d \,a^{3}}"," ",0,"I/d/a^3*tan(d*x+c)+1/16/d/a^3*ln(tan(d*x+c)+I)+31/8*I/d/a^3/(tan(d*x+c)-I)-1/6*I/d/a^3/(tan(d*x+c)-I)^3-9/8/d/a^3/(tan(d*x+c)-I)^2-49/16/d/a^3*ln(tan(d*x+c)-I)","A"
68,1,98,105,0.153000," ","int(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{7 i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{15 i \ln \left(\tan \left(d x +c \right)-i\right)}{16 a^{3} d}-\frac{1}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{17}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/16*I/d/a^3*ln(tan(d*x+c)+I)+7/8*I/d/a^3/(tan(d*x+c)-I)^2+15/16*I/d/a^3*ln(tan(d*x+c)-I)-1/6/d/a^3/(tan(d*x+c)-I)^3+17/8/d/a^3/(tan(d*x+c)-I)","A"
69,1,97,79,0.155000," ","int(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x)","-\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{i}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{7 i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}+\frac{5}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{\ln \left(\tan \left(d x +c \right)-i\right)}{16 d \,a^{3}}"," ",0,"-1/16/d/a^3*ln(tan(d*x+c)+I)+1/6*I/d/a^3/(tan(d*x+c)-I)^3-7/8*I/d/a^3/(tan(d*x+c)-I)+5/8/d/a^3/(tan(d*x+c)-I)^2+1/16/d/a^3*ln(tan(d*x+c)-I)","A"
70,1,98,74,0.149000," ","int(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x)","-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{16 a^{3} d}-\frac{3 i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{1}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-1/16*I/d/a^3*ln(tan(d*x+c)+I)+1/16*I/d/a^3*ln(tan(d*x+c)-I)-3/8*I/d/a^3/(tan(d*x+c)-I)^2+1/6/d/a^3/(tan(d*x+c)-I)^3-1/8/d/a^3/(tan(d*x+c)-I)","A"
71,1,97,72,0.157000," ","int(tan(d*x+c)/(a+I*a*tan(d*x+c))^3,x)","\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{i}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{1}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{\ln \left(\tan \left(d x +c \right)-i\right)}{16 d \,a^{3}}"," ",0,"1/16/d/a^3*ln(tan(d*x+c)+I)-1/6*I/d/a^3/(tan(d*x+c)-I)^3-1/8*I/d/a^3/(tan(d*x+c)-I)-1/8/d/a^3/(tan(d*x+c)-I)^2-1/16/d/a^3*ln(tan(d*x+c)-I)","A"
72,1,98,74,0.124000," ","int(1/(a+I*a*tan(d*x+c))^3,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{16 a^{3} d}-\frac{i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{1}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/16*I/d/a^3*ln(tan(d*x+c)+I)-1/16*I/d/a^3*ln(tan(d*x+c)-I)-1/8*I/d/a^3/(tan(d*x+c)-I)^2-1/6/d/a^3/(tan(d*x+c)-I)^3+1/8/d/a^3/(tan(d*x+c)-I)","A"
73,1,111,86,0.498000," ","int(cot(d*x+c)/(a+I*a*tan(d*x+c))^3,x)","-\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}+\frac{\ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}+\frac{i}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{7 i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)}-\frac{3}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{15 \ln \left(\tan \left(d x +c \right)-i\right)}{16 d \,a^{3}}"," ",0,"-1/16/d/a^3*ln(tan(d*x+c)+I)+1/a^3/d*ln(tan(d*x+c))+1/6*I/d/a^3/(tan(d*x+c)-I)^3-7/8*I/d/a^3/(tan(d*x+c)-I)-3/8/d/a^3/(tan(d*x+c)-I)^2-15/16/d/a^3*ln(tan(d*x+c)-I)","A"
74,1,130,119,0.422000," ","int(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x)","-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{1}{d \,a^{3} \tan \left(d x +c \right)}-\frac{3 i \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}+\frac{5 i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{49 i \ln \left(\tan \left(d x +c \right)-i\right)}{16 a^{3} d}+\frac{1}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{17}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-1/16*I/d/a^3*ln(tan(d*x+c)+I)-1/d/a^3/tan(d*x+c)-3*I/a^3/d*ln(tan(d*x+c))+5/8*I/a^3/d/(tan(d*x+c)-I)^2+49/16*I/a^3/d*ln(tan(d*x+c)-I)+1/6/d/a^3/(tan(d*x+c)-I)^3-17/8/d/a^3/(tan(d*x+c)-I)","A"
75,1,131,154,0.161000," ","int(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^4,x)","\frac{\tan \left(d x +c \right)}{a^{4} d}-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{49 i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{129 i \ln \left(\tan \left(d x +c \right)-i\right)}{32 d \,a^{4}}-\frac{11}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{111}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"tan(d*x+c)/a^4/d-1/32*I/d/a^4*ln(tan(d*x+c)+I)+49/16*I/d/a^4/(tan(d*x+c)-I)^2-1/8*I/d/a^4/(tan(d*x+c)-I)^4+129/32*I/d/a^4*ln(tan(d*x+c)-I)-11/12/d/a^4/(tan(d*x+c)-I)^3+111/16/d/a^4/(tan(d*x+c)-I)","A"
76,1,116,131,0.151000," ","int(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x)","\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{3 i}{4 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{49 i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{1}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{31}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{31 \ln \left(\tan \left(d x +c \right)-i\right)}{32 d \,a^{4}}"," ",0,"1/32/d/a^4*ln(tan(d*x+c)+I)+3/4*I/d/a^4/(tan(d*x+c)-I)^3-49/16*I/d/a^4/(tan(d*x+c)-I)-1/8/d/a^4/(tan(d*x+c)-I)^4+31/16/d/a^4/(tan(d*x+c)-I)^2+31/32/d/a^4*ln(tan(d*x+c)-I)","A"
77,1,118,111,0.148000," ","int(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i}{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)}{32 d \,a^{4}}-\frac{17 i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{7}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{15}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/32*I/d/a^4*ln(tan(d*x+c)+I)+1/8*I/d/a^4/(tan(d*x+c)-I)^4-1/32*I/d/a^4*ln(tan(d*x+c)-I)-17/16*I/d/a^4/(tan(d*x+c)-I)^2+7/12/d/a^4/(tan(d*x+c)-I)^3-15/16/d/a^4/(tan(d*x+c)-I)","A"
78,1,116,110,0.167000," ","int(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x)","-\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{5 i}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{1}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{7}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{\ln \left(\tan \left(d x +c \right)-i\right)}{32 d \,a^{4}}"," ",0,"-1/32/d/a^4*ln(tan(d*x+c)+I)+1/16*I/d/a^4/(tan(d*x+c)-I)-5/12*I/d/a^4/(tan(d*x+c)-I)^3+1/8/d/a^4/(tan(d*x+c)-I)^4-7/16/d/a^4/(tan(d*x+c)-I)^2+1/32/d/a^4*ln(tan(d*x+c)-I)","A"
79,1,118,98,0.164000," ","int(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x)","-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i}{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)}{32 d \,a^{4}}-\frac{1}{4 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{1}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-1/32*I/d/a^4*ln(tan(d*x+c)+I)+1/16*I/d/a^4/(tan(d*x+c)-I)^2-1/8*I/d/a^4/(tan(d*x+c)-I)^4+1/32*I/d/a^4*ln(tan(d*x+c)-I)-1/4/d/a^4/(tan(d*x+c)-I)^3-1/16/d/a^4/(tan(d*x+c)-I)","A"
80,1,116,95,0.127000," ","int(tan(d*x+c)/(a+I*a*tan(d*x+c))^4,x)","\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}-\frac{1}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{1}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{\ln \left(\tan \left(d x +c \right)-i\right)}{32 d \,a^{4}}"," ",0,"1/32/d/a^4*ln(tan(d*x+c)+I)+1/12*I/d/a^4/(tan(d*x+c)-I)^3-1/16*I/d/a^4/(tan(d*x+c)-I)-1/8/d/a^4/(tan(d*x+c)-I)^4-1/16/d/a^4/(tan(d*x+c)-I)^2-1/32/d/a^4*ln(tan(d*x+c)-I)","A"
81,1,118,98,0.131000," ","int(1/(a+I*a*tan(d*x+c))^4,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i}{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)}{32 d \,a^{4}}-\frac{i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{1}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/32*I/d/a^4*ln(tan(d*x+c)+I)+1/8*I/d/a^4/(tan(d*x+c)-I)^4-1/32*I/d/a^4*ln(tan(d*x+c)-I)-1/16*I/d/a^4/(tan(d*x+c)-I)^2-1/12/d/a^4/(tan(d*x+c)-I)^3+1/16/d/a^4/(tan(d*x+c)-I)","A"
82,1,130,105,0.500000," ","int(cot(d*x+c)/(a+I*a*tan(d*x+c))^4,x)","-\frac{\ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{\ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}+\frac{i}{4 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{15 i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}+\frac{1}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{7}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{31 \ln \left(\tan \left(d x +c \right)-i\right)}{32 d \,a^{4}}"," ",0,"-1/32/d/a^4*ln(tan(d*x+c)+I)+1/a^4/d*ln(tan(d*x+c))+1/4*I/a^4/d/(tan(d*x+c)-I)^3-15/16*I/a^4/d/(tan(d*x+c)-I)+1/8/d/a^4/(tan(d*x+c)-I)^4-7/16/d/a^4/(tan(d*x+c)-I)^2-31/32/d/a^4*ln(tan(d*x+c)-I)","A"
83,1,150,144,0.421000," ","int(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x)","-\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}-\frac{1}{d \,a^{4} \tan \left(d x +c \right)}-\frac{4 i \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}+\frac{17 i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{i}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{129 i \ln \left(\tan \left(d x +c \right)-i\right)}{32 d \,a^{4}}+\frac{5}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{49}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"-1/32*I/d/a^4*ln(tan(d*x+c)+I)-1/d/a^4/tan(d*x+c)-4*I/a^4/d*ln(tan(d*x+c))+17/16*I/a^4/d/(tan(d*x+c)-I)^2-1/8*I/d/a^4/(tan(d*x+c)-I)^4+129/32*I/d/a^4*ln(tan(d*x+c)-I)+5/12/d/a^4/(tan(d*x+c)-I)^3-49/16/d/a^4/(tan(d*x+c)-I)","A"
84,1,94,134,0.208000," ","int((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^4,x)","\frac{2 i \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7}-\frac{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5}+\frac{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3}-\frac{a^{\frac{7}{2}} \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*I/d/a^3*(1/7*(a+I*a*tan(d*x+c))^(7/2)-2/5*(a+I*a*tan(d*x+c))^(5/2)*a+2/3*(a+I*a*tan(d*x+c))^(3/2)*a^2-1/2*a^(7/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
85,1,92,102,0.191000," ","int((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^3,x)","-\frac{2 \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}-\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}+a^{2} \sqrt{a +i a \tan \left(d x +c \right)}-\frac{a^{\frac{5}{2}} \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/d/a^2*(1/5*(a+I*a*tan(d*x+c))^(5/2)-1/3*(a+I*a*tan(d*x+c))^(3/2)*a+a^2*(a+I*a*tan(d*x+c))^(1/2)-1/2*a^(5/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
86,1,58,59,0.186000," ","int((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^2,x)","-\frac{2 i \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3}-\frac{a^{\frac{3}{2}} \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}"," ",0,"-2*I/d/a*(1/3*(a+I*a*tan(d*x+c))^(3/2)-1/2*a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
87,1,53,54,0.162000," ","int((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c),x)","\frac{2 \sqrt{a +i a \tan \left(d x +c \right)}-\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{d}"," ",0,"1/d*(2*(a+I*a*tan(d*x+c))^(1/2)-a^(1/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
88,1,36,35,0.138000," ","int((a+I*a*tan(d*x+c))^(1/2),x)","-\frac{i \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{2}\, \sqrt{a}}{d}"," ",0,"-I*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*2^(1/2)*a^(1/2)/d","A"
89,1,230,61,1.429000," ","int(cot(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)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(i \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)+i \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\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)-\ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+I*arctan(1/(-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))-ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c)))*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)","B"
90,1,586,89,1.417000," ","int(cot(d*x+c)^2*(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(2 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)+i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)-2 i \sqrt{2}\, \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{-\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 \cos \left(d x +c \right) \sin \left(d x +c \right)-i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-2 \sqrt{2}\, \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)+2 \left(\cos^{2}\left(d x +c \right)\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 \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) \sin \left(d x +c \right)}"," ",0,"-1/2/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(2*I*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))+I*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+2*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))-2*I*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*(-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*cos(d*x+c)*sin(d*x+c)-I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(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))+2*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))-2*cos(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)","B"
91,1,904,115,1.554000," ","int(cot(d*x+c)^3*(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(-16 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)+6 i \left(\cos^{4}\left(d x +c \right)\right)-8 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \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)-6 i \left(\cos^{2}\left(d x +c \right)\right)-7 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-14 i \left(\cos^{2}\left(d x +c \right)\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)+7 i \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)+16 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)+8 i \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \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)+7 i \left(\cos^{4}\left(d x +c \right)\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)-6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+14 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+2 i \cos \left(d x +c \right)+8 i \sqrt{2}\, \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)+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-8 \sqrt{2}\, \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)-2 i \left(\cos^{3}\left(d x +c \right)\right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)-7 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)\right)}{8 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,"1/8/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-16*I*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))+6*I*cos(d*x+c)^4-8*cos(d*x+c)^4*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))-6*I*cos(d*x+c)^2-7*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-14*I*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))+7*I*(-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))+16*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))+8*I*cos(d*x+c)^4*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))+7*I*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))-6*cos(d*x+c)^3*sin(d*x+c)+14*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+2*I*cos(d*x+c)+8*I*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))+4*cos(d*x+c)^2*sin(d*x+c)-8*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*cos(d*x+c)^3+2*cos(d*x+c)*sin(d*x+c)-7*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c)))/(I*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)^3","B"
92,1,111,163,0.164000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7}-\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5}+\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3}+a^{3} \sqrt{a +i a \tan \left(d x +c \right)}-a^{\frac{7}{2}} \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/d/a^2*(1/7*(a+I*a*tan(d*x+c))^(7/2)-1/5*(a+I*a*tan(d*x+c))^(5/2)*a+1/3*(a+I*a*tan(d*x+c))^(3/2)*a^2+a^3*(a+I*a*tan(d*x+c))^(1/2)-a^(7/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
93,1,76,80,0.163000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 i \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}+a^{2} \sqrt{a +i a \tan \left(d x +c \right)}-a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{d a}"," ",0,"-2*I/d/a*(1/5*(a+I*a*tan(d*x+c))^(5/2)+a^2*(a+I*a*tan(d*x+c))^(1/2)-a^(5/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
94,1,70,74,0.138000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\frac{2 \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)}-2 a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{d}"," ",0,"1/d*(2/3*(a+I*a*tan(d*x+c))^(3/2)+2*a*(a+I*a*tan(d*x+c))^(1/2)-2*a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
95,1,54,57,0.111000," ","int((a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 i a \left(\sqrt{a +i a \tan \left(d x +c \right)}-\sqrt{a}\, \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*a*((a+I*a*tan(d*x+c))^(1/2)-a^(1/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
96,1,231,62,1.347000," ","int(cot(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)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(2 i \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)+i \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 \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)-\ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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) 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*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(2*I*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+I*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-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))-ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c)))*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)*a","B"
97,1,631,115,1.346000," ","int(cot(d*x+c)^2*(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(4 i \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) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+4 i \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) \sin \left(d x +c \right) \sqrt{2}+3 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \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) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+3 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+4 \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) \sin \left(d x +c \right) \sqrt{2}+3 \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) \cos \left(d x +c \right) \sin \left(d x +c \right)+3 \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) \sin \left(d x +c \right)-2 i \left(\cos^{2}\left(d x +c \right)\right)-2 i \cos \left(d x +c \right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)\right) a}{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)*(4*I*(-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)*sin(d*x+c)*2^(1/2)+4*I*(-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))*sin(d*x+c)*2^(1/2)+3*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)*sin(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))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+3*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*sin(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))*sin(d*x+c)*2^(1/2)+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))*cos(d*x+c)*sin(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))*sin(d*x+c)-2*I*cos(d*x+c)^2-2*I*cos(d*x+c)+2*cos(d*x+c)*sin(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/(1+cos(d*x+c))*a","B"
98,1,1142,148,1.456000," ","int(cot(d*x+c)^3*(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(16 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)+16 i \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \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)+4 i \left(\cos^{2}\left(d x +c \right)\right)-16 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \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)+11 i \left(\cos^{2}\left(d x +c \right)\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)-11 i \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)-11 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-16 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)-16 i \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{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-11 i \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)+11 i \left(\cos^{3}\left(d x +c \right)\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)-11 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+16 \cos \left(d x +c \right) \sqrt{2}\, \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)-10 i \cos \left(d x +c \right)-16 i \sqrt{2}\, \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)-14 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+11 \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+16 \sqrt{2}\, \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)+14 i \left(\cos^{3}\left(d x +c \right)\right)-10 \cos \left(d x +c \right) \sin \left(d x +c \right)+11 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)\right) a}{8 d \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,"-1/8/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(16*I*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))+16*I*cos(d*x+c)^3*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))+4*I*cos(d*x+c)^2-16*cos(d*x+c)^3*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))+11*I*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*(-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*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-16*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))-16*I*cos(d*x+c)*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))-11*I*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))+11*I*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))-11*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+16*cos(d*x+c)*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))-10*I*cos(d*x+c)-16*I*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))-14*cos(d*x+c)^2*sin(d*x+c)+11*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+16*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))+14*I*cos(d*x+c)^3-10*cos(d*x+c)*sin(d*x+c)+11*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c)))/(I*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)/(1+cos(d*x+c))*a","B"
99,1,131,168,0.174000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{9}{2}}}{9}-\frac{a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7}+\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} a^{2}}{5}+\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{3}}{3}+2 a^{4} \sqrt{a +i a \tan \left(d x +c \right)}-2 a^{\frac{9}{2}} \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/d/a^2*(1/9*(a+I*a*tan(d*x+c))^(9/2)-1/7*a*(a+I*a*tan(d*x+c))^(7/2)+1/5*(a+I*a*tan(d*x+c))^(5/2)*a^2+1/3*(a+I*a*tan(d*x+c))^(3/2)*a^3+2*a^4*(a+I*a*tan(d*x+c))^(1/2)-2*a^(9/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
100,1,96,103,0.167000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 i \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7}+\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3}+2 a^{3} \sqrt{a +i a \tan \left(d x +c \right)}-2 a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{d a}"," ",0,"-2*I/d/a*(1/7*(a+I*a*tan(d*x+c))^(7/2)+1/3*(a+I*a*tan(d*x+c))^(3/2)*a^2+2*a^3*(a+I*a*tan(d*x+c))^(1/2)-2*a^(7/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
101,1,89,96,0.135000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\frac{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}+\frac{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}+4 a^{2} \sqrt{a +i a \tan \left(d x +c \right)}-4 a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{d}"," ",0,"1/d*(2/5*(a+I*a*tan(d*x+c))^(5/2)+2/3*(a+I*a*tan(d*x+c))^(3/2)*a+4*a^2*(a+I*a*tan(d*x+c))^(1/2)-4*a^(5/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
102,1,73,80,0.109000," ","int((a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 i a \left(\frac{\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)}-2 a^{\frac{3}{2}} \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*a*(1/3*(a+I*a*tan(d*x+c))^(3/2)+2*a*(a+I*a*tan(d*x+c))^(1/2)-2*a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
103,1,329,84,1.349000," ","int(cot(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(4 i \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+i \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) \sin \left(d x +c \right)-4 \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) \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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 \sin \left(d x +c \right)+2 \cos \left(d x +c \right)-2\right) a^{2}}{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)*(4*I*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)))^(1/2)*sin(d*x+c)+I*(-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)-4*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)))^(1/2)*sin(d*x+c)-ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+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*sin(d*x+c)+2*cos(d*x+c)-2)/(I*sin(d*x+c)+cos(d*x+c)-1)*a^2","B"
104,1,608,92,1.331000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\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(8 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)+8 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)+5 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-8 i \sqrt{2}\, \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)+5 \left(\cos^{2}\left(d x +c \right)\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)-8 \sqrt{2}\, \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)-5 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+2 i \cos \left(d x +c \right) \sin \left(d x +c \right)-5 \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 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right) a^{2}}{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*sin(d*x+c)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(8*I*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+8*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))+5*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-8*I*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*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))-8*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))-5*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+2*I*cos(d*x+c)*sin(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))+2*cos(d*x+c)^2-2*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^2","B"
105,1,677,121,1.418000," ","int(cot(d*x+c)^3*(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(32 i \left(\cos^{2}\left(d x +c \right)\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}+23 i \left(\cos^{2}\left(d x +c \right)\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)-32 \left(\cos^{2}\left(d x +c \right)\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}-32 i \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-23 \left(\cos^{2}\left(d x +c \right)\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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+22 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-23 i \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) \sin \left(d x +c \right)+32 \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-18 i \cos \left(d x +c \right) \sin \left(d x +c \right)+22 \left(\cos^{3}\left(d x +c \right)\right)+23 \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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)-4 \left(\cos^{2}\left(d x +c \right)\right)-18 \cos \left(d x +c \right)\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*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(32*I*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)+23*I*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))-32*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)-32*I*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)-23*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+22*I*cos(d*x+c)^2*sin(d*x+c)-23*I*(-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)+32*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)))^(1/2)*sin(d*x+c)-18*I*sin(d*x+c)*cos(d*x+c)+22*cos(d*x+c)^3+23*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+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*cos(d*x+c)^2-18*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^2","B"
106,1,926,153,1.438000," ","int(cot(d*x+c)^4*(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(-52 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+182 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+192 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \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)-270 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+135 \left(\cos^{4}\left(d x +c \right)\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)+135 i \left(\cos^{4}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-114 i \cos \left(d x +c \right) \sin \left(d x +c \right)-384 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)+192 i \sqrt{2}\, \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)+135 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+182 \left(\cos^{4}\left(d x +c \right)\right)-270 \left(\cos^{2}\left(d x +c \right)\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)-384 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \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)+192 i \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \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)-130 \left(\cos^{3}\left(d x +c \right)\right)+192 \sqrt{2}\, \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)-166 \left(\cos^{2}\left(d x +c \right)\right)+135 \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)+114 \cos \left(d x +c \right)\right) a^{2}}{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)*(-52*I*cos(d*x+c)^2*sin(d*x+c)-384*I*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))+192*cos(d*x+c)^4*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))+182*I*cos(d*x+c)^3*sin(d*x+c)+135*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))-270*I*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+135*I*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-384*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))-114*I*sin(d*x+c)*cos(d*x+c)+192*I*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))+182*cos(d*x+c)^4-270*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))+192*I*cos(d*x+c)^4*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))+135*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-130*cos(d*x+c)^3+192*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))-166*cos(d*x+c)^2+135*(-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))+114*cos(d*x+c))/(-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^2","B"
107,1,92,103,0.109000," ","int((a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 i a \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}+\frac{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}+4 a^{2} \sqrt{a +i a \tan \left(d x +c \right)}-4 a^{\frac{5}{2}} \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*a*(1/5*(a+I*a*tan(d*x+c))^(5/2)+2/3*(a+I*a*tan(d*x+c))^(3/2)*a+4*a^2*(a+I*a*tan(d*x+c))^(1/2)-4*a^(5/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
108,1,131,167,0.185000," ","int(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\frac{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7}-\frac{6 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5}+\frac{8 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3}-4 a^{3} \sqrt{a +i a \tan \left(d x +c \right)}-\frac{a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{2}-\frac{a^{4}}{\sqrt{a +i a \tan \left(d x +c \right)}}}{d \,a^{4}}"," ",0,"2/d/a^4*(1/7*(a+I*a*tan(d*x+c))^(7/2)-3/5*(a+I*a*tan(d*x+c))^(5/2)*a+4/3*(a+I*a*tan(d*x+c))^(3/2)*a^2-2*a^3*(a+I*a*tan(d*x+c))^(1/2)-1/4*a^(7/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-1/2*a^4/(a+I*a*tan(d*x+c))^(1/2))","A"
109,1,113,140,0.185000," ","int(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 i \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}-\frac{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}+2 a^{2} \sqrt{a +i a \tan \left(d x +c \right)}-\frac{a^{\frac{5}{2}} \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}}{2 \sqrt{a +i a \tan \left(d x +c \right)}}\right)}{d \,a^{3}}"," ",0,"2*I/d/a^3*(1/5*(a+I*a*tan(d*x+c))^(5/2)-2/3*(a+I*a*tan(d*x+c))^(3/2)*a+2*a^2*(a+I*a*tan(d*x+c))^(1/2)-1/4*a^(5/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))+1/2*a^3/(a+I*a*tan(d*x+c))^(1/2))","A"
110,1,93,106,0.180000," ","int(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 \left(\frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3}-a \sqrt{a +i a \tan \left(d x +c \right)}-\frac{a^{\frac{3}{2}} \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}}{2 \sqrt{a +i a \tan \left(d x +c \right)}}\right)}{d \,a^{2}}"," ",0,"-2/d/a^2*(1/3*(a+I*a*tan(d*x+c))^(3/2)-a*(a+I*a*tan(d*x+c))^(1/2)-1/4*a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-1/2*a^2/(a+I*a*tan(d*x+c))^(1/2))","A"
111,1,73,79,0.176000," ","int(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 i \left(\sqrt{a +i a \tan \left(d x +c \right)}-\frac{\sqrt{a}\, \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 \sqrt{a +i a \tan \left(d x +c \right)}}\right)}{d a}"," ",0,"-2*I/d/a*((a+I*a*tan(d*x+c))^(1/2)-1/4*a^(1/2)*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*a*tan(d*x+c))^(1/2))","A"
112,1,53,54,0.162000," ","int(tan(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{-\frac{\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{1}{\sqrt{a +i a \tan \left(d x +c \right)}}}{d}"," ",0,"1/d*(-1/2*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/(a+I*a*tan(d*x+c))^(1/2))","A"
113,1,59,56,0.141000," ","int(1/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 i a \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{4 a^{\frac{3}{2}}}+\frac{1}{2 a \sqrt{a +i a \tan \left(d x +c \right)}}\right)}{d}"," ",0,"2*I/d*a*(-1/4/a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2))+1/2/a/(a+I*a*tan(d*x+c))^(1/2))","A"
114,1,674,80,1.523000," ","int(cot(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 \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)+\sqrt{2}\, \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{\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 \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-2 i \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) \sin \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)+4 i \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \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 \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-4 \left(\cos^{2}\left(d x +c \right)\right)+2 \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)\right)}{4 d a}"," ",0,"-1/4/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-I*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^(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))+2*I*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-2*I*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^(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*sin(d*x+c)*cos(d*x+c)+2*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*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+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*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-4*cos(d*x+c)^2+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)))/a","B"
115,1,1380,116,1.537000," ","int(cot(d*x+c)^2/(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(4 i \left(\cos^{4}\left(d x +c \right)\right)+\sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\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{\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 \left(\cos^{2}\left(d x +c \right)\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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\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 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\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)-4 i \left(\cos^{2}\left(d x +c \right)\right)+i \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)+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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) \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)-i \left(\cos^{2}\left(d x +c \right)\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)-\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) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+4 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+i \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)-i \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) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-i \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) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-\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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right)-i \left(\cos^{3}\left(d x +c \right)\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)-8 \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)\right)}{4 d \left(\cos^{2}\left(d x +c \right)-1\right) a}"," ",0,"-1/4/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(4*I*cos(d*x+c)^4+2^(1/2)*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))-I*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+I*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))+I*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))-4*I*cos(d*x+c)^2+I*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))+cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-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))-I*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))-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*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+4*cos(d*x+c)^3*sin(d*x+c)+cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+I*(-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*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*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*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/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))*sin(d*x+c)-I*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))-8*cos(d*x+c)*sin(d*x+c)-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c)))/(cos(d*x+c)^2-1)/a","B"
116,1,1382,147,1.676000," ","int(cot(d*x+c)^3/(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(-4 i \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)-4 \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) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-16 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 i \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-11 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-4 \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) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-11 \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^{3}\left(d x +c \right)\right)+11 i \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-11 \left(\cos^{2}\left(d x +c \right)\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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+28 i \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sqrt{2}\, \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{\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)-11 i \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) \sin \left(d x +c \right)-11 \left(\cos^{2}\left(d x +c \right)\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)+11 i \left(\cos^{2}\left(d x +c \right)\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)+16 \left(\cos^{4}\left(d x +c \right)\right)+4 \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)+11 \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)+11 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+11 \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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)-11 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right)+11 \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)-24 \left(\cos^{2}\left(d x +c \right)\right)\right)}{16 d \left(\cos^{2}\left(d x +c \right)-1\right) a}"," ",0,"-1/16/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-4*I*(-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)-4*(-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*2^(1/2)-16*I*cos(d*x+c)^3*sin(d*x+c)+4*I*(-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*sin(d*x+c)*2^(1/2)-11*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2-4*(-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*2^(1/2)-11*(-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+11*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)-11*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+28*I*sin(d*x+c)*cos(d*x+c)+4*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))-11*I*(-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)-11*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*(-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*sin(d*x+c)+16*cos(d*x+c)^4+4*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*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))+11*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+11*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+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)-11*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3+11*(-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))-24*cos(d*x+c)^2)/(cos(d*x+c)^2-1)/a","B"
117,1,131,167,0.162000," ","int(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\frac{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5}-2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}} a +8 a^{2} \sqrt{a +i a \tan \left(d x +c \right)}+\frac{9 a^{3}}{2 \sqrt{a +i a \tan \left(d x +c \right)}}-\frac{a^{4}}{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{4}}{d \,a^{4}}"," ",0,"2/d/a^4*(1/5*(a+I*a*tan(d*x+c))^(5/2)-(a+I*a*tan(d*x+c))^(3/2)*a+4*a^2*(a+I*a*tan(d*x+c))^(1/2)+9/4*a^3/(a+I*a*tan(d*x+c))^(1/2)-1/6*a^4/(a+I*a*tan(d*x+c))^(3/2)-1/8*a^(5/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
118,1,113,140,0.160000," ","int(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 i \left(\frac{\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)}-\frac{7 a^{2}}{4 \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{a^{3}}{6 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8}\right)}{d \,a^{3}}"," ",0,"2*I/d/a^3*(1/3*(a+I*a*tan(d*x+c))^(3/2)-2*a*(a+I*a*tan(d*x+c))^(1/2)-7/4*a^2/(a+I*a*tan(d*x+c))^(1/2)+1/6*a^3/(a+I*a*tan(d*x+c))^(3/2)-1/8*a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
119,1,91,106,0.165000," ","int(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{a +i a \tan \left(d x +c \right)}+\frac{5 a}{4 \sqrt{a +i a \tan \left(d x +c \right)}}-\frac{a^{2}}{6 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8}\right)}{d \,a^{2}}"," ",0,"-2/d/a^2*((a+I*a*tan(d*x+c))^(1/2)+5/4*a/(a+I*a*tan(d*x+c))^(1/2)-1/6*a^2/(a+I*a*tan(d*x+c))^(3/2)-1/8*a^(1/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
120,1,75,79,0.149000," ","int(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 i \left(-\frac{3}{4 \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{a}{6 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 \sqrt{a}}\right)}{d a}"," ",0,"-2*I/d/a*(-3/4/(a+I*a*tan(d*x+c))^(1/2)+1/6/(a+I*a*tan(d*x+c))^(3/2)*a-1/8*2^(1/2)/a^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
121,1,72,76,0.143000," ","int(tan(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{-\frac{1}{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{1}{2 a \sqrt{a +i a \tan \left(d x +c \right)}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{4 a^{\frac{3}{2}}}}{d}"," ",0,"1/d*(-1/3/(a+I*a*tan(d*x+c))^(3/2)+1/2/a/(a+I*a*tan(d*x+c))^(1/2)-1/4/a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
122,1,78,79,0.119000," ","int(1/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 i a \left(\frac{1}{4 a^{2} \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{1}{6 a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 a^{\frac{5}{2}}}\right)}{d}"," ",0,"2*I/d*a*(1/4/a^2/(a+I*a*tan(d*x+c))^(1/2)+1/6/a/(a+I*a*tan(d*x+c))^(3/2)-1/8/a^(5/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
123,1,703,103,1.556000," ","int(cot(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(-3 i \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 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \sqrt{2}\, \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{\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 \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) \sin \left(d x +c \right)+12 i \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-16 \left(\cos^{4}\left(d x +c \right)\right)+3 \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 \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 \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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)+12 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+36 i \cos \left(d x +c \right) \sin \left(d x +c \right)+12 \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 \left(\cos^{2}\left(d x +c \right)\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)*(-3*I*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*I*cos(d*x+c)^3*sin(d*x+c)+3*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))-12*I*(-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)+12*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)-16*cos(d*x+c)^4+3*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))+12*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*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+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)+12*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+36*I*sin(d*x+c)*cos(d*x+c)+12*(-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*cos(d*x+c)^2)/a^2","B"
124,1,1411,145,1.351000," ","int(cot(d*x+c)^2/(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(-36 i \left(\cos^{4}\left(d x +c \right)\right)+18 i \left(\cos^{2}\left(d x +c \right)\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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-16 i \left(\cos^{6}\left(d x +c \right)\right)+52 i \left(\cos^{2}\left(d x +c \right)\right)-18 i \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)-3 \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\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{\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 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+18 i \left(\cos^{2}\left(d x +c \right)\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)-18 i \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-18 i \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)+18 \left(\cos^{2}\left(d x +c \right)\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)-18 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+3 i \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) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 i \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) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+18 i \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^{3}\left(d x +c \right)\right)+3 \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) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-18 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-44 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-3 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\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 i \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\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)-18 \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) \sin \left(d x +c \right)+18 \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+18 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+84 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{24 d \left(\cos^{2}\left(d x +c \right)-1\right) a^{2}}"," ",0,"1/24/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-36*I*cos(d*x+c)^4+18*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-16*I*cos(d*x+c)^6+52*I*cos(d*x+c)^2-18*I*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))-3*2^(1/2)*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))-16*cos(d*x+c)^5*sin(d*x+c)+18*I*(-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)^2-18*I*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-18*I*(-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*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))-18*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+3*I*(-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)+3*I*(-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)+18*I*(-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+3*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))-18*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-44*cos(d*x+c)^3*sin(d*x+c)-3*I*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))-3*I*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))-18*(-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*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+18*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+84*cos(d*x+c)*sin(d*x+c))/(cos(d*x+c)^2-1)/a^2","B"
125,1,1409,178,1.415000," ","int(cot(d*x+c)^3/(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(-6 i \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)-136 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 i \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-69 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-6 \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) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+32 \left(\cos^{6}\left(d x +c \right)\right)+69 i \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+252 i \cos \left(d x +c \right) \sin \left(d x +c \right)-69 i \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) \sin \left(d x +c \right)-6 \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) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-69 \left(\cos^{2}\left(d x +c \right)\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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-69 \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^{3}\left(d x +c \right)\right)-32 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+69 i \left(\cos^{2}\left(d x +c \right)\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)+6 \sqrt{2}\, \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{\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)-69 \left(\cos^{2}\left(d x +c \right)\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 \left(\cos^{4}\left(d x +c \right)\right)+69 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-69 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right)+6 \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)+69 \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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)+69 \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)+69 \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)-176 \left(\cos^{2}\left(d x +c \right)\right)\right)}{48 d \left(\cos^{2}\left(d x +c \right)-1\right) a^{2}}"," ",0,"-1/48/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-6*I*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)-136*I*cos(d*x+c)^3*sin(d*x+c)+6*I*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*sin(d*x+c)-69*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2-6*(-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*2^(1/2)+32*cos(d*x+c)^6+69*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)+252*I*sin(d*x+c)*cos(d*x+c)-69*I*(-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)-6*(-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*2^(1/2)-69*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-69*(-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)^3-32*I*cos(d*x+c)^5*sin(d*x+c)+69*I*(-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*sin(d*x+c)+6*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))-69*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*cos(d*x+c)^4+69*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-69*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3+6*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*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+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)+69*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))+69*(-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))-176*cos(d*x+c)^2)/(cos(d*x+c)^2-1)/a^2","B"
126,1,131,167,0.158000," ","int(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\frac{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3}-6 a \sqrt{a +i a \tan \left(d x +c \right)}-\frac{31 a^{2}}{4 \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{3 a^{3}}{2 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{a^{4}}{5 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8}}{d \,a^{4}}"," ",0,"2/d/a^4*(1/3*(a+I*a*tan(d*x+c))^(3/2)-3*a*(a+I*a*tan(d*x+c))^(1/2)-31/8*a^2/(a+I*a*tan(d*x+c))^(1/2)+3/4*a^3/(a+I*a*tan(d*x+c))^(3/2)-1/10*a^4/(a+I*a*tan(d*x+c))^(5/2)-1/16*a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
127,1,111,140,0.165000," ","int(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 i \left(\sqrt{a +i a \tan \left(d x +c \right)}+\frac{17 a}{8 \sqrt{a +i a \tan \left(d x +c \right)}}-\frac{7 a^{2}}{12 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{a^{3}}{10 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16}\right)}{d \,a^{3}}"," ",0,"2*I/d/a^3*((a+I*a*tan(d*x+c))^(1/2)+17/8*a/(a+I*a*tan(d*x+c))^(1/2)-7/12*a^2/(a+I*a*tan(d*x+c))^(3/2)+1/10*a^3/(a+I*a*tan(d*x+c))^(5/2)-1/16*a^(1/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
128,1,93,106,0.156000," ","int(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 \left(-\frac{7}{8 \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{5 a}{12 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{a^{2}}{10 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16 \sqrt{a}}\right)}{d \,a^{2}}"," ",0,"-2/d/a^2*(-7/8/(a+I*a*tan(d*x+c))^(1/2)+5/12/(a+I*a*tan(d*x+c))^(3/2)*a-1/10*a^2/(a+I*a*tan(d*x+c))^(5/2)-1/16*2^(1/2)/a^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
129,1,94,102,0.147000," ","int(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 i \left(-\frac{1}{4 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{1}{8 a \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{a}{10 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16 a^{\frac{3}{2}}}\right)}{d a}"," ",0,"-2*I/d/a*(-1/4/(a+I*a*tan(d*x+c))^(3/2)+1/8/a/(a+I*a*tan(d*x+c))^(1/2)+1/10*a/(a+I*a*tan(d*x+c))^(5/2)-1/16/a^(3/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
130,1,91,98,0.159000," ","int(tan(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{-\frac{1}{5 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{1}{4 a^{2} \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{1}{6 a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 a^{\frac{5}{2}}}}{d}"," ",0,"1/d*(-1/5/(a+I*a*tan(d*x+c))^(5/2)+1/4/a^2/(a+I*a*tan(d*x+c))^(1/2)+1/6/a/(a+I*a*tan(d*x+c))^(3/2)-1/8/a^(5/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
131,1,97,102,0.115000," ","int(1/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 i a \left(\frac{1}{8 a^{3} \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{1}{12 a^{2} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{1}{10 a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16 a^{\frac{7}{2}}}\right)}{d}"," ",0,"2*I/d*a*(1/8/a^3/(a+I*a*tan(d*x+c))^(1/2)+1/12/a^2/(a+I*a*tan(d*x+c))^(3/2)+1/10/a/(a+I*a*tan(d*x+c))^(5/2)-1/16/a^(7/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
132,1,730,125,1.390000," ","int(cot(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(64 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-64 \left(\cos^{6}\left(d x +c \right)\right)+64 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \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)+40 i \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-40 i \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) \sin \left(d x +c \right)-32 \left(\cos^{4}\left(d x +c \right)\right)+5 \sqrt{2}\, \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{\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)+140 i \cos \left(d x +c \right) \sin \left(d x +c \right)+40 i \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+40 \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)+40 \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \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)+5 \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)-100 \left(\cos^{2}\left(d x +c \right)\right)+40 \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)\right)}{80 d \,a^{3}}"," ",0,"-1/80/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(64*I*cos(d*x+c)^5*sin(d*x+c)-64*cos(d*x+c)^6+64*I*cos(d*x+c)^3*sin(d*x+c)-5*I*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)+40*I*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-40*I*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))-32*cos(d*x+c)^4+5*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))+140*I*sin(d*x+c)*cos(d*x+c)+40*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+40*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))+40*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+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)+5*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))-100*cos(d*x+c)^2+40*(-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^3","B"
133,1,1438,173,1.384000," ","int(cot(d*x+c)^2/(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(-300 i \left(\cos^{2}\left(d x +c \right)\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)+564 i \left(\cos^{4}\left(d x +c \right)\right)-1260 \cos \left(d x +c \right) \sin \left(d x +c \right)+192 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-300 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+300 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-15 i \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) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-15 \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) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\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{\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)+160 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+300 i \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)-15 i \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) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+300 i \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-300 \left(\cos^{2}\left(d x +c \right)\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)-300 i \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^{3}\left(d x +c \right)\right)-300 i \left(\cos^{2}\left(d x +c \right)\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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+15 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\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)-820 i \left(\cos^{2}\left(d x +c \right)\right)+300 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+64 i \left(\cos^{6}\left(d x +c \right)\right)+300 \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) \sin \left(d x +c \right)+668 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+192 i \left(\cos^{8}\left(d x +c \right)\right)+300 i \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)+15 i \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\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)-300 \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{-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)\right)}{240 d \left(\cos^{2}\left(d x +c \right)-1\right) a^{3}}"," ",0,"-1/240/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1260*cos(d*x+c)*sin(d*x+c)-300*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+668*cos(d*x+c)^3*sin(d*x+c)-15*I*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*(-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*sin(d*x+c)*cos(d*x+c)^7-300*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))-15*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*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-300*I*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))-300*I*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))+300*I*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))+300*(-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)+15*2^(1/2)*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))+160*cos(d*x+c)^5*sin(d*x+c)+192*I*cos(d*x+c)^8+64*I*cos(d*x+c)^6+564*I*cos(d*x+c)^4-820*I*cos(d*x+c)^2+300*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+300*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))-300*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c))+15*I*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*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*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*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)-1)/sin(d*x+c)))/(cos(d*x+c)^2-1)/a^3","B"
134,1,116,125,0.121000," ","int(1/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 i a \left(\frac{1}{16 a^{4} \sqrt{a +i a \tan \left(d x +c \right)}}+\frac{1}{24 a^{3} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{1}{20 a^{2} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{1}{14 a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +i a \tan \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{32 a^{\frac{9}{2}}}\right)}{d}"," ",0,"2*I/d*a*(1/16/a^4/(a+I*a*tan(d*x+c))^(1/2)+1/24/a^3/(a+I*a*tan(d*x+c))^(3/2)+1/20/a^2/(a+I*a*tan(d*x+c))^(5/2)+1/14/a/(a+I*a*tan(d*x+c))^(7/2)-1/32/a^(9/2)*2^(1/2)*arctanh(1/2*(a+I*a*tan(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))","A"
135,1,393,85,0.176000," ","int((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e)),x)","\frac{2 i a \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}+\frac{2 a d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{2 i a \,d^{2} \sqrt{d \tan \left(f x +e \right)}}{f}+\frac{i a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}+\frac{i a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{i a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{a \,d^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \,d^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \,d^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/5*I*a*(d*tan(f*x+e))^(5/2)/f+2/3*a*d*(d*tan(f*x+e))^(3/2)/f-2*I*a*d^2*(d*tan(f*x+e))^(1/2)/f+1/4*I*a/f*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*I*a/f*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*I*a/f*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*a/f*d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f*d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f*d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
136,1,367,65,0.176000," ","int((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e)),x)","\frac{2 i a \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{2 a d \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{a d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}-\frac{a d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{a d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{i a \,d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{i a \,d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{i a \,d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/3*I*a*(d*tan(f*x+e))^(3/2)/f+2*a*d*(d*tan(f*x+e))^(1/2)/f-1/4*a/f*d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*I*a/f*d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*I*a/f*d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*I*a/f*d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
137,1,341,48,0.172000," ","int((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x)","\frac{2 i a \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}-\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{a d \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2*I*a*(d*tan(f*x+e))^(1/2)/f-1/4*I*a/f*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*I*a/f*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*I*a/f*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*a/f*d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f*d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f*d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
138,1,330,30,0.196000," ","int((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x)","\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d}+\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}+\frac{i a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{i a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{i a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"1/4*a/f/d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*I*a/f/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*I*a/f/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*I*a/f/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","C"
139,1,358,50,0.173000," ","int((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x)","\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{2}}+\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}-\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}-\frac{a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a}{d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"1/4*I*a/f/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*I*a/f/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*I*a/f/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*a/f/d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f/d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f/d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*a/d/f/(d*tan(f*x+e))^(1/2)","C"
140,1,378,70,0.169000," ","int((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x)","-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{3}}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3}}+\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3}}-\frac{i a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{i a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{i a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a}{3 d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{2 i a}{d^{2} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/4*a/f/d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f/d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f/d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*I*a/f/d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*I*a/f/d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*I*a/f/d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/3*a/d/f/(d*tan(f*x+e))^(3/2)-2*I*a/d^2/f/(d*tan(f*x+e))^(1/2)","B"
141,1,397,89,0.177000," ","int((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x)","-\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{4}}-\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{4}}+\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{4}}+\frac{a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a}{5 d f \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}-\frac{2 i a}{3 d^{2} f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{2 a}{d^{3} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/4*I*a/f/d^4*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*I*a/f/d^4*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*I*a/f/d^4*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*a/f/d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f/d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f/d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/5*a/d/f/(d*tan(f*x+e))^(5/2)-2/3*I*a/d^2/f/(d*tan(f*x+e))^(3/2)+2*a/d^3/f/(d*tan(f*x+e))^(1/2)","B"
142,1,393,85,0.172000," ","int((d*tan(f*x+e))^(5/2)*(a-I*a*tan(f*x+e)),x)","-\frac{2 i a \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}+\frac{2 a d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{2 i a \,d^{2} \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{i a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}-\frac{i a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{i a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{a \,d^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \,d^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \,d^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/5*I*a*(d*tan(f*x+e))^(5/2)/f+2/3*a*d*(d*tan(f*x+e))^(3/2)/f+2*I*a*d^2*(d*tan(f*x+e))^(1/2)/f-1/4*I*a/f*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*I*a/f*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*I*a/f*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*a/f*d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f*d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f*d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
143,1,367,65,0.181000," ","int((d*tan(f*x+e))^(3/2)*(a-I*a*tan(f*x+e)),x)","-\frac{2 i a \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{2 a d \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{a d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}-\frac{a d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{a d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{i a \,d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{i a \,d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{i a \,d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3*I*a*(d*tan(f*x+e))^(3/2)/f+2*a*d*(d*tan(f*x+e))^(1/2)/f-1/4*a/f*d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*I*a/f*d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*I*a/f*d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*I*a/f*d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
144,1,341,48,0.172000," ","int((d*tan(f*x+e))^(1/2)*(a-I*a*tan(f*x+e)),x)","-\frac{2 i a \sqrt{d \tan \left(f x +e \right)}}{f}+\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}+\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{a d \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2*I*a*(d*tan(f*x+e))^(1/2)/f+1/4*I*a/f*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*I*a/f*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*I*a/f*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*a/f*d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f*d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f*d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
145,1,330,30,0.196000," ","int((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x)","\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d}+\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}-\frac{i a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{i a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{i a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"1/4*a/f/d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*I*a/f/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*I*a/f/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*I*a/f/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","C"
146,1,358,50,0.174000," ","int((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x)","-\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{2}}-\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}+\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}-\frac{a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a}{d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/4*I*a/f/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*I*a/f/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*I*a/f/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*a/f/d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f/d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f/d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*a/d/f/(d*tan(f*x+e))^(1/2)","C"
147,1,378,70,0.171000," ","int((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x)","-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{3}}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3}}+\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3}}+\frac{i a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{i a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{i a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 i a}{d^{2} f \sqrt{d \tan \left(f x +e \right)}}-\frac{2 a}{3 d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}"," ",0,"-1/4*a/f/d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f/d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f/d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*I*a/f/d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*I*a/f/d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*I*a/f/d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2*I*a/d^2/f/(d*tan(f*x+e))^(1/2)-2/3*a/d/f/(d*tan(f*x+e))^(3/2)","B"
148,1,397,89,0.172000," ","int((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x)","\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{4}}+\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{4}}-\frac{i a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{4}}+\frac{a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 a}{d^{3} f \sqrt{d \tan \left(f x +e \right)}}+\frac{2 i a}{3 d^{2} f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{2 a}{5 d f \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}"," ",0,"1/4*I*a/f/d^4*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*I*a/f/d^4*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*I*a/f/d^4*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*a/f/d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f/d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f/d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2*a/d^3/f/(d*tan(f*x+e))^(1/2)+2/3*I*a/d^2/f/(d*tan(f*x+e))^(3/2)-2/5*a/d/f/(d*tan(f*x+e))^(5/2)","B"
149,1,431,114,0.169000," ","int((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^2,x)","-\frac{2 a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 d f}+\frac{4 i a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}+\frac{4 a^{2} d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{4 i a^{2} d^{2} \sqrt{d \tan \left(f x +e \right)}}{f}+\frac{i a^{2} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f}+\frac{i a^{2} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{i a^{2} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{a^{2} d^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} d^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} d^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/7*a^2*(d*tan(f*x+e))^(7/2)/d/f+4/5*I*a^2*(d*tan(f*x+e))^(5/2)/f+4/3*a^2*d*(d*tan(f*x+e))^(3/2)/f-4*I*a^2*d^2*(d*tan(f*x+e))^(1/2)/f+1/2*I/f*a^2*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+I/f*a^2*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-I/f*a^2*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2/f*a^2*d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^2*d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^2*d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
150,1,403,92,0.171000," ","int((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^2,x)","-\frac{2 a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d f}+\frac{4 i a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{4 a^{2} d \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{a^{2} d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f}-\frac{a^{2} d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{a^{2} d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{i a^{2} d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{i a^{2} d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{i a^{2} d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/5*a^2*(d*tan(f*x+e))^(5/2)/d/f+4/3*I*a^2*(d*tan(f*x+e))^(3/2)/f+4*a^2*d*(d*tan(f*x+e))^(1/2)/f-1/2/f*a^2*d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^2*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^2*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*I/f*a^2*d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-I/f*a^2*d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+I/f*a^2*d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
151,1,375,73,0.170000," ","int((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x)","-\frac{2 a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 d f}+\frac{4 i a^{2} \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{i a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f}-\frac{i a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{i a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{a^{2} d \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3*a^2*(d*tan(f*x+e))^(3/2)/d/f+4*I*a^2*(d*tan(f*x+e))^(1/2)/f-1/2*I/f*a^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-I/f*a^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+I/f*a^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f*a^2*d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^2*d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^2*d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
152,1,362,54,0.205000," ","int((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(1/2),x)","-\frac{2 a^{2} \sqrt{d \tan \left(f x +e \right)}}{d f}+\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f d}+\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d}-\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d}+\frac{i a^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{i a^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{i a^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2*a^2*(d*tan(f*x+e))^(1/2)/d/f+1/2/f*a^2/d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^2/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^2/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*I/f*a^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+I/f*a^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-I/f*a^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","C"
153,1,371,54,0.167000," ","int((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x)","\frac{i a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{2}}+\frac{i a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2}}-\frac{i a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2}}-\frac{a^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{2}}{d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"1/2*I/f*a^2/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+I/f*a^2/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-I/f*a^2/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2/f*a^2/d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^2/d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^2/d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*a^2/d/f/(d*tan(f*x+e))^(1/2)","C"
154,1,393,76,0.173000," ","int((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x)","-\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{3}}-\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3}}+\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3}}-\frac{i a^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{i a^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{i a^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{2}}{3 d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{4 i a^{2}}{d^{2} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/2/f*a^2/d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^2/d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^2/d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*I/f*a^2/d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-I/f*a^2/d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+I/f*a^2/d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/3*a^2/d/f/(d*tan(f*x+e))^(3/2)-4*I*a^2/d^2/f/(d*tan(f*x+e))^(1/2)","B"
155,1,414,97,0.171000," ","int((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(7/2),x)","-\frac{i a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{4}}-\frac{i a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4}}+\frac{i a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4}}+\frac{a^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{2}}{5 d f \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}-\frac{4 i a^{2}}{3 d^{2} f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{4 a^{2}}{d^{3} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/2*I/f*a^2/d^4*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-I/f*a^2/d^4*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+I/f*a^2/d^4*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f*a^2/d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^2/d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^2/d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/5*a^2/d/f/(d*tan(f*x+e))^(5/2)-4/3*I*a^2/d^2/f/(d*tan(f*x+e))^(3/2)+4*a^2/d^3/f/(d*tan(f*x+e))^(1/2)","B"
156,1,454,148,0.253000," ","int((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^3,x)","-\frac{2 i a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9 f \,d^{2}}-\frac{6 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 d f}+\frac{8 i a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}+\frac{8 a^{3} d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{8 i a^{3} d^{2} \sqrt{d \tan \left(f x +e \right)}}{f}+\frac{i a^{3} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f}+\frac{2 i a^{3} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{2 i a^{3} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{a^{3} d^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{3} d^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3} d^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/9*I/f*a^3/d^2*(d*tan(f*x+e))^(9/2)-6/7*a^3*(d*tan(f*x+e))^(7/2)/d/f+8/5*I*a^3*(d*tan(f*x+e))^(5/2)/f+8/3*a^3*d*(d*tan(f*x+e))^(3/2)/f-8*I*a^3*d^2*(d*tan(f*x+e))^(1/2)/f+I/f*a^3*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+2*I/f*a^3*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*I/f*a^3*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3*d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-2/f*a^3*d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2/f*a^3*d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
157,1,426,126,0.256000," ","int((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^3,x)","-\frac{2 i a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f \,d^{2}}-\frac{6 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d f}+\frac{8 i a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{8 a^{3} d \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{a^{3} d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f}-\frac{2 a^{3} d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{2 a^{3} d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{i a^{3} d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 i a^{3} d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 i a^{3} d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/7*I/f*a^3/d^2*(d*tan(f*x+e))^(7/2)-6/5*a^3*(d*tan(f*x+e))^(5/2)/d/f+8/3*I*a^3*(d*tan(f*x+e))^(3/2)/f+8*a^3*d*(d*tan(f*x+e))^(1/2)/f-1/f*a^3*d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-2/f*a^3*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2/f*a^3*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-I/f*a^3*d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-2*I/f*a^3*d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2*I/f*a^3*d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
158,1,397,107,0.262000," ","int((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x)","-\frac{2 i a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f \,d^{2}}-\frac{2 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{d f}+\frac{8 i a^{3} \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{i a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f}-\frac{2 i a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{2 i a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{a^{3} d \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3} d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{3} d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/5*I/f*a^3/d^2*(d*tan(f*x+e))^(5/2)-2*a^3*(d*tan(f*x+e))^(3/2)/d/f+8*I*a^3*(d*tan(f*x+e))^(1/2)/f-I/f*a^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-2*I/f*a^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2*I/f*a^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3*d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+2/f*a^3*d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/f*a^3*d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
159,1,384,88,0.212000," ","int((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(1/2),x)","-\frac{2 i a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f \,d^{2}}-\frac{6 a^{3} \sqrt{d \tan \left(f x +e \right)}}{d f}+\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f d}+\frac{2 a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d}-\frac{2 a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d}+\frac{i a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 i a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 i a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3*I/f*a^3/d^2*(d*tan(f*x+e))^(3/2)-6*a^3*(d*tan(f*x+e))^(1/2)/d/f+1/f*a^3/d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+2/f*a^3/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/f*a^3/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+I/f*a^3/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+2*I/f*a^3/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*I/f*a^3/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
160,1,394,67,0.188000," ","int((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x)","-\frac{2 i a^{3} \sqrt{d \tan \left(f x +e \right)}}{f \,d^{2}}+\frac{i a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \,d^{2}}+\frac{2 i a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2}}-\frac{2 i a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2}}-\frac{a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{3}}{f d \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-2*I/f*a^3/d^2*(d*tan(f*x+e))^(1/2)+I/f*a^3/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+2*I/f*a^3/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*I/f*a^3/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3/d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-2/f*a^3/d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2/f*a^3/d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/f*a^3/d/(d*tan(f*x+e))^(1/2)","B"
161,1,394,89,0.184000," ","int((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x)","-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \,d^{3}}-\frac{2 a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3}}+\frac{2 a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3}}-\frac{i a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 i a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 i a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{6 i a^{3}}{f \,d^{2} \sqrt{d \tan \left(f x +e \right)}}-\frac{2 a^{3}}{3 f d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}"," ",0,"-1/f*a^3/d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-2/f*a^3/d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2/f*a^3/d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-I/f*a^3/d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-2*I/f*a^3/d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2*I/f*a^3/d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-6*I/f*a^3/d^2/(d*tan(f*x+e))^(1/2)-2/3/f*a^3/d/(d*tan(f*x+e))^(3/2)","B"
162,1,414,110,0.189000," ","int((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x)","-\frac{i a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \,d^{4}}-\frac{2 i a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4}}+\frac{2 i a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4}}+\frac{a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 i a^{3}}{f \,d^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{2 a^{3}}{5 f d \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}+\frac{8 a^{3}}{d^{3} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-I/f*a^3/d^4*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-2*I/f*a^3/d^4*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+2*I/f*a^3/d^4*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3/d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+2/f*a^3/d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/f*a^3/d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*I/f*a^3/d^2/(d*tan(f*x+e))^(3/2)-2/5/f*a^3/d/(d*tan(f*x+e))^(5/2)+8*a^3/d^3/f/(d*tan(f*x+e))^(1/2)","B"
163,1,436,132,0.185000," ","int((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x)","\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \,d^{5}}+\frac{2 a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{5}}-\frac{2 a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{5}}+\frac{i a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{f \,d^{4} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{2 i a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 i a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{6 i a^{3}}{5 f \,d^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}-\frac{2 a^{3}}{7 f d \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}+\frac{8 i a^{3}}{d^{4} f \sqrt{d \tan \left(f x +e \right)}}+\frac{8 a^{3}}{3 d^{3} f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}"," ",0,"1/f*a^3/d^5*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+2/f*a^3/d^5*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/f*a^3/d^5*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+I/f*a^3/d^4/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+2*I/f*a^3/d^4/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*I/f*a^3/d^4/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-6/5*I/f*a^3/d^2/(d*tan(f*x+e))^(5/2)-2/7/f*a^3/d/(d*tan(f*x+e))^(7/2)+8*I*a^3/d^4/f/(d*tan(f*x+e))^(1/2)+8/3*a^3/d^3/f/(d*tan(f*x+e))^(3/2)","B"
164,1,154,238,0.282000," ","int((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e)),x)","-\frac{2 i d^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f a}+\frac{2 d^{3} \sqrt{d \tan \left(f x +e \right)}}{a f}-\frac{i d^{4} \sqrt{d \tan \left(f x +e \right)}}{2 f a \left(d \tan \left(f x +e \right)-i d \right)}+\frac{3 i d^{4} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{f a \sqrt{-i d}}+\frac{i d^{4} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{2 f a \sqrt{i d}}"," ",0,"-2/3*I/f/a*d^2*(d*tan(f*x+e))^(3/2)+2*d^3*(d*tan(f*x+e))^(1/2)/a/f-1/2*I/f/a*d^4*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)+3*I/f/a*d^4/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/2*I/f/a*d^4/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
165,1,130,217,0.292000," ","int((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x)","-\frac{2 i d^{2} \sqrt{d \tan \left(f x +e \right)}}{f a}-\frac{d^{3} \sqrt{d \tan \left(f x +e \right)}}{2 f a \left(d \tan \left(f x +e \right)-i d \right)}+\frac{2 d^{3} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{f a \sqrt{-i d}}-\frac{d^{3} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{2 f a \sqrt{i d}}"," ",0,"-2*I/f/a*d^2*(d*tan(f*x+e))^(1/2)-1/2/f/a*d^3*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)+2/f/a*d^3/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/2/f/a*d^3/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
166,1,111,195,0.269000," ","int((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x)","\frac{i d^{2} \sqrt{d \tan \left(f x +e \right)}}{2 f a \left(d \tan \left(f x +e \right)-i d \right)}-\frac{i d^{2} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{f a \sqrt{-i d}}-\frac{i d^{2} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{2 f a \sqrt{i d}}"," ",0,"1/2*I/f/a*d^2*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)-I/f/a*d^2/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/2*I/f/a*d^2/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
167,1,69,63,0.283000," ","int((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x)","\frac{d \sqrt{d \tan \left(f x +e \right)}}{2 f a \left(d \tan \left(f x +e \right)-i d \right)}+\frac{d \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{2 f a \sqrt{i d}}"," ",0,"1/2/f/a*d*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)+1/2/f/a*d/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
168,1,102,197,0.290000," ","int(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x)","-\frac{i \sqrt{d \tan \left(f x +e \right)}}{2 f a \left(d \tan \left(f x +e \right)-i d \right)}-\frac{i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{f a \sqrt{-i d}}+\frac{i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{2 f a \sqrt{i d}}"," ",0,"-1/2*I/f/a*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)-I/f/a/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/2*I/f/a/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
169,1,129,218,0.268000," ","int(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x)","-\frac{\sqrt{d \tan \left(f x +e \right)}}{2 f a d \left(d \tan \left(f x +e \right)-i d \right)}-\frac{2 \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{f a d \sqrt{-i d}}-\frac{\arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{2 f a d \sqrt{i d}}-\frac{2}{a d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/2/f/a/d*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)-2/f/a/d/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/2/f/a/d/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))-2/a/d/f/(d*tan(f*x+e))^(1/2)","A"
170,1,154,240,0.264000," ","int(1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x)","\frac{i \sqrt{d \tan \left(f x +e \right)}}{2 f a \,d^{2} \left(d \tan \left(f x +e \right)-i d \right)}+\frac{3 i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{f a \,d^{2} \sqrt{-i d}}-\frac{i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{2 f a \,d^{2} \sqrt{i d}}-\frac{2}{3 a d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{2 i}{f a \,d^{2} \sqrt{d \tan \left(f x +e \right)}}"," ",0,"1/2*I/f/a/d^2*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)+3*I/f/a/d^2/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/2*I/f/a/d^2/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))-2/3/a/d/f/(d*tan(f*x+e))^(3/2)+2*I/f/a/d^2/(d*tan(f*x+e))^(1/2)","A"
171,1,188,273,0.276000," ","int((d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 d^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 a^{2} f}-\frac{4 i d^{4} \sqrt{d \tan \left(f x +e \right)}}{f \,a^{2}}-\frac{15 d^{5} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}+\frac{13 i d^{6} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}+\frac{47 d^{5} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{2} \sqrt{-i d}}+\frac{d^{5} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{4 f \,a^{2} \sqrt{i d}}"," ",0,"-2/3*d^3*(d*tan(f*x+e))^(3/2)/a^2/f-4*I/f/a^2*d^4*(d*tan(f*x+e))^(1/2)-15/8/f/a^2*d^5/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(3/2)+13/8*I/f/a^2*d^6/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(1/2)+47/8/f/a^2*d^5/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/4/f/a^2*d^5/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
172,1,168,251,0.268000," ","int((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 d^{3} \sqrt{d \tan \left(f x +e \right)}}{a^{2} f}+\frac{11 i d^{4} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}+\frac{9 d^{5} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{23 i d^{4} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{2} \sqrt{-i d}}+\frac{i d^{4} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{4 f \,a^{2} \sqrt{i d}}"," ",0,"-2*d^3*(d*tan(f*x+e))^(1/2)/a^2/f+11/8*I/f/a^2*d^4/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(3/2)+9/8/f/a^2*d^5/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(1/2)-23/8*I/f/a^2*d^4/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/4*I/f/a^2*d^4/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
173,1,145,230,0.270000," ","int((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x)","\frac{7 d^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{5 i d^{4} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{7 d^{3} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{2} \sqrt{-i d}}-\frac{d^{3} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{4 f \,a^{2} \sqrt{i d}}"," ",0,"7/8/f/a^2*d^3/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(3/2)-5/8*I/f/a^2*d^4/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(1/2)-7/8/f/a^2*d^3/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/4/f/a^2*d^3/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
174,1,147,227,0.266000," ","int((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{3 i d^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{d^{3} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{i d^{2} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{2} \sqrt{-i d}}-\frac{i d^{2} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{4 f \,a^{2} \sqrt{i d}}"," ",0,"-3/8*I/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(3/2)-1/8/f/a^2*d^3/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(1/2)-1/8*I/f/a^2*d^2/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/4*I/f/a^2*d^2/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
175,1,139,227,0.301000," ","int((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x)","\frac{d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{3 i d^{2} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{d \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{2} \sqrt{-i d}}+\frac{d \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{4 f \,a^{2} \sqrt{i d}}"," ",0,"1/8/f/a^2*d/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(3/2)-3/8*I/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(1/2)-1/8/f/a^2*d/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/4/f/a^2*d/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
176,1,136,231,0.329000," ","int(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{5 i \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{7 d \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{7 i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{2} \sqrt{-i d}}+\frac{i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{4 f \,a^{2} \sqrt{i d}}"," ",0,"-5/8*I/f/a^2/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(3/2)-7/8/f/a^2*d/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(1/2)-7/8*I/f/a^2/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/4*I/f/a^2/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
177,1,163,252,0.313000," ","int(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{9 \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} d \left(d \tan \left(f x +e \right)-i d \right)^{2}}+\frac{11 i \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}-\frac{23 \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{2} d \sqrt{-i d}}-\frac{\arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{4 f \,a^{2} d \sqrt{i d}}-\frac{2}{a^{2} d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-9/8/f/a^2/d/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(3/2)+11/8*I/f/a^2/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(1/2)-23/8/f/a^2/d/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/4/f/a^2/d/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))-2/a^2/d/f/(d*tan(f*x+e))^(1/2)","A"
178,1,190,274,0.337000," ","int(1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x)","\frac{13 i \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} d^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2}}+\frac{15 \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{2} d \left(d \tan \left(f x +e \right)-i d \right)^{2}}+\frac{47 i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{2} d^{2} \sqrt{-i d}}-\frac{i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{4 f \,a^{2} d^{2} \sqrt{i d}}-\frac{2}{3 a^{2} d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{4 i}{f \,a^{2} d^{2} \sqrt{d \tan \left(f x +e \right)}}"," ",0,"13/8*I/f/a^2/d^2/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(3/2)+15/8/f/a^2/d/(d*tan(f*x+e)-I*d)^2*(d*tan(f*x+e))^(1/2)+47/8*I/f/a^2/d^2/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/4*I/f/a^2/d^2/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))-2/3/a^2/d/f/(d*tan(f*x+e))^(3/2)+4*I/f/a^2/d^2/(d*tan(f*x+e))^(1/2)","A"
179,1,203,289,0.382000," ","int((d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i d^{4} \sqrt{d \tan \left(f x +e \right)}}{f \,a^{3}}+\frac{5 d^{5} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{2 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{49 i d^{6} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{7 d^{7} \sqrt{d \tan \left(f x +e \right)}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{29 d^{5} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{3} \sqrt{-i d}}+\frac{d^{5} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{8 f \,a^{3} \sqrt{i d}}"," ",0,"2*I/f/a^3*d^4*(d*tan(f*x+e))^(1/2)+5/2/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(5/2)-49/12*I/f/a^3*d^6/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(3/2)-7/4/f/a^3*d^7/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(1/2)-29/8/f/a^3*d^5/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/8/f/a^3*d^5/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
180,1,184,267,0.351000," ","int((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^3,x)","-\frac{9 i d^{4} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{19 d^{5} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}+\frac{5 i d^{6} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}+\frac{3 i d^{4} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{4 f \,a^{3} \sqrt{-i d}}+\frac{i d^{4} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{8 f \,a^{3} \sqrt{i d}}"," ",0,"-9/8*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(5/2)-19/12/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(3/2)+5/8*I/f/a^3*d^6/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(1/2)+3/4*I/f/a^3*d^4/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/8*I/f/a^3*d^4/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
181,1,145,260,0.352000," ","int((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x)","-\frac{d^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}+\frac{i d^{4} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{d^{3} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{3} \sqrt{-i d}}-\frac{d^{3} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{8 f \,a^{3} \sqrt{i d}}"," ",0,"-1/4/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(5/2)+1/12*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(3/2)-1/8/f/a^3*d^3/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/8/f/a^3*d^3/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
182,1,148,130,0.354000," ","int((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x)","-\frac{i d^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{5 d^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}+\frac{i d^{4} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{i d^{2} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{8 f \,a^{3} \sqrt{i d}}"," ",0,"-1/8*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(5/2)-5/12/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(3/2)+1/8*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(1/2)-1/8*I/f/a^3*d^2/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
183,1,141,224,0.391000," ","int((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x)","-\frac{i d^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{d^{3} \sqrt{d \tan \left(f x +e \right)}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{d \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{3} \sqrt{-i d}}+\frac{d \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{8 f \,a^{3} \sqrt{i d}}"," ",0,"-1/12*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(3/2)-1/4/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(1/2)-1/8/f/a^3*d/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/8/f/a^3*d/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
184,1,173,268,0.451000," ","int(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x)","-\frac{5 i \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{19 d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}+\frac{9 i d^{2} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{3 i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{4 f \,a^{3} \sqrt{-i d}}+\frac{i \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{8 f \,a^{3} \sqrt{i d}}"," ",0,"-5/8*I/f/a^3/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(5/2)-19/12/f/a^3*d/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(3/2)+9/8*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(1/2)-3/4*I/f/a^3/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))+1/8*I/f/a^3/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))","A"
185,1,197,289,0.402000," ","int(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x)","-\frac{7 \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{4 f \,a^{3} d \left(d \tan \left(f x +e \right)-i d \right)^{3}}+\frac{49 i \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}+\frac{5 d \sqrt{d \tan \left(f x +e \right)}}{2 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{29 \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{-i d}}\right)}{8 f \,a^{3} d \sqrt{-i d}}-\frac{\arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{i d}}\right)}{8 f \,a^{3} d \sqrt{i d}}-\frac{2}{a^{3} d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-7/4/f/a^3/d/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(5/2)+49/12*I/f/a^3/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(3/2)+5/2/f/a^3*d/(d*tan(f*x+e)-I*d)^3*(d*tan(f*x+e))^(1/2)-29/8/f/a^3/d/(-I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(-I*d)^(1/2))-1/8/f/a^3/d/(I*d)^(1/2)*arctan((d*tan(f*x+e))^(1/2)/(I*d)^(1/2))-2/a^3/d/f/(d*tan(f*x+e))^(1/2)","A"
186,1,472,137,0.319000," ","int((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(\sqrt{\tan}\left(d x +c \right)\right) \left(6 i \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 \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 \tan \left(d x +c \right)+4 i \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 -4 \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)-4 \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 +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}+7 \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}\, \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)*(6*I*(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*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)+4*I*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-4*(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)^2-4*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+2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+7*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"
187,1,229,108,0.251000," ","int((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2),x)","\frac{\left(\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 \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 \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 \right) \left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\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*(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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+I*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)*tan(d*x+c)^(1/2)*(a*(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"
188,1,347,82,0.258000," ","int(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)}\, a \left(i \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}-\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)+2 i \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)+2 \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)\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)*a*(I*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)-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*I*(-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)+2*(-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*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"
189,1,121,40,0.248000," ","int((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x)","-\frac{i \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 \left(\sqrt{\tan}\left(d x +c \right)\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}}{2 d \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}}"," ",0,"-1/2*I/d*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*tan(d*x+c)^(1/2)*(a*(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)","B"
190,1,157,68,0.251000," ","int((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x)","\frac{\left(\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 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right) \sqrt{a \left(1+i \tan \left(d x +c \right)\right)}}{2 d \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{\tan \left(d x +c \right)}}"," ",0,"1/2/d*(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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))*(a*(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)^(1/2)","B"
191,1,196,96,0.253000," ","int((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x)","\frac{\left(3 i \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 -4 i \tan \left(d x +c \right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-4 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\right) \sqrt{a \left(1+i \tan \left(d x +c \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}}"," ",0,"1/6/d/tan(d*x+c)^(3/2)*(3*I*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-4*I*tan(d*x+c)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-4*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))*(a*(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)","B"
192,1,357,123,0.229000," ","int((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 \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 \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 +52 \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)-16 \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}-56 i \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}+12 i \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}\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)/tan(d*x+c)^(5/2)*(15*I*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*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+52*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3-16*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-56*I*tan(d*x+c)^2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)+12*I*(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"
193,1,449,200,0.214000," ","int(tan(d*x+c)^(5/2)*(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)}\, a \left(-16 i \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 \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 +69 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 +54 i \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 \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 -28 \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)+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{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*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*(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+69*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+54*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(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-28*(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)+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)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
194,1,405,171,0.215000," ","int(tan(d*x+c)^(3/2)*(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)}\, a \left(4 i \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 -4 i \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)+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 -4 \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 -10 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}-11 \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*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*a*(4*I*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-4*I*(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)+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)-4*(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-10*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-11*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"
195,1,363,143,0.230000," ","int(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)}\, a \left(i \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 +2 i \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 \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{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 \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}}"," ",0,"1/2/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*a*(I*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+2*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)+3*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)+(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*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"
196,1,326,82,0.239000," ","int((a+I*a*tan(d*x+c))^(3/2)/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(i \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}+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}-\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}-2 \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)\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*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)+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)-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)-2*(-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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
197,1,320,69,0.207000," ","int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(3/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(i \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 +\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 +4 \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 \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)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}}"," ",0,"-1/2/d*(a*(1+I*tan(d*x+c)))^(1/2)*a*(I*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+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+4*(-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*(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)^(1/2)/(-I*a)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)","B"
198,1,370,97,0.216000," ","int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(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 +12 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 +16 i \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 \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)}{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}\, \sqrt{-i a}}"," ",0,"-1/6/d*(a*(1+I*tan(d*x+c)))^(1/2)*a/tan(d*x+c)^(3/2)*(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+12*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+16*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)+4*(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)","B"
199,1,412,159,0.206000," ","int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(7/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(5 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 +5 \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 +20 \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 -8 i \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 \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)-4 \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)}{10 d \tan \left(d x +c \right)^{\frac{5}{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,"1/10/d*(a*(1+I*tan(d*x+c)))^(1/2)*a*(5*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+5*(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+20*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-8*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)+24*(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)^2-4*(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)^(5/2)/(I*a)^(1/2)/(-I*a)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)","B"
200,1,457,188,0.212000," ","int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(9/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a \left(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 +420 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 -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 +152 \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)+536 i \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}-96 i \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 \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)}{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)*(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+420*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-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+152*(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+536*I*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)-96*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)-60*(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)","B"
201,1,492,204,0.213000," ","int(tan(d*x+c)^(5/2)*(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)}\, a^{2} \left(96 \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}-272 i \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}+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 +384 \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 +1089 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 +894 i \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 \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)+1536 \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*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)-272*I*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)+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+384*(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+1089*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+894*I*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-428*(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)+1536*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"
202,1,450,173,0.196000," ","int(tan(d*x+c)^(3/2)*(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)}\, a^{2} \left(48 i \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 -52 i \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)+16 \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)+192 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{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 -135 \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 -114 \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)}{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*(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-52*I*(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)+16*(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+192*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*(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-135*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-114*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2))/(I*a)^(1/2)/(-I*a)^(1/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)","B"
203,1,407,143,0.224000," ","int(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)}\, a^{2} \left(8 i \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 +18 i \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 \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)+23 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{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 +32 \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*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*a^2*(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+18*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-4*(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)+23*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*(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+32*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"
204,1,365,112,0.247000," ","int((a+I*a*tan(d*x+c))^(5/2)/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(-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}-5 \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 i \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 +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 -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) 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*(-2*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-5*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*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+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)-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))*a)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
205,1,388,112,0.217000," ","int((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(3/2),x)","\frac{\left(-i \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 -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 \tan \left(d x +c \right)-\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 -4 \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 \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)}\, a^{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/d*(-I*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-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-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-4*(-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*(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)*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)/(-I*a)^(1/2)","B"
206,1,372,100,0.216000," ","int((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(5/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(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 +12 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 +14 i \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)+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}\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)*(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+12*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+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)+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)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
207,1,414,127,0.217000," ","int((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(7/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(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 +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 +60 \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 -22 i \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)+76 \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)-6 \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)}{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*(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+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+60*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-22*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)+76*(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)^2-6*(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)^(5/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
208,1,459,163,0.215000," ","int((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(9/2),x)","\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(21 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 +84 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 -21 \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 +32 \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)+104 i \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}-18 i \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 \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)}{21 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,"1/21/d*(a*(1+I*tan(d*x+c)))^(1/2)*a^2/tan(d*x+c)^(7/2)*(21*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+84*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-21*(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+32*(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+104*I*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)-18*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)-6*(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)","B"
209,1,501,193,0.217000," ","int((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(11/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(d x +c \right)\right)}\, a^{2} \left(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 +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 +1260 \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 -472 i \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}+1576 \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}+190 i \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)-276 \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)+70 \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)}{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*(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+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+1260*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-472*I*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)+1576*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)+190*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)-276*(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+70*(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)^(9/2)/(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)/(I*a)^(1/2)/(-I*a)^(1/2)","B"
210,1,667,170,0.233000," ","int(tan(d*x+c)^(7/2)/(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(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) \left(\tan^{2}\left(d x +c \right)\right) a +4 i \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}-2 i \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 -22 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 \tan \left(d x +c \right)+16 i \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 \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 +11 \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) \left(\tan^{2}\left(d x +c \right)\right) a +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}\, \left(\tan^{2}\left(d x +c \right)\right)-11 \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 +14 \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)}{8 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,"-1/8/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*(2*I*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+4*I*(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)^3-2*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))*a-22*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+16*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)+4*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+11*(-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)^2*a+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)^2-11*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+14*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(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)^2","B"
211,1,620,140,0.218000," ","int(tan(d*x+c)^(5/2)/(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(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 -\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 \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 i \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}+\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 -8 i \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 \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 +12 \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)\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*(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-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*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*I*(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+(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))*(-I*a)^(1/2)*a-8*I*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-4*(-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+12*(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))/(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"
212,1,580,109,0.230000," ","int(tan(d*x+c)^(3/2)/(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 \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 -i \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 +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}\, \sqrt{2}\, \tan \left(d x +c \right) 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 \tan \left(d x +c \right)+4 \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) \left(\tan^{2}\left(d x +c \right)\right) a +4 i \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 \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{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*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-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)+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)*2^(1/2)*tan(d*x+c)*a-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))*(-I*a)^(1/2)*tan(d*x+c)*a+4*(-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)^2*a+4*I*(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*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*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"
213,1,350,69,0.239000," ","int(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(2 i \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{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 -4 i \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \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 \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}\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)/a*(2*I*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^(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-4*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-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))*a+4*tan(d*x+c)*(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"
214,1,352,67,0.236000," ","int(1/(a+I*a*tan(d*x+c))^(1/2)/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) \left(i \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 \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 \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 \tan \left(d x +c \right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+4 \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*(a*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^(1/2)/a*(I*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*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*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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+4*(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"
215,1,395,97,0.234000," ","int(1/(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(2 i \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 -\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 \tan \left(d x +c \right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+\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 \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)-8 \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)*(2*I*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^(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*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)+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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-8*(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"
216,1,398,128,0.236000," ","int(1/(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 \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 i \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 \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 +36 \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)+28 i \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)+8 \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*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*I*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*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+36*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+28*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+8*(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"
217,1,473,158,0.236000," ","int(1/(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(30 i \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 \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 -396 i \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 \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 \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)+16 i \tan \left(d x +c \right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-144 \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)+24 \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)*(30*I*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*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-396*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+15*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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^4+16*I*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-144*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+24*(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"
218,1,811,170,0.204000," ","int(tan(d*x+c)^(7/2)/(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 \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 \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}-9 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 +9 \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 +108 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 -140 i \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}-36 \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 -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) a -36 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 +84 i \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i a}+108 \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 -200 \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)\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/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)/a^2*(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)^3*a+24*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)-9*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+9*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+108*I*(-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)^2*a-140*I*(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)^2-36*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-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))*a-36*I*(-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+84*I*(I*a)^(1/2)*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)+108*(-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-200*(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))/(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"
219,1,771,140,0.184000," ","int(tan(d*x+c)^(5/2)/(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(9 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 +24 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 -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^{3}\left(d x +c \right)\right) a -3 i \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 -72 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 \tan \left(d x +c \right)+80 i \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)+9 \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 +72 \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) \left(\tan^{2}\left(d x +c \right)\right) a -44 \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)-24 \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 +36 \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)}{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}\, \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)*(9*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+24*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-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)^3*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))*a-72*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+80*I*(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)+9*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+72*(-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)^2*a-44*(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)^2-24*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+36*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(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)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^3","B"
220,1,464,99,0.181000," ","int(tan(d*x+c)^(3/2)/(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 \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 \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 -20 i \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 \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 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-3 \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 \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}\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}}"," ",0,"-1/24/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)/a^2*(3*I*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*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-20*I*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2+9*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*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-3*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*tan(d*x+c)*(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)^3/(-I*a)^(1/2)","B"
221,1,463,99,0.204000," ","int(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(4 \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 \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 \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 \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 \tan \left(d x +c \right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}+9 \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 \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*(4*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+9*I*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*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*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*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)+9*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*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"
222,1,464,98,0.221000," ","int(1/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 \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 \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 \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 \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 i \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-3 \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 \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}\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*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*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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+9*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*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-3*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*tan(d*x+c)*(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"
223,1,509,128,0.193000," ","int(1/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(9 i \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 \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 i \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 \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 \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 \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)+48 i \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-204 \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}\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)*(9*I*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*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*I*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*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2+9*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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+48*I*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-204*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2))/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"
224,1,549,159,0.192000," ","int(1/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(3 i \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 \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)-9 i \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 +156 i \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)+9 \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 -32 \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}-276 i \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)-3 \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 \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} \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)^{3} \sqrt{-i a}}"," ",0,"-1/24/d*(a*(1+I*tan(d*x+c)))^(1/2)/a^2/tan(d*x+c)^(3/2)*(3*I*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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3-9*I*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+156*I*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^4+9*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-32*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-276*I*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^2-3*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*(-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)","B"
225,1,1007,201,0.195000," ","int(tan(d*x+c)^(9/2)/(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(2228 \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}-600 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 +60 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 +240 i \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^{4}\left(d x +c \right)\right)-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^{4}\left(d x +c \right)\right) a -60 i \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 -600 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 -4948 i \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}+90 \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 -2400 \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 +3600 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 +1260 i \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{i a}\, \sqrt{-i 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) a +2400 \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 -4220 \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)\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*(2228*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)-600*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+60*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+240*I*(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)^4-15*(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)^4*a-60*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-600*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-4948*I*(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+90*(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-2400*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+3600*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+1260*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2)-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))*a+2400*(-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-4220*(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))/(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"
226,1,963,170,0.190000," ","int(tan(d*x+c)^(7/2)/(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(5 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 -30 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 -320 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 +196 i \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}+20 \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 \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 +5 i \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 +320 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 \tan \left(d x +c \right)-460 i \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)-20 \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 -480 \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) \left(\tan^{2}\left(d x +c \right)\right) a +516 \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)+80 \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 -140 \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)}{80 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,"-1/80/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)*(5*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-30*I*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-320*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+196*I*(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)^3+20*(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*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+5*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+320*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-460*I*(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)-20*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-480*(-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)^2*a+516*(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+80*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-140*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(I*a)^(1/2)*(-I*a)^(1/2))/a^3/(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"
227,1,575,130,0.189000," ","int(tan(d*x+c)^(5/2)/(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(148 \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 \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 \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 \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 \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)+90 \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 \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-15 \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 \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}\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*(148*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+60*I*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*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*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*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2+90*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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-15*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*tan(d*x+c)*(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"
228,1,576,129,0.184000," ","int(tan(d*x+c)^(3/2)/(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(15 i \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 \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)-90 i \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 -52 i \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 \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 i \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 i \tan \left(d x +c \right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-60 \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 \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*(15*I*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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-90*I*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-52*I*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3+60*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*I*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*I*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)-60*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*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"
229,1,575,131,0.212000," ","int(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(20 i \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 -5 \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 -4 \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 \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 +30 \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 +4 i \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)-5 \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 +20 i \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}\, \sqrt{-i a}-20 \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}\right)}{80 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,"1/80/d*tan(d*x+c)^(1/2)*(a*(1+I*tan(d*x+c)))^(1/2)/a^3*(20*I*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-5*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-4*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3-20*I*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+30*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+4*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-5*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+20*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)-20*tan(d*x+c)*(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"
230,1,576,128,0.228000," ","int(1/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(15 i \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 i \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 +268 i \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 \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 i \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 -1060 i \tan \left(d x +c \right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-60 \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 \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)-420 \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)*(15*I*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-90*I*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+268*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+60*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*I*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-1060*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-60*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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-420*(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"
231,1,620,158,0.196000," ","int(1/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(1268 \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 \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 \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 -5660 \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)-60 i \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 -4468 i \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)+90 \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 +2940 i \tan \left(d x +c \right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-15 \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 +480 \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*(1268*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^4+60*I*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*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-5660*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-60*I*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-4468*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^3+90*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+2940*I*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)-15*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+480*(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"
232,1,661,189,0.197000," ","int(1/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(15 i \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 -90 i \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 +2828 i \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 \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 \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 -12260 i \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 \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 \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)+640 i \tan \left(d x +c \right) \sqrt{-i a}\, \sqrt{a \tan \left(d x +c \right) \left(1+i \tan \left(d x +c \right)\right)}-6020 \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)-160 \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)}\, \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)*(15*I*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-90*I*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+2828*I*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^5+60*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*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-12260*I*(-I*a)^(1/2)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*tan(d*x+c)^3-60*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*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^4+640*I*(-I*a)^(1/2)*tan(d*x+c)*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)-6020*(a*tan(d*x+c)*(1+I*tan(d*x+c)))^(1/2)*(-I*a)^(1/2)*tan(d*x+c)^2-160*(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)/(-I*a)^(1/2)/(-tan(d*x+c)+I)^4","B"
233,1,291,275,0.316000," ","int(tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c)),x)","\frac{3 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{d a}-\frac{3 i \left(\tan^{\frac{4}{3}}\left(d x +c \right)\right)}{4 d a}-\frac{17 i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{12 d a}+\frac{1}{6 d a \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}+\frac{i \ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{8 d a}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{4 d a}-\frac{\tan^{\frac{1}{3}}\left(d x +c \right)}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}-\frac{i}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}+\frac{17 i \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{24 d a}-\frac{17 \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{12 d a}-\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{4 d a}"," ",0,"3*tan(d*x+c)^(1/3)/d/a-3/4*I/d/a*tan(d*x+c)^(4/3)-17/12*I/d/a*ln(tan(d*x+c)^(1/3)+I)+1/6/d/a/(tan(d*x+c)^(1/3)+I)+1/8*I/d/a*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/4/d/a*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/6/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)*tan(d*x+c)^(1/3)-1/6*I/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+17/24*I/d/a*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-17/12/d/a*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/4*I/d/a*ln(tan(d*x+c)^(1/3)-I)","A"
234,1,275,259,0.262000," ","int(tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c)),x)","-\frac{3 i \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{2 d a}+\frac{13 i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{12 d a}-\frac{1}{6 d a \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}-\frac{i \ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{8 d a}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{4 d a}-\frac{\tan^{\frac{1}{3}}\left(d x +c \right)}{3 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}+\frac{i}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}-\frac{13 i \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{24 d a}-\frac{13 \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{12 d a}+\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{4 d a}"," ",0,"-3/2*I/d/a*tan(d*x+c)^(2/3)+13/12*I/d/a*ln(tan(d*x+c)^(1/3)+I)-1/6/d/a/(tan(d*x+c)^(1/3)+I)-1/8*I/d/a*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/4/d/a*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/3/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)*tan(d*x+c)^(1/3)+1/6*I/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-13/24*I/d/a*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-13/12/d/a*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/4*I/d/a*ln(tan(d*x+c)^(1/3)-I)","A"
235,1,258,242,0.263000," ","int(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c)),x)","\frac{5 i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{12 d a}-\frac{1}{6 d a \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}-\frac{i \ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{8 d a}-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{4 d a}+\frac{\tan^{\frac{1}{3}}\left(d x +c \right)}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}+\frac{i}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}-\frac{5 i \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{24 d a}+\frac{5 \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{12 d a}+\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{4 d a}"," ",0,"5/12*I/d/a*ln(tan(d*x+c)^(1/3)+I)-1/6/d/a/(tan(d*x+c)^(1/3)+I)-1/8*I/d/a*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-1/4/d/a*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/6/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)*tan(d*x+c)^(1/3)+1/6*I/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-5/24*I/d/a*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+5/12/d/a*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/4*I/d/a*ln(tan(d*x+c)^(1/3)-I)","A"
236,1,258,243,0.264000," ","int(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c)),x)","-\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{12 d a}+\frac{1}{6 d a \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}+\frac{i \ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{8 d a}-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{4 d a}+\frac{\tan^{\frac{1}{3}}\left(d x +c \right)}{3 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}-\frac{i}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}+\frac{i \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{24 d a}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{12 d a}-\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{4 d a}"," ",0,"-1/12*I/d/a*ln(tan(d*x+c)^(1/3)+I)+1/6/d/a/(tan(d*x+c)^(1/3)+I)+1/8*I/d/a*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-1/4/d/a*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/3/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)*tan(d*x+c)^(1/3)-1/6*I/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/24*I/d/a*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/12/d/a*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/4*I/d/a*ln(tan(d*x+c)^(1/3)-I)","A"
237,1,257,244,0.248000," ","int(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c)),x)","-\frac{i}{6 d a \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}+\frac{5 \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{12 d a}-\frac{\ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{8 d a}-\frac{i \sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{4 d a}-\frac{i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{3 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}-\frac{1}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}-\frac{5 \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{24 d a}+\frac{5 i \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{12 d a}+\frac{\ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{4 d a}"," ",0,"-1/6*I/d/a/(tan(d*x+c)^(1/3)+I)+5/12/d/a*ln(tan(d*x+c)^(1/3)+I)-1/8/d/a*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-1/4*I/d/a*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/3*I/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)*tan(d*x+c)^(1/3)-1/6/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-5/24/d/a*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+5/12*I/d/a*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/4/d/a*ln(tan(d*x+c)^(1/3)-I)","A"
238,1,273,260,0.268000," ","int(1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c)),x)","-\frac{i}{6 d a \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}+\frac{13 \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{12 d a}-\frac{\ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{8 d a}+\frac{i \sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{4 d a}-\frac{3}{2 a d \tan \left(d x +c \right)^{\frac{2}{3}}}+\frac{i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}-\frac{1}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}-\frac{13 \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{24 d a}-\frac{13 i \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{12 d a}+\frac{\ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{4 d a}"," ",0,"-1/6*I/d/a/(tan(d*x+c)^(1/3)+I)+13/12/d/a*ln(tan(d*x+c)^(1/3)+I)-1/8/d/a*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/4*I/d/a*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-3/2/a/d/tan(d*x+c)^(2/3)+1/6*I/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)*tan(d*x+c)^(1/3)-1/6/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-13/24/d/a*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-13/12*I/d/a*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/4/d/a*ln(tan(d*x+c)^(1/3)-I)","A"
239,1,290,277,0.262000," ","int(1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c)),x)","\frac{i}{6 d a \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}-\frac{17 \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{12 d a}+\frac{\ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{8 d a}+\frac{i \sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{4 d a}-\frac{3}{4 a d \tan \left(d x +c \right)^{\frac{4}{3}}}+\frac{3 i}{d a \tan \left(d x +c \right)^{\frac{1}{3}}}+\frac{i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{3 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}+\frac{1}{6 d a \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}+\frac{17 \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{24 d a}-\frac{17 i \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{12 d a}-\frac{\ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{4 d a}"," ",0,"1/6*I/d/a/(tan(d*x+c)^(1/3)+I)-17/12/d/a*ln(tan(d*x+c)^(1/3)+I)+1/8/d/a*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/4*I/d/a*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-3/4/a/d/tan(d*x+c)^(4/3)+3*I/d/a/tan(d*x+c)^(1/3)+1/3*I/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)*tan(d*x+c)^(1/3)+1/6/d/a/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+17/24/d/a*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-17/12*I/d/a*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/4/d/a*ln(tan(d*x+c)^(1/3)-I)","A"
240,1,390,305,0.328000," ","int(tan(d*x+c)^(14/3)/(a+I*a*tan(d*x+c))^2,x)","-\frac{3 \left(\tan^{\frac{5}{3}}\left(d x +c \right)\right)}{5 a^{2} d}-\frac{3 i \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{d \,a^{2}}+\frac{i}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)^{2}}+\frac{233 i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{72 d \,a^{2}}-\frac{23}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}+\frac{i \ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{16 d \,a^{2}}-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{8 d \,a^{2}}+\frac{17 i \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{9 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{65 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{36 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{23 \tan \left(d x +c \right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{11 i}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{233 i \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{144 d \,a^{2}}-\frac{233 \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{72 d \,a^{2}}-\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"-3/5*tan(d*x+c)^(5/3)/a^2/d-3*I/d/a^2*tan(d*x+c)^(2/3)+1/36*I/d/a^2/(tan(d*x+c)^(1/3)+I)^2+233/72*I/d/a^2*ln(tan(d*x+c)^(1/3)+I)-23/36/d/a^2/(tan(d*x+c)^(1/3)+I)+1/16*I/d/a^2*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-1/8/d/a^2*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))+17/9*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(2/3)+65/36/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(1/3)-23/18/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)-11/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2-233/144*I/d/a^2*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-233/72/d/a^2*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/8*I/d/a^2*ln(tan(d*x+c)^(1/3)-I)","A"
241,1,373,288,0.322000," ","int(tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c))^2,x)","-\frac{3 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{a^{2} d}+\frac{i}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)^{2}}+\frac{89 i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{72 d \,a^{2}}-\frac{5}{12 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}+\frac{i \ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{16 d \,a^{2}}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{8 d \,a^{2}}+\frac{i \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{\tan^{\frac{1}{3}}\left(d x +c \right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{5 \tan \left(d x +c \right)}{12 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{7 i}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{89 i \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{144 d \,a^{2}}+\frac{89 \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{72 d \,a^{2}}-\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"-3*tan(d*x+c)^(1/3)/a^2/d+1/36*I/d/a^2/(tan(d*x+c)^(1/3)+I)^2+89/72*I/d/a^2*ln(tan(d*x+c)^(1/3)+I)-5/12/d/a^2/(tan(d*x+c)^(1/3)+I)+1/16*I/d/a^2*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/8/d/a^2*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(2/3)+1/18/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(1/3)+5/12/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)-7/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2-89/144*I/d/a^2*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+89/72/d/a^2*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/8*I/d/a^2*ln(tan(d*x+c)^(1/3)-I)","A"
242,1,357,272,0.294000," ","int(tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c))^2,x)","-\frac{41 i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{72 d \,a^{2}}-\frac{i}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)^{2}}+\frac{11}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}-\frac{i \ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{16 d \,a^{2}}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{8 d \,a^{2}}-\frac{8 i \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{9 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{29 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{36 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{11 \tan \left(d x +c \right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{5 i}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{41 i \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{144 d \,a^{2}}+\frac{41 \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{72 d \,a^{2}}+\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"-41/72*I/d/a^2*ln(tan(d*x+c)^(1/3)+I)-1/36*I/d/a^2/(tan(d*x+c)^(1/3)+I)^2+11/36/d/a^2/(tan(d*x+c)^(1/3)+I)-1/16*I/d/a^2*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/8/d/a^2*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-8/9*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(2/3)-29/36/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(1/3)+11/18/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)+5/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2+41/144*I/d/a^2*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+41/72/d/a^2*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/8*I/d/a^2*ln(tan(d*x+c)^(1/3)-I)","A"
243,1,357,271,0.311000," ","int(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^2,x)","-\frac{i}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)^{2}}+\frac{7 i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{72 d \,a^{2}}+\frac{1}{12 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}-\frac{i \ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{16 d \,a^{2}}-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{8 d \,a^{2}}-\frac{i \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{\tan^{\frac{1}{3}}\left(d x +c \right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{\tan \left(d x +c \right)}{12 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{i}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{7 i \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{144 d \,a^{2}}+\frac{7 \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{72 d \,a^{2}}+\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"-1/36*I/d/a^2/(tan(d*x+c)^(1/3)+I)^2+7/72*I/d/a^2*ln(tan(d*x+c)^(1/3)+I)+1/12/d/a^2/(tan(d*x+c)^(1/3)+I)-1/16*I/d/a^2*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-1/8/d/a^2*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(2/3)-1/18/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(1/3)-1/12/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)+1/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2-7/144*I/d/a^2*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+7/72/d/a^2*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/8*I/d/a^2*ln(tan(d*x+c)^(1/3)-I)","A"
244,1,357,272,0.317000," ","int(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^2,x)","-\frac{7 i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{72 d \,a^{2}}+\frac{i}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)^{2}}+\frac{1}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}+\frac{i \ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{16 d \,a^{2}}-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{8 d \,a^{2}}-\frac{i \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{9 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{7 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{36 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{\tan \left(d x +c \right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{i}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{7 i \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{144 d \,a^{2}}+\frac{7 \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{72 d \,a^{2}}-\frac{i \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"-7/72*I/d/a^2*ln(tan(d*x+c)^(1/3)+I)+1/36*I/d/a^2/(tan(d*x+c)^(1/3)+I)^2+1/36/d/a^2/(tan(d*x+c)^(1/3)+I)+1/16*I/d/a^2*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-1/8/d/a^2*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/9*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(2/3)-7/36/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(1/3)+1/18/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)+1/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2+7/144*I/d/a^2*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+7/72/d/a^2*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/8*I/d/a^2*ln(tan(d*x+c)^(1/3)-I)","A"
245,1,355,273,0.280000," ","int(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^2,x)","-\frac{7 i}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}+\frac{1}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)^{2}}+\frac{23 \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{72 d \,a^{2}}-\frac{\ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{16 d \,a^{2}}-\frac{i \sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{8 d \,a^{2}}-\frac{11 \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{25 i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{36 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{7 i \tan \left(d x +c \right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{2}{9 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{23 \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{144 d \,a^{2}}+\frac{23 i \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{72 d \,a^{2}}+\frac{\ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"-7/36*I/d/a^2/(tan(d*x+c)^(1/3)+I)+1/36/d/a^2/(tan(d*x+c)^(1/3)+I)^2+23/72/d/a^2*ln(tan(d*x+c)^(1/3)+I)-1/16/d/a^2*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-1/8*I/d/a^2*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-11/18/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(2/3)+25/36*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(1/3)-7/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)+2/9/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2-23/144/d/a^2*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+23/72*I/d/a^2*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/8/d/a^2*ln(tan(d*x+c)^(1/3)-I)","A"
246,1,371,289,0.292000," ","int(1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c))^2,x)","-\frac{5 i}{12 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}+\frac{1}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)^{2}}+\frac{119 \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{72 d \,a^{2}}-\frac{\ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{16 d \,a^{2}}+\frac{i \sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{8 d \,a^{2}}-\frac{3}{2 a^{2} d \tan \left(d x +c \right)^{\frac{2}{3}}}+\frac{\tan^{\frac{2}{3}}\left(d x +c \right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{5 i \tan \left(d x +c \right)}{12 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{4}{9 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{119 \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{144 d \,a^{2}}-\frac{119 i \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{72 d \,a^{2}}+\frac{\ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"-5/12*I/d/a^2/(tan(d*x+c)^(1/3)+I)+1/36/d/a^2/(tan(d*x+c)^(1/3)+I)^2+119/72/d/a^2*ln(tan(d*x+c)^(1/3)+I)-1/16/d/a^2*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/8*I/d/a^2*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-3/2/a^2/d/tan(d*x+c)^(2/3)+1/18/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(2/3)-1/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(1/3)+5/12*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)+4/9/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2-119/144/d/a^2*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-119/72*I/d/a^2*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))+1/8/d/a^2*ln(tan(d*x+c)^(1/3)-I)","A"
247,1,388,306,0.293000," ","int(1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c))^2,x)","\frac{19 i}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}-\frac{1}{36 d \,a^{2} \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)^{2}}-\frac{191 \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+i\right)}{72 d \,a^{2}}+\frac{\ln \left(i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{16 d \,a^{2}}+\frac{i \sqrt{3}\, \arctanh \left(\frac{\left(i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{8 d \,a^{2}}-\frac{3}{4 a^{2} d \tan \left(d x +c \right)^{\frac{4}{3}}}+\frac{6 i}{d \,a^{2} \tan \left(d x +c \right)^{\frac{1}{3}}}+\frac{29 \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{61 i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{36 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{19 i \tan \left(d x +c \right)}{18 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}-\frac{5}{9 d \,a^{2} \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)^{2}}+\frac{191 \ln \left(-i \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)-1\right)}{144 d \,a^{2}}-\frac{191 i \sqrt{3}\, \arctanh \left(\frac{\left(-i+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}}{3}\right)}{72 d \,a^{2}}-\frac{\ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)-i\right)}{8 d \,a^{2}}"," ",0,"19/36*I/d/a^2/(tan(d*x+c)^(1/3)+I)-1/36/d/a^2/(tan(d*x+c)^(1/3)+I)^2-191/72/d/a^2*ln(tan(d*x+c)^(1/3)+I)+1/16/d/a^2*ln(I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)+1/8*I/d/a^2*3^(1/2)*arctanh(1/3*(I+2*tan(d*x+c)^(1/3))*3^(1/2))-3/4/a^2/d/tan(d*x+c)^(4/3)+6*I/d/a^2/tan(d*x+c)^(1/3)+29/18/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(2/3)-61/36*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)^(1/3)+19/18*I/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2*tan(d*x+c)-5/9/d/a^2/(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)^2+191/144/d/a^2*ln(-I*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3)-1)-191/72*I/d/a^2*3^(1/2)*arctanh(1/3*(-I+2*tan(d*x+c)^(1/3))*3^(1/2))-1/8/d/a^2*ln(tan(d*x+c)^(1/3)-I)","A"
248,0,0,64,1.391000," ","int(tan(d*x+c)^(4/3)*(a+I*a*tan(d*x+c))^(1/2),x)","\int \left(\tan^{\frac{4}{3}}\left(d x +c \right)\right) \sqrt{a +i a \tan \left(d x +c \right)}\, dx"," ",0,"int(tan(d*x+c)^(4/3)*(a+I*a*tan(d*x+c))^(1/2),x)","F"
249,0,0,64,1.381000," ","int(tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(1/2),x)","\int \left(\tan^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{a +i a \tan \left(d x +c \right)}\, dx"," ",0,"int(tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(1/2),x)","F"
250,0,0,64,1.376000," ","int(tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(1/2),x)","\int \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right) \sqrt{a +i a \tan \left(d x +c \right)}\, dx"," ",0,"int(tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(1/2),x)","F"
251,0,0,64,1.580000," ","int((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x)","\int \frac{\sqrt{a +i a \tan \left(d x +c \right)}}{\tan \left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x)","F"
252,0,0,64,1.434000," ","int((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x)","\int \frac{\sqrt{a +i a \tan \left(d x +c \right)}}{\tan \left(d x +c \right)^{\frac{2}{3}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x)","F"
253,0,0,64,1.418000," ","int((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x)","\int \frac{\sqrt{a +i a \tan \left(d x +c \right)}}{\tan \left(d x +c \right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x)","F"
254,0,0,64,1.342000," ","int(tan(d*x+c)^(4/3)*(a+I*a*tan(d*x+c))^(3/2),x)","\int \left(\tan^{\frac{4}{3}}\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)^(4/3)*(a+I*a*tan(d*x+c))^(3/2),x)","F"
255,0,0,64,1.319000," ","int(tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(3/2),x)","\int \left(\tan^{\frac{2}{3}}\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)^(2/3)*(a+I*a*tan(d*x+c))^(3/2),x)","F"
256,0,0,64,1.342000," ","int(tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(3/2),x)","\int \left(\tan^{\frac{1}{3}}\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)^(1/3)*(a+I*a*tan(d*x+c))^(3/2),x)","F"
257,0,0,64,1.442000," ","int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/3),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{\tan \left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/3),x)","F"
258,0,0,64,1.363000," ","int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(2/3),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{\tan \left(d x +c \right)^{\frac{2}{3}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(2/3),x)","F"
259,0,0,64,1.359000," ","int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(4/3),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{\tan \left(d x +c \right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(4/3),x)","F"
260,0,0,63,1.397000," ","int(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{\tan^{\frac{4}{3}}\left(d x +c \right)}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(1/2),x)","F"
261,0,0,63,1.492000," ","int(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{\tan^{\frac{2}{3}}\left(d x +c \right)}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(1/2),x)","F"
262,0,0,63,1.386000," ","int(tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{\tan^{\frac{1}{3}}\left(d x +c \right)}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x)","F"
263,0,0,63,1.520000," ","int(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x)","\int \frac{1}{\sqrt{a +i a \tan \left(d x +c \right)}\, \tan \left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x)","F"
264,0,0,63,1.427000," ","int(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x)","\int \frac{1}{\sqrt{a +i a \tan \left(d x +c \right)}\, \tan \left(d x +c \right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x)","F"
265,0,0,63,1.442000," ","int(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x)","\int \frac{1}{\sqrt{a +i a \tan \left(d x +c \right)}\, \tan \left(d x +c \right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x)","F"
266,0,0,66,1.332000," ","int(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x)","\int \frac{\tan^{\frac{4}{3}}\left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x)","F"
267,0,0,66,1.429000," ","int(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x)","\int \frac{\tan^{\frac{2}{3}}\left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x)","F"
268,0,0,66,1.328000," ","int(tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x)","\int \frac{\tan^{\frac{1}{3}}\left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x)","F"
269,0,0,66,1.470000," ","int(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x)","\int \frac{1}{\tan \left(d x +c \right)^{\frac{1}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x)","F"
270,0,0,66,1.408000," ","int(1/tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x)","\int \frac{1}{\tan \left(d x +c \right)^{\frac{2}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x)","F"
271,0,0,66,1.398000," ","int(1/tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x)","\int \frac{1}{\tan \left(d x +c \right)^{\frac{4}{3}} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x)","F"
272,1,198,178,0.163000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x)","-\frac{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{3}}}{7 d \,a^{2}}+\frac{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}{4 d a}-\frac{3 \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)}{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)}{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)}{2 d}"," ",0,"-3/7/d/a^2*(a+I*a*tan(d*x+c))^(7/3)+3/4*(a+I*a*tan(d*x+c))^(4/3)/d/a-3*(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))+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))+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))","A"
273,1,161,135,0.156000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x)","-\frac{3 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}{4 d a}-\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)}{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{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)}{4 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)}{2 d}"," ",0,"-3/4*I*(a+I*a*tan(d*x+c))^(4/3)/d/a-1/2*I*a^(1/3)/d*2^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))+1/4*I*a^(1/3)/d*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))+1/2*I*a^(1/3)/d*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"
274,1,154,129,0.133000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x)","\frac{3 \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)}{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)}{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)}{2 d}"," ",0,"3*(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))-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))-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))","A"
275,1,138,112,0.118000," ","int((a+I*a*tan(d*x+c))^(1/3),x)","\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)}{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{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)}{4 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)}{2 d}"," ",0,"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))-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))-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"
276,0,0,194,0.834000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x)","\int \cot \left(d x +c \right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x)","F"
277,0,0,224,0.753000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x)","F"
278,0,0,247,0.786000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x)","F"
279,1,138,112,0.109000," ","int((a+I*a*tan(d*x+c))^(2/3),x)","\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)}{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)}{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)}{2 d}"," ",0,"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))-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))+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"
280,1,217,197,0.150000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x)","-\frac{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{10}{3}}}{10 d \,a^{2}}+\frac{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{3}}}{7 d a}-\frac{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}{4 d}-\frac{3 a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{d}-\frac{a^{\frac{4}{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)}{d}+\frac{a^{\frac{4}{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)}{2 d}+\frac{a^{\frac{4}{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)}{d}"," ",0,"-3/10/d/a^2*(a+I*a*tan(d*x+c))^(10/3)+3/7*(a+I*a*tan(d*x+c))^(7/3)/d/a-3/4*(a+I*a*tan(d*x+c))^(4/3)/d-3*a*(a+I*a*tan(d*x+c))^(1/3)/d-1/d*a^(4/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))+1/2/d*a^(4/3)*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))+1/d*a^(4/3)*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"
281,1,182,156,0.152000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x)","-\frac{3 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{3}}}{7 d a}-\frac{3 i a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{d}-\frac{i a^{\frac{4}{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)}{d}+\frac{i a^{\frac{4}{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)}{2 d}+\frac{i a^{\frac{4}{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)}{d}"," ",0,"-3/7*I*(a+I*a*tan(d*x+c))^(7/3)/d/a-3*I*a*(a+I*a*tan(d*x+c))^(1/3)/d-I/d*a^(4/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))+1/2*I/d*a^(4/3)*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))+I/d*a^(4/3)*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"
282,1,173,149,0.129000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x)","\frac{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}{4 d}+\frac{3 a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{d}+\frac{a^{\frac{4}{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)}{d}-\frac{a^{\frac{4}{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)}{2 d}-\frac{a^{\frac{4}{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)}{d}"," ",0,"3/4*(a+I*a*tan(d*x+c))^(4/3)/d+3*a*(a+I*a*tan(d*x+c))^(1/3)/d+1/d*a^(4/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/2/d*a^(4/3)*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))-1/d*a^(4/3)*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"
283,1,159,133,0.103000," ","int((a+I*a*tan(d*x+c))^(4/3),x)","\frac{3 i a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{d}+\frac{i a^{\frac{4}{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)}{d}-\frac{i a^{\frac{4}{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)}{2 d}-\frac{i a^{\frac{4}{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)}{d}"," ",0,"3*I*a*(a+I*a*tan(d*x+c))^(1/3)/d+I/d*a^(4/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/2*I/d*a^(4/3)*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))-I/d*a^(4/3)*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"
284,0,0,193,0.814000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x)","\int \cot \left(d x +c \right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cot(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x)","F"
285,0,0,245,0.746000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x)","F"
286,0,0,248,0.803000," ","int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x)","F"
287,1,159,133,0.101000," ","int((a+I*a*tan(d*x+c))^(5/3),x)","\frac{3 i a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{2 d}+\frac{i a^{\frac{5}{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)}{d}-\frac{i a^{\frac{5}{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)}{2 d}+\frac{i a^{\frac{5}{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)}{d}"," ",0,"3/2*I*a*(a+I*a*tan(d*x+c))^(2/3)/d+I/d*a^(5/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/2*I/d*a^(5/3)*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))+I/d*a^(5/3)*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"
288,0,0,73,0.849000," ","int(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(1/3),x)","\int \frac{\tan^{m}\left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(1/3),x)","F"
289,0,0,63,1.128000," ","int(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/3),x)","\int \frac{\sqrt{\tan}\left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/3),x)","F"
290,1,227,213,0.142000," ","int(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/3),x)","\frac{3 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{8}{3}}}{8 d \,a^{3}}-\frac{6 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{3}}}{5 d \,a^{2}}+\frac{3 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{d a}+\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)}{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{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)}{8 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)}{4 d \,a^{\frac{1}{3}}}+\frac{3 i}{2 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}"," ",0,"3/8*I/d/a^3*(a+I*a*tan(d*x+c))^(8/3)-6/5*I/d/a^2*(a+I*a*tan(d*x+c))^(5/3)+3*I/d/a*(a+I*a*tan(d*x+c))^(2/3)+1/4*I/d/a^(1/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/8*I/d/a^(1/3)*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))+1/4*I/d/a^(1/3)*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))+3/2*I/d/(a+I*a*tan(d*x+c))^(1/3)","A"
291,1,198,178,0.128000," ","int(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/3),x)","-\frac{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{3}}}{5 d \,a^{2}}+\frac{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{2 d a}-\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)}{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)}{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)}{4 d \,a^{\frac{1}{3}}}+\frac{3}{2 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}"," ",0,"-3/5/d/a^2*(a+I*a*tan(d*x+c))^(5/3)+3/2*(a+I*a*tan(d*x+c))^(2/3)/d/a-1/4/d/a^(1/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))+1/8/d/a^(1/3)*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))-1/4/d/a^(1/3)*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))+3/2/d/(a+I*a*tan(d*x+c))^(1/3)","A"
292,1,181,155,0.129000," ","int(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x)","-\frac{3 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{2 d a}-\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)}{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{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)}{8 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)}{4 d \,a^{\frac{1}{3}}}-\frac{3 i}{2 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}"," ",0,"-3/2*I*(a+I*a*tan(d*x+c))^(2/3)/d/a-1/4*I/d/a^(1/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))+1/8*I/d/a^(1/3)*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))-1/4*I/d/a^(1/3)*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))-3/2*I/d/(a+I*a*tan(d*x+c))^(1/3)","A"
293,1,154,129,0.122000," ","int(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)}{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)}{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)}{4 d \,a^{\frac{1}{3}}}-\frac{3}{2 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}"," ",0,"1/4/d/a^(1/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/8/d/a^(1/3)*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))+1/4/d/a^(1/3)*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))-3/2/d/(a+I*a*tan(d*x+c))^(1/3)","A"
294,1,158,132,0.102000," ","int(1/(a+I*a*tan(d*x+c))^(1/3),x)","\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)}{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{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)}{8 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)}{4 d \,a^{\frac{1}{3}}}+\frac{3 i}{2 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}"," ",0,"1/4*I/d/a^(1/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/8*I/d/a^(1/3)*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))+1/4*I/d/a^(1/3)*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))+3/2*I/d/(a+I*a*tan(d*x+c))^(1/3)","A"
295,0,0,212,0.792000," ","int(cot(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x)","\int \frac{\cot \left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cot(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x)","F"
296,0,0,244,0.792000," ","int(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x)","\int \frac{\cot^{2}\left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x)","F"
297,1,158,132,0.113000," ","int(1/(a+I*a*tan(d*x+c))^(2/3),x)","\frac{3 i}{4 d \left(a +i a \tan \left(d x +c \right)\right)^{\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)}{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{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)}{8 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)}{4 d \,a^{\frac{2}{3}}}"," ",0,"3/4*I/d/(a+I*a*tan(d*x+c))^(2/3)+1/4*I/d/a^(2/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/8*I/d/a^(2/3)*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))-1/4*I/d/a^(2/3)*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"
298,0,0,76,0.755000," ","int(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(4/3),x)","\int \frac{\tan^{m}\left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(4/3),x)","F"
299,0,0,66,1.002000," ","int(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(4/3),x)","\int \frac{\sqrt{\tan}\left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(4/3),x)","F"
300,1,227,213,0.146000," ","int(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(4/3),x)","\frac{3 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{3}}}{5 d \,a^{3}}-\frac{3 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{d \,a^{2}}+\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)}{8 d \,a^{\frac{4}{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)}{16 d \,a^{\frac{4}{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)}{8 d \,a^{\frac{4}{3}}}-\frac{21 i}{4 d a \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}+\frac{3 i}{8 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}"," ",0,"3/5*I/d/a^3*(a+I*a*tan(d*x+c))^(5/3)-3*I/d/a^2*(a+I*a*tan(d*x+c))^(2/3)+1/8*I/d/a^(4/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/16*I/d/a^(4/3)*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))+1/8*I/d/a^(4/3)*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))-21/4*I/d/a/(a+I*a*tan(d*x+c))^(1/3)+3/8*I/d/(a+I*a*tan(d*x+c))^(4/3)","A"
301,1,198,178,0.126000," ","int(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(4/3),x)","-\frac{3 \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{2 d \,a^{2}}-\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)}{8 d \,a^{\frac{4}{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)}{16 d \,a^{\frac{4}{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)}{8 d \,a^{\frac{4}{3}}}-\frac{15}{4 a d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}+\frac{3}{8 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}"," ",0,"-3/2/d/a^2*(a+I*a*tan(d*x+c))^(2/3)-1/8/d/a^(4/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))+1/16/d/a^(4/3)*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))-1/8/d/a^(4/3)*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))-15/4/a/d/(a+I*a*tan(d*x+c))^(1/3)+3/8/d/(a+I*a*tan(d*x+c))^(4/3)","A"
302,1,181,155,0.128000," ","int(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x)","-\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)}{8 d \,a^{\frac{4}{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)}{16 d \,a^{\frac{4}{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)}{8 d \,a^{\frac{4}{3}}}+\frac{9 i}{4 a d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}-\frac{3 i}{8 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}"," ",0,"-1/8*I/d/a^(4/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))+1/16*I/d/a^(4/3)*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))-1/8*I/d/a^(4/3)*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))+9/4*I/a/d/(a+I*a*tan(d*x+c))^(1/3)-3/8*I/d/(a+I*a*tan(d*x+c))^(4/3)","A"
303,1,176,151,0.128000," ","int(tan(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),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)}{8 d \,a^{\frac{4}{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)}{16 d \,a^{\frac{4}{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)}{8 d \,a^{\frac{4}{3}}}-\frac{3}{8 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}+\frac{3}{4 a d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}"," ",0,"1/8/d/a^(4/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/16/d/a^(4/3)*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))+1/8/d/a^(4/3)*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))-3/8/d/(a+I*a*tan(d*x+c))^(4/3)+3/4/a/d/(a+I*a*tan(d*x+c))^(1/3)","A"
304,1,181,155,0.098000," ","int(1/(a+I*a*tan(d*x+c))^(4/3),x)","\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)}{8 d \,a^{\frac{4}{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)}{16 d \,a^{\frac{4}{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)}{8 d \,a^{\frac{4}{3}}}+\frac{3 i}{4 a d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{1}{3}}}+\frac{3 i}{8 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}"," ",0,"1/8*I/d/a^(4/3)*2^(2/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/16*I/d/a^(4/3)*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))+1/8*I/d/a^(4/3)*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))+3/4*I/a/d/(a+I*a*tan(d*x+c))^(1/3)+3/8*I/d/(a+I*a*tan(d*x+c))^(4/3)","A"
305,0,0,234,0.807000," ","int(cot(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x)","\int \frac{\cot \left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cot(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x)","F"
306,0,0,267,0.810000," ","int(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x)","\int \frac{\cot^{2}\left(d x +c \right)}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x)","F"
307,1,181,155,0.115000," ","int(1/(a+I*a*tan(d*x+c))^(5/3),x)","\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)}{8 d \,a^{\frac{5}{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)}{16 d \,a^{\frac{5}{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)}{8 d \,a^{\frac{5}{3}}}+\frac{3 i}{8 a d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{2}{3}}}+\frac{3 i}{10 d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{3}}}"," ",0,"1/8*I/d/a^(5/3)*2^(1/3)*ln((a+I*a*tan(d*x+c))^(1/3)-2^(1/3)*a^(1/3))-1/16*I/d/a^(5/3)*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))-1/8*I/d/a^(5/3)*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))+3/8*I/a/d/(a+I*a*tan(d*x+c))^(2/3)+3/10*I/d/(a+I*a*tan(d*x+c))^(5/3)","A"
308,0,0,44,1.241000," ","int((e*tan(d*x+c))^m*(a+I*a*tan(d*x+c)),x)","\int \left(e \tan \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)\, dx"," ",0,"int((e*tan(d*x+c))^m*(a+I*a*tan(d*x+c)),x)","F"
309,0,0,44,0.815000," ","int((e*tan(d*x+c))^m*(a-I*a*tan(d*x+c)),x)","\int \left(e \tan \left(d x +c \right)\right)^{m} \left(a -i a \tan \left(d x +c \right)\right)\, dx"," ",0,"int((e*tan(d*x+c))^m*(a-I*a*tan(d*x+c)),x)","F"
310,0,0,188,1.128000," ","int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^4,x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{4}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^4,x)","F"
311,0,0,127,1.072000," ","int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x)","F"
312,0,0,76,1.485000," ","int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x)","F"
313,0,0,44,1.085000," ","int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e)),x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e)),x)","F"
314,0,0,146,1.893000," ","int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{a +i a \tan \left(f x +e \right)}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","F"
315,0,0,194,1.979000," ","int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","F"
316,0,0,256,2.122000," ","int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x)","F"
317,0,0,305,2.121000," ","int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^4,x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{4}}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^4,x)","F"
318,0,0,44,0.817000," ","int((d*tan(f*x+e))^n*(a-I*a*tan(f*x+e)),x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a -i a \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*tan(f*x+e))^n*(a-I*a*tan(f*x+e)),x)","F"
319,0,0,146,1.751000," ","int((d*tan(f*x+e))^n/(a-I*a*tan(f*x+e)),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{a -i a \tan \left(f x +e \right)}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a-I*a*tan(f*x+e)),x)","F"
320,0,0,79,1.689000," ","int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(3/2),x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(3/2),x)","F"
321,0,0,79,1.797000," ","int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(1/2),x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \sqrt{a +i a \tan \left(f x +e \right)}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(1/2),x)","F"
322,0,0,78,1.492000," ","int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(1/2),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{\sqrt{a +i a \tan \left(f x +e \right)}}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(1/2),x)","F"
323,0,0,81,1.464000," ","int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(3/2),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(3/2),x)","F"
324,0,0,84,2.088000," ","int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x)","F"
325,0,0,191,1.118000," ","int(tan(d*x+c)^4*(a+I*a*tan(d*x+c))^m,x)","\int \left(\tan^{4}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(tan(d*x+c)^4*(a+I*a*tan(d*x+c))^m,x)","F"
326,0,0,135,1.847000," ","int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^m,x)","\int \left(\tan^{3}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^m,x)","F"
327,0,0,73,1.568000," ","int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x)","\int \left(\tan^{2}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x)","F"
328,0,0,63,2.119000," ","int(tan(d*x+c)*(a+I*a*tan(d*x+c))^m,x)","\int \tan \left(d x +c \right) \left(a +i a \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(tan(d*x+c)*(a+I*a*tan(d*x+c))^m,x)","F"
329,0,0,42,1.198000," ","int((a+I*a*tan(d*x+c))^m,x)","\int \left(a +i a \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^m,x)","F"
330,0,0,83,2.032000," ","int(cot(d*x+c)*(a+I*a*tan(d*x+c))^m,x)","\int \cot \left(d x +c \right) \left(a +i a \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cot(d*x+c)*(a+I*a*tan(d*x+c))^m,x)","F"
331,0,0,107,1.539000," ","int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x)","F"
332,0,0,69,0.984000," ","int(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^m,x)","\int \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^m,x)","F"
333,0,0,69,1.079000," ","int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^m,x)","\int \left(\sqrt{\tan}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^m,x)","F"
334,0,0,69,1.102000," ","int((a+I*a*tan(d*x+c))^m/tan(d*x+c)^(1/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{m}}{\sqrt{\tan \left(d x +c \right)}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^m/tan(d*x+c)^(1/2),x)","F"
335,0,0,69,1.013000," ","int((a+I*a*tan(d*x+c))^m/tan(d*x+c)^(3/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{m}}{\tan \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^m/tan(d*x+c)^(3/2),x)","F"
336,1,388,94,0.217000," ","int((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e)),x)","\frac{2 a \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}+\frac{2 a d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{2 a \,d^{2} \sqrt{d \tan \left(f x +e \right)}}{f}+\frac{a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}+\frac{a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{a \,d^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \,d^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \,d^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/5*a*(d*tan(f*x+e))^(5/2)/f+2/3*a*d*(d*tan(f*x+e))^(3/2)/f-2*a*d^2*(d*tan(f*x+e))^(1/2)/f+1/4*a/f*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*a/f*d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f*d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f*d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
337,1,363,76,0.206000," ","int((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e)),x)","\frac{2 a \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{2 a d \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{a d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}-\frac{a d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{a d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{a \,d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \,d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \,d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/3*a*(d*tan(f*x+e))^(3/2)/f+2*a*d*(d*tan(f*x+e))^(1/2)/f-1/4*a/f*d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*a/f*d^2*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f*d^2*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f*d^2*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
338,1,337,59,0.203000," ","int((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e)),x)","\frac{2 a \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{a d \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2*a*(d*tan(f*x+e))^(1/2)/f-1/4*a/f*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*a/f*d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f*d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f*d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
339,1,327,41,0.210000," ","int((a+a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x)","\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d}+\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}+\frac{a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"1/4*a/f/d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*a/f*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
340,1,355,61,0.170000," ","int((a+a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x)","\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{2}}+\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}-\frac{a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a}{d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"1/4*a/f/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*a/f/d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f/d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f/d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*a/d/f/(d*tan(f*x+e))^(1/2)","B"
341,1,374,81,0.179000," ","int((a+a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x)","-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{3}}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3}}+\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3}}-\frac{a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a}{d^{2} f \sqrt{d \tan \left(f x +e \right)}}-\frac{2 a}{3 d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}"," ",0,"-1/4*a/f/d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f/d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f/d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4*a/f/d^2*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f/d^2*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f/d^2*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*a/d^2/f/(d*tan(f*x+e))^(1/2)-2/3*a/d/f/(d*tan(f*x+e))^(3/2)","B"
342,1,393,100,0.179000," ","int((a+a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x)","-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{4}}-\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{4}}+\frac{a \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{4}}+\frac{a \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a}{3 d^{2} f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{2 a}{5 d f \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}+\frac{2 a}{d^{3} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/4*a/f/d^4*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2*a/f/d^4*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2*a/f/d^4*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4*a/f/d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2*a/f/d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2*a/f/d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/3*a/d^2/f/(d*tan(f*x+e))^(3/2)-2/5*a/d/f/(d*tan(f*x+e))^(5/2)+2*a/d^3/f/(d*tan(f*x+e))^(1/2)","B"
343,1,234,216,0.228000," ","int((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^2,x)","\frac{2 a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 d f}+\frac{4 a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}-\frac{4 a^{2} d^{2} \sqrt{d \tan \left(f x +e \right)}}{f}+\frac{a^{2} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f}-\frac{a^{2} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{a^{2} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}"," ",0,"2/7*a^2*(d*tan(f*x+e))^(7/2)/d/f+4/5*a^2*(d*tan(f*x+e))^(5/2)/f-4*a^2*d^2*(d*tan(f*x+e))^(1/2)/f+1/2/f*a^2*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^2*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^2*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","A"
344,1,213,195,0.226000," ","int((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^2,x)","\frac{2 a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d f}+\frac{4 a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{a^{2} d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/5*a^2*(d*tan(f*x+e))^(5/2)/d/f+4/3*a^2*(d*tan(f*x+e))^(3/2)/f-1/2/f*a^2*d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^2*d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^2*d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","A"
345,1,204,195,0.228000," ","int((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e))^2,x)","\frac{2 a^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 d f}+\frac{4 a^{2} \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f}+\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}"," ",0,"2/3*a^2*(d*tan(f*x+e))^(3/2)/d/f+4*a^2*(d*tan(f*x+e))^(1/2)/f-1/2/f*a^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","A"
346,1,186,177,0.209000," ","int((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(1/2),x)","\frac{2 a^{2} \sqrt{d \tan \left(f x +e \right)}}{d f}+\frac{a^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2*a^2*(d*tan(f*x+e))^(1/2)/d/f+1/2/f*a^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","A"
347,1,195,177,0.186000," ","int((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x)","\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{2}}+\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2}}-\frac{a^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2}}-\frac{2 a^{2}}{d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"1/2/f*a^2/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^2/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^2/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2*a^2/d/f/(d*tan(f*x+e))^(1/2)","A"
348,1,216,198,0.171000," ","int((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x)","-\frac{a^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{2}}{3 d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{4 a^{2}}{d^{2} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/2/f*a^2/d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^2/d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^2/d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/3*a^2/d/f/(d*tan(f*x+e))^(3/2)-4*a^2/d^2/f/(d*tan(f*x+e))^(1/2)","A"
349,1,467,177,0.285000," ","int((d*tan(f*x+e))^(7/2)*(a+a*tan(f*x+e))^3,x)","\frac{2 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{11}{2}}}{11 f \,d^{2}}+\frac{2 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{3 d f}+\frac{4 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f}-\frac{4 a^{3} d \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}-\frac{4 a^{3} d^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{4 a^{3} d^{3} \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{a^{3} d^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f}-\frac{a^{3} d^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{a^{3} d^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{a^{3} d^{4} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} d^{4} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} d^{4} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/11/f*a^3/d^2*(d*tan(f*x+e))^(11/2)+2/3*a^3*(d*tan(f*x+e))^(9/2)/d/f+4/7*a^3*(d*tan(f*x+e))^(7/2)/f-4/5*a^3*d*(d*tan(f*x+e))^(5/2)/f-4/3*a^3*d^2*(d*tan(f*x+e))^(3/2)/f+4*a^3*d^3*(d*tan(f*x+e))^(1/2)/f-1/2/f*a^3*d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^3*d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3*d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f*a^3*d^4*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^3*d^4*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3*d^4*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
350,1,446,157,0.256000," ","int((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^3,x)","\frac{2 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9 f \,d^{2}}+\frac{6 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 d f}+\frac{4 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}-\frac{4 a^{3} d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{4 a^{3} d^{2} \sqrt{d \tan \left(f x +e \right)}}{f}+\frac{a^{3} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f}+\frac{a^{3} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{a^{3} d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{a^{3} d^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} d^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} d^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/9/f*a^3/d^2*(d*tan(f*x+e))^(9/2)+6/7*a^3*(d*tan(f*x+e))^(7/2)/d/f+4/5*a^3*(d*tan(f*x+e))^(5/2)/f-4/3*a^3*d*(d*tan(f*x+e))^(3/2)/f-4*a^3*d^2*(d*tan(f*x+e))^(1/2)/f+1/2/f*a^3*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^3*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f*a^3*d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^3*d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3*d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
351,1,419,135,0.257000," ","int((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^3,x)","\frac{2 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f \,d^{2}}+\frac{6 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d f}+\frac{4 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{4 a^{3} d \sqrt{d \tan \left(f x +e \right)}}{f}+\frac{a^{3} d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f}+\frac{a^{3} d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{a^{3} d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{a^{3} d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/7/f*a^3/d^2*(d*tan(f*x+e))^(7/2)+6/5*a^3*(d*tan(f*x+e))^(5/2)/d/f+4/3*a^3*(d*tan(f*x+e))^(3/2)/f-4*a^3*d*(d*tan(f*x+e))^(1/2)/f+1/2/f*a^3*d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^3*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2/f*a^3*d^2*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^3*d^2*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3*d^2*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
352,1,391,117,0.255000," ","int((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e))^3,x)","\frac{2 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f \,d^{2}}+\frac{2 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{d f}+\frac{4 a^{3} \sqrt{d \tan \left(f x +e \right)}}{f}-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f}-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}+\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f}-\frac{a^{3} d \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/5/f*a^3/d^2*(d*tan(f*x+e))^(5/2)+2*a^3*(d*tan(f*x+e))^(3/2)/d/f+4*a^3*(d*tan(f*x+e))^(1/2)/f-1/2/f*a^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2/f*a^3*d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^3*d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3*d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
353,1,379,98,0.222000," ","int((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(1/2),x)","\frac{2 a^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f \,d^{2}}+\frac{6 a^{3} \sqrt{d \tan \left(f x +e \right)}}{d f}-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f d}-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d}+\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d}+\frac{a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/3/f*a^3/d^2*(d*tan(f*x+e))^(3/2)+6*a^3*(d*tan(f*x+e))^(1/2)/d/f-1/2/f*a^3/d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^3/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f*a^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","B"
354,1,388,99,0.184000," ","int((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x)","\frac{2 a^{3} \sqrt{d \tan \left(f x +e \right)}}{d^{2} f}+\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{2}}+\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2}}-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2}}+\frac{a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{3}}{f d \sqrt{d \tan \left(f x +e \right)}}"," ",0,"2*a^3*(d*tan(f*x+e))^(1/2)/d^2/f+1/2/f*a^3/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^3/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f*a^3/d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^3/d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3/d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/f*a^3/d/(d*tan(f*x+e))^(1/2)","B"
355,1,388,98,0.196000," ","int((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x)","\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{3}}+\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3}}-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3}}-\frac{a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{3}}{3 f d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{6 a^{3}}{d^{2} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"1/2/f*a^3/d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^3/d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3/d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2/f*a^3/d^2*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^3/d^2*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3/d^2*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/3/f*a^3/d/(d*tan(f*x+e))^(3/2)-6*a^3/d^2/f/(d*tan(f*x+e))^(1/2)","B"
356,1,409,120,0.192000," ","int((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x)","-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{4}}-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4}}+\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4}}-\frac{a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{3}}{5 f d \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}-\frac{2 a^{3}}{d^{2} f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{4 a^{3}}{d^{3} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/2/f*a^3/d^4*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^3/d^4*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3/d^4*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2/f*a^3/d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^3/d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3/d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/5/f*a^3/d/(d*tan(f*x+e))^(5/2)-2*a^3/d^2/f/(d*tan(f*x+e))^(3/2)-4*a^3/d^3/f/(d*tan(f*x+e))^(1/2)","B"
357,1,430,140,0.205000," ","int((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x)","-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{5}}-\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{5}}+\frac{a^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{5}}+\frac{a^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{2 f \,d^{4} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{f \,d^{4} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2 a^{3}}{7 f d \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}-\frac{6 a^{3}}{5 d^{2} f \left(d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}+\frac{4 a^{3}}{d^{4} f \sqrt{d \tan \left(f x +e \right)}}-\frac{4 a^{3}}{3 d^{3} f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/f*a^3/d^5*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/f*a^3/d^5*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/f*a^3/d^5*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f*a^3/d^4*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/f*a^3/d^4*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/f*a^3/d^4*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-2/7/f*a^3/d/(d*tan(f*x+e))^(7/2)-6/5*a^3/d^2/f/(d*tan(f*x+e))^(5/2)+4*a^3/d^4/f/(d*tan(f*x+e))^(1/2)-4/3*a^3/d^3/f/(d*tan(f*x+e))^(3/2)","B"
358,1,395,93,0.278000," ","int((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x)","\frac{2 d^{2} \sqrt{d \tan \left(f x +e \right)}}{a f}-\frac{d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a}-\frac{d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a}+\frac{d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a}-\frac{d^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{\frac{5}{2}} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{a f}"," ",0,"2*d^2*(d*tan(f*x+e))^(1/2)/a/f-1/8/f/a*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a*d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a*d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a*d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-d^(5/2)*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a/f","B"
359,1,367,70,0.282000," ","int((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x)","-\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a}-\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a}+\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a}+\frac{d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{\frac{3}{2}} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{a f}"," ",0,"-1/8/f/a*d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a*d^2*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/4/f/a*d^2*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4/f/a*d^2*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+d^(3/2)*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a/f","B"
360,1,359,72,0.314000," ","int((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e)),x)","\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a}+\frac{d \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right) \sqrt{d}}{a f}"," ",0,"1/8/f/a*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/4/f/a*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4/f/a*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a*d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/4/f/a*d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4/f/a*d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-arctan((d*tan(f*x+e))^(1/2)/d^(1/2))*d^(1/2)/a/f","B"
361,1,364,67,0.309000," ","int(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e)),x)","\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a d}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a d}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a d}-\frac{\sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{a f \sqrt{d}}"," ",0,"1/8/f/a/d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/4/f/a/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4/f/a/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a/f/d^(1/2)","B"
362,1,395,93,0.280000," ","int(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x)","-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a \,d^{2}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \,d^{2}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \,d^{2}}-\frac{\sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{a \,d^{\frac{3}{2}} f}-\frac{2}{a d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/8/f/a/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a/d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a/d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a/d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a/d^(3/2)/f-2/a/d/f/(d*tan(f*x+e))^(1/2)","B"
363,1,415,112,0.282000," ","int(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x)","-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a \,d^{3}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \,d^{3}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \,d^{3}}+\frac{\sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f a \,d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{a \,d^{\frac{5}{2}} f}-\frac{2}{3 a d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{2}{a \,d^{2} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/8/f/a/d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a/d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a/d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a/d^2*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/4/f/a/d^2*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4/f/a/d^2*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a/d^(5/2)/f-2/3/a/d/f/(d*tan(f*x+e))^(3/2)+2/a/d^2/f/(d*tan(f*x+e))^(1/2)","B"
364,1,234,217,0.290000," ","int((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x)","-\frac{d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f \,a^{2}}-\frac{d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2}}+\frac{d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2}}-\frac{d^{3} \sqrt{d \tan \left(f x +e \right)}}{2 f \,a^{2} \left(d \tan \left(f x +e \right)+d \right)}+\frac{3 d^{\frac{5}{2}} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{2 a^{2} f}"," ",0,"-1/8/f/a^2*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a^2*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a^2*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2/f/a^2*d^3*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)+d)+3/2*d^(5/2)*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^2/f","A"
365,1,234,215,0.260000," ","int((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x)","\frac{d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f \,a^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{2} \sqrt{d \tan \left(f x +e \right)}}{2 f \,a^{2} \left(d \tan \left(f x +e \right)+d \right)}-\frac{d^{\frac{3}{2}} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{2 a^{2} f}"," ",0,"1/8/f/a^2*d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/4/f/a^2*d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4/f/a^2*d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f/a^2*d^2*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)+d)-1/2*d^(3/2)*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^2/f","A"
366,1,223,214,0.286000," ","int((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^2,x)","-\frac{d \sqrt{d \tan \left(f x +e \right)}}{2 f \,a^{2} \left(d \tan \left(f x +e \right)+d \right)}-\frac{\arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right) \sqrt{d}}{2 a^{2} f}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f \,a^{2}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2}}"," ",0,"-1/2/f/a^2*d*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)+d)-1/2*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))*d^(1/2)/a^2/f+1/8/f/a^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/4/f/a^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4/f/a^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)","A"
367,1,222,217,0.316000," ","int(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^2,x)","-\frac{\sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f \,a^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{d \tan \left(f x +e \right)}}{2 f \,a^{2} \left(d \tan \left(f x +e \right)+d \right)}+\frac{3 \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{2 a^{2} f \sqrt{d}}"," ",0,"-1/8/f/a^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f/a^2*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)+d)+3/2*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^2/f/d^(1/2)","A"
368,1,255,238,0.283000," ","int(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x)","-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f \,a^{2} d^{2}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2} d^{2}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2} d^{2}}-\frac{\sqrt{d \tan \left(f x +e \right)}}{2 f \,a^{2} d \left(d \tan \left(f x +e \right)+d \right)}-\frac{5 \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{2 a^{2} d^{\frac{3}{2}} f}-\frac{2}{a^{2} d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/8/f/a^2/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/4/f/a^2/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/4/f/a^2/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/2/f/a^2/d*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)+d)-5/2*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^2/d^(3/2)/f-2/a^2/d/f/(d*tan(f*x+e))^(1/2)","A"
369,1,276,259,0.319000," ","int(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x)","\frac{\sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{8 f \,a^{2} d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2} d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{4 f \,a^{2} d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{d \tan \left(f x +e \right)}}{2 f \,a^{2} d^{2} \left(d \tan \left(f x +e \right)+d \right)}+\frac{7 \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{2 a^{2} d^{\frac{5}{2}} f}-\frac{2}{3 a^{2} d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{4}{a^{2} d^{2} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"1/8/f/a^2/d^2/(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/4/f/a^2/d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/4/f/a^2/d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/2/f/a^2/d^2*(d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)+d)+7/2*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^2/d^(5/2)/f-2/3/a^2/d/f/(d*tan(f*x+e))^(3/2)+4/a^2/d^2/f/(d*tan(f*x+e))^(1/2)","A"
370,1,461,156,0.355000," ","int((d*tan(f*x+e))^(9/2)/(a+a*tan(f*x+e))^3,x)","\frac{2 d^{4} \sqrt{d \tan \left(f x +e \right)}}{a^{3} f}+\frac{d^{4} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3}}+\frac{d^{4} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}-\frac{d^{4} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}-\frac{d^{5} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{5} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{5} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{13 d^{5} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{11 d^{6} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}-\frac{31 d^{\frac{9}{2}} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{8 a^{3} f}"," ",0,"2*d^4*(d*tan(f*x+e))^(1/2)/a^3/f+1/16/f/a^3*d^4*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/8/f/a^3*d^4*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a^3*d^4*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/16/f/a^3*d^5*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/8/f/a^3*d^5*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a^3*d^5*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+13/8/f/a^3*d^5/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(3/2)+11/8/f/a^3*d^6/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(1/2)-31/8*d^(9/2)*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^3/f","B"
371,1,440,136,0.329000," ","int((d*tan(f*x+e))^(7/2)/(a+a*tan(f*x+e))^3,x)","-\frac{d^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3}}-\frac{d^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}+\frac{d^{3} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}-\frac{d^{4} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{4} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{4} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{9 d^{4} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}-\frac{7 d^{5} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{11 d^{\frac{7}{2}} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{8 a^{3} f}"," ",0,"-1/16/f/a^3*d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/8/f/a^3*d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a^3*d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/16/f/a^3*d^4*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/8/f/a^3*d^4*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a^3*d^4*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-9/8/f/a^3*d^4/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(3/2)-7/8/f/a^3*d^5/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(1/2)+11/8*d^(7/2)*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^3/f","B"
372,1,440,135,0.326000," ","int((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x)","-\frac{d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3}}-\frac{d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}+\frac{d^{2} \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}+\frac{d^{3} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{5 d^{3} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{3 d^{4} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{d^{\frac{5}{2}} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{8 a^{3} f}"," ",0,"-1/16/f/a^3*d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/8/f/a^3*d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a^3*d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/16/f/a^3*d^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/8/f/a^3*d^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a^3*d^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+5/8/f/a^3*d^3/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(3/2)+3/8/f/a^3*d^4/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(1/2)+1/8*d^(5/2)*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^3/f","B"
373,1,434,135,0.319000," ","int((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x)","\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3}}+\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}-\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}+\frac{d^{2} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{2} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{d^{3} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}-\frac{5 d^{\frac{3}{2}} \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{8 a^{3} f}"," ",0,"1/16/f/a^3*d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/8/f/a^3*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a^3*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/16/f/a^3*d^2*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/8/f/a^3*d^2*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a^3*d^2*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a^3*d^2/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(3/2)+1/8/f/a^3*d^3/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(1/2)-5/8*d^(3/2)*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^3/f","B"
374,1,423,132,0.343000," ","int((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^3,x)","\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3}}-\frac{d \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{3 d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}-\frac{5 d^{2} \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{\arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right) \sqrt{d}}{8 a^{3} f}"," ",0,"1/16/f/a^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/8/f/a^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/16/f/a^3*d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/8/f/a^3*d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a^3*d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-3/8/f/a^3*d/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(3/2)-5/8/f/a^3*d^2/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(1/2)+1/8*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))*d^(1/2)/a^3/f","B"
375,1,426,136,0.364000," ","int(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^3,x)","-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} d}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d}-\frac{\sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{7 \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{9 d \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{11 \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{8 a^{3} f \sqrt{d}}"," ",0,"-1/16/f/a^3/d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/8/f/a^3/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a^3/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/16/f/a^3*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/8/f/a^3*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a^3*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+7/8/f/a^3/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(3/2)+9/8/f/a^3*d/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(1/2)+11/8*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^3/f/d^(1/2)","B"
376,1,458,156,0.332000," ","int(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x)","-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} d^{2}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d^{2}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d^{2}}+\frac{\sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{11 \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{3} d \left(d \tan \left(f x +e \right)+d \right)^{2}}-\frac{13 \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)+d \right)^{2}}-\frac{31 \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{8 a^{3} d^{\frac{3}{2}} f}-\frac{2}{a^{3} d f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"-1/16/f/a^3/d^2*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/8/f/a^3/d^2*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/8/f/a^3/d^2*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/16/f/a^3/d*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/8/f/a^3/d*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a^3/d*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-11/8/f/a^3/d/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(3/2)-13/8/f/a^3/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(1/2)-31/8*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^3/d^(3/2)/f-2/a^3/d/f/(d*tan(f*x+e))^(1/2)","B"
377,1,482,178,0.338000," ","int(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x)","\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} d^{3}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d^{3}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d^{3}}+\frac{\sqrt{2}\, \ln \left(\frac{d \tan \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{16 f \,a^{3} d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d^{2} \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{8 f \,a^{3} d^{2} \left(d^{2}\right)^{\frac{1}{4}}}+\frac{15 \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{3} d^{2} \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{17 \sqrt{d \tan \left(f x +e \right)}}{8 f \,a^{3} d \left(d \tan \left(f x +e \right)+d \right)^{2}}+\frac{59 \arctan \left(\frac{\sqrt{d \tan \left(f x +e \right)}}{\sqrt{d}}\right)}{8 a^{3} d^{\frac{5}{2}} f}-\frac{2}{3 a^{3} d f \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{6}{a^{3} d^{2} f \sqrt{d \tan \left(f x +e \right)}}"," ",0,"1/16/f/a^3/d^3*(d^2)^(1/4)*2^(1/2)*ln((d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/8/f/a^3/d^3*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a^3/d^3*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+1/16/f/a^3/d^2*2^(1/2)/(d^2)^(1/4)*ln((d*tan(f*x+e)-(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(f*x+e)+(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/8/f/a^3/d^2*2^(1/2)/(d^2)^(1/4)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)-1/8/f/a^3/d^2*2^(1/2)/(d^2)^(1/4)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(f*x+e))^(1/2)+1)+15/8/f/a^3/d^2/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(3/2)+17/8/f/a^3/d/(d*tan(f*x+e)+d)^2*(d*tan(f*x+e))^(1/2)+59/8*arctan((d*tan(f*x+e))^(1/2)/d^(1/2))/a^3/d^(5/2)/f-2/3/a^3/d/f/(d*tan(f*x+e))^(3/2)+6/a^3/d^2/f/(d*tan(f*x+e))^(1/2)","B"
378,1,351,210,0.467000," ","int((1+tan(f*x+e))^(1/2)*tan(f*x+e)^5,x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9 f}-\frac{6 \left(1+\tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f}+\frac{4 \left(1+\tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}+\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/9/f*(1+tan(f*x+e))^(9/2)-6/7/f*(1+tan(f*x+e))^(7/2)+4/5*(1+tan(f*x+e))^(5/2)/f+2*(1+tan(f*x+e))^(1/2)/f+1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))-1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","A"
379,1,336,164,0.242000," ","int((1+tan(f*x+e))^(1/2)*tan(f*x+e)^3,x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}-\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/5*(1+tan(f*x+e))^(5/2)/f-2/3*(1+tan(f*x+e))^(3/2)/f-2*(1+tan(f*x+e))^(1/2)/f-1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
380,1,306,128,0.174000," ","int((1+tan(f*x+e))^(1/2)*tan(f*x+e),x)","\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2*(1+tan(f*x+e))^(1/2)/f+1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))-1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","B"
381,1,2731,129,1.692000," ","int(cot(f*x+e)*(1+tan(f*x+e))^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/8/f*((cos(f*x+e)+sin(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(1+sin(f*x+e))*(8*I*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),-I*2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-8*I*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-20*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+8*2^(1/2)*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)-2*2^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)+8*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),-I*2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+8*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+6*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-4*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-4*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),-2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+4*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)-4*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2))*4^(1/2)/(cos(f*x+e)+sin(f*x+e))/sin(f*x+e)^4/(2+2^(1/2))","C"
382,1,11145,173,1.363000," ","int(cot(f*x+e)^3*(1+tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
383,1,16815,219,1.654000," ","int(cot(f*x+e)^5*(1+tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
384,1,318,247,0.226000," ","int((1+tan(f*x+e))^(1/2)*tan(f*x+e)^4,x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f}-\frac{4 \left(1+\tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}"," ",0,"2/7/f*(1+tan(f*x+e))^(7/2)-4/5*(1+tan(f*x+e))^(5/2)/f+1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))","A"
385,1,305,203,0.199000," ","int((1+tan(f*x+e))^(1/2)*tan(f*x+e)^2,x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}"," ",0,"2/3*(1+tan(f*x+e))^(3/2)/f-1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))","A"
386,1,288,188,0.152000," ","int((1+tan(f*x+e))^(1/2),x)","\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}"," ",0,"1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))","A"
387,1,8262,225,1.303000," ","int(cot(f*x+e)^2*(1+tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
388,1,13941,271,1.514000," ","int(cot(f*x+e)^4*(1+tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
389,1,371,291,0.249000," ","int(tan(f*x+e)^5*(1+tan(f*x+e))^(3/2),x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{11}{2}}}{11 f}-\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{9}{2}}}{3 f}+\frac{4 \left(1+\tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f}+\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{2 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{2 f}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/11/f*(1+tan(f*x+e))^(11/2)-2/3/f*(1+tan(f*x+e))^(9/2)+4/7/f*(1+tan(f*x+e))^(7/2)+2/3*(1+tan(f*x+e))^(3/2)/f+2*(1+tan(f*x+e))^(1/2)/f-1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/2/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/2/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","A"
390,1,354,245,0.207000," ","int(tan(f*x+e)^3*(1+tan(f*x+e))^(3/2),x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f}-\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}-\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{2 f}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{2 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/7/f*(1+tan(f*x+e))^(7/2)-2/5*(1+tan(f*x+e))^(5/2)/f-2/3*(1+tan(f*x+e))^(3/2)/f-2*(1+tan(f*x+e))^(1/2)/f+1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/2/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/2/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","A"
391,1,326,209,0.151000," ","int(tan(f*x+e)*(1+tan(f*x+e))^(3/2),x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{2 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{2 f}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/3*(1+tan(f*x+e))^(3/2)/f+2*(1+tan(f*x+e))^(1/2)/f-1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/2/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/2/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","A"
392,1,2391,195,1.358000," ","int(cot(f*x+e)*(1+tan(f*x+e))^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/8/f*((cos(f*x+e)+sin(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(1+sin(f*x+e))*(16*I*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*(-(2^(1/2)*sin(f*x+e)-2^(1/2)-cos(f*x+e)+sin(f*x+e)-1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),-I*2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-16*I*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*(-(2^(1/2)*sin(f*x+e)-2^(1/2)-cos(f*x+e)+sin(f*x+e)-1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+16*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*(-(2^(1/2)*sin(f*x+e)-2^(1/2)-cos(f*x+e)+sin(f*x+e)-1)/cos(f*x+e))^(1/2)*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-6*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*(-(2^(1/2)*sin(f*x+e)-2^(1/2)-cos(f*x+e)+sin(f*x+e)-1)/cos(f*x+e))^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-12*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*(-(2^(1/2)*sin(f*x+e)-2^(1/2)-cos(f*x+e)+sin(f*x+e)-1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-3*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+3*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+12*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*(-(2^(1/2)*sin(f*x+e)-2^(1/2)-cos(f*x+e)+sin(f*x+e)-1)/cos(f*x+e))^(1/2)*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-12*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*(-(2^(1/2)*sin(f*x+e)-2^(1/2)-cos(f*x+e)+sin(f*x+e)-1)/cos(f*x+e))^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-4*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-4*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),-2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+3*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2)))*4^(1/2)/(cos(f*x+e)+sin(f*x+e))/sin(f*x+e)^4/(2+2^(1/2))","C"
393,1,9721,239,1.259000," ","int(cot(f*x+e)^3*(1+tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
394,1,14663,285,1.412000," ","int(cot(f*x+e)^5*(1+tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
395,1,344,181,0.220000," ","int(tan(f*x+e)^4*(1+tan(f*x+e))^(3/2),x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9 f}-\frac{4 \left(1+\tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f}+\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}+\frac{2 \arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}+\frac{2 \arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/9/f*(1+tan(f*x+e))^(9/2)-4/7/f*(1+tan(f*x+e))^(7/2)+2*(1+tan(f*x+e))^(1/2)/f+1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+2/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+2/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))","A"
396,1,327,135,0.217000," ","int(tan(f*x+e)^2*(1+tan(f*x+e))^(3/2),x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}-\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}-\frac{2 \arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}-\frac{2 \arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/5*(1+tan(f*x+e))^(5/2)/f-2*(1+tan(f*x+e))^(1/2)/f-1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-2/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-2/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
397,1,314,122,0.146000," ","int((1+tan(f*x+e))^(3/2),x)","\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}+\frac{2 \arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{f \sqrt{-2+2 \sqrt{2}}}+\frac{2 \arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2*(1+tan(f*x+e))^(1/2)/f+1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+2/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+2/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
398,1,6692,142,1.178000," ","int(cot(f*x+e)^2*(1+tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
399,1,11218,190,1.271000," ","int(cot(f*x+e)^4*(1+tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
400,1,342,189,0.224000," ","int(tan(f*x+e)^5/(1+tan(f*x+e))^(1/2),x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f}-\frac{6 \left(1+\tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}+\frac{4 \left(1+\tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/7/f*(1+tan(f*x+e))^(7/2)-6/5*(1+tan(f*x+e))^(5/2)/f+4/3*(1+tan(f*x+e))^(3/2)/f+1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/2/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/2/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))","A"
401,1,329,143,0.197000," ","int(tan(f*x+e)^3/(1+tan(f*x+e))^(1/2),x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/3*(1+tan(f*x+e))^(3/2)/f-2*(1+tan(f*x+e))^(1/2)/f-1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/2/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/2/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
402,1,297,107,0.154000," ","int(tan(f*x+e)/(1+tan(f*x+e))^(1/2),x)","\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right)}{f \sqrt{-2+2 \sqrt{2}}}"," ",0,"1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/2/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/2/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
403,1,2030,123,1.245000," ","int(cot(f*x+e)/(1+tan(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)+2 \sin \left(f x +e \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right)-\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)+2 \sin \left(f x +e \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right)-2 \sqrt{2}\, \EllipticE \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right) \sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(1+\sqrt{2}\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{2}\, \sin \left(f x +e \right)-\sqrt{2}+\cos \left(f x +e \right)-\sin \left(f x +e \right)+1}{\cos \left(f x +e \right)}}\, \sqrt{\frac{-\sqrt{2}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-\sin \left(f x +e \right)+\sqrt{2}+1}{\cos \left(f x +e \right)}}+28 \sqrt{2}\, \sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(1+\sqrt{2}\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{2}\, \sin \left(f x +e \right)-\sqrt{2}+\cos \left(f x +e \right)-\sin \left(f x +e \right)+1}{\cos \left(f x +e \right)}}\, \sqrt{\frac{-\sqrt{2}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-\sin \left(f x +e \right)+\sqrt{2}+1}{\cos \left(f x +e \right)}}\, \EllipticPi \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, \frac{\sqrt{2}}{2+\sqrt{2}}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right)-16 \sqrt{2}\, \sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(1+\sqrt{2}\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{2}\, \sin \left(f x +e \right)-\sqrt{2}+\cos \left(f x +e \right)-\sin \left(f x +e \right)+1}{\cos \left(f x +e \right)}}\, \sqrt{\frac{-\sqrt{2}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-\sin \left(f x +e \right)+\sqrt{2}+1}{\cos \left(f x +e \right)}}\, \EllipticPi \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, \frac{i \sqrt{2}}{2+\sqrt{2}}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right)-16 \sqrt{2}\, \sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(1+\sqrt{2}\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{2}\, \sin \left(f x +e \right)-\sqrt{2}+\cos \left(f x +e \right)-\sin \left(f x +e \right)+1}{\cos \left(f x +e \right)}}\, \sqrt{\frac{-\sqrt{2}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-\sin \left(f x +e \right)+\sqrt{2}+1}{\cos \left(f x +e \right)}}\, \EllipticPi \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, -\frac{i \sqrt{2}}{2+\sqrt{2}}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right)+8 \sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)+2 \sin \left(f x +e \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \EllipticPi \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, -\frac{\sqrt{2}}{2+\sqrt{2}}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right)+\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)+2 \sin \left(f x +e \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right)-6 \sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)+2 \sin \left(f x +e \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\, \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \EllipticPi \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, \frac{\sqrt{2}}{2+\sqrt{2}}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right)-4 \EllipticE \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right) \sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(1+\sqrt{2}\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{2}\, \sin \left(f x +e \right)-\sqrt{2}+\cos \left(f x +e \right)-\sin \left(f x +e \right)+1}{\cos \left(f x +e \right)}}\, \sqrt{\frac{-\sqrt{2}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-\sin \left(f x +e \right)+\sqrt{2}+1}{\cos \left(f x +e \right)}}+4 \EllipticF \left(\frac{\sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2}, i \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\right) \sqrt{\frac{\left(-1+\sin \left(f x +e \right)\right) \left(1+\sqrt{2}\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{2}\, \sin \left(f x +e \right)-\sqrt{2}+\cos \left(f x +e \right)-\sin \left(f x +e \right)+1}{\cos \left(f x +e \right)}}\, \sqrt{\frac{-\sqrt{2}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-\sin \left(f x +e \right)+\sqrt{2}+1}{\cos \left(f x +e \right)}}\right) \left(1+\sin \left(f x +e \right)\right) \sqrt{4}}{16 f \left(\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \sin \left(f x +e \right)^{4} \left(2+\sqrt{2}\right)}"," ",0,"1/16/f*((cos(f*x+e)+sin(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-2*2^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)+28*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-16*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-16*2^(1/2)*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),-I*2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+8*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),-2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))+((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-6*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)+2*sin(f*x+e)+2^(1/2)-2)/cos(f*x+e)*2^(1/2))^(1/2)*((cos(f*x+e)*2^(1/2)-2^(1/2)*sin(f*x+e)-2*sin(f*x+e)+2^(1/2)+2)/cos(f*x+e)*2^(1/2))^(1/2)*EllipticPi(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),2^(1/2)/(2+2^(1/2)),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))-4*EllipticE(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2)+4*EllipticF(1/2*((-1+sin(f*x+e))/cos(f*x+e)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I*((2-2^(1/2))/(2+2^(1/2)))^(1/2))*((-1+sin(f*x+e))*(1+2^(1/2))/cos(f*x+e))^(1/2)*((2^(1/2)*sin(f*x+e)-2^(1/2)+cos(f*x+e)-sin(f*x+e)+1)/cos(f*x+e))^(1/2)*((-2^(1/2)*sin(f*x+e)+cos(f*x+e)-sin(f*x+e)+2^(1/2)+1)/cos(f*x+e))^(1/2))*(1+sin(f*x+e))*4^(1/2)/(cos(f*x+e)+sin(f*x+e))/sin(f*x+e)^4/(2+2^(1/2))","C"
404,1,8963,167,1.413000," ","int(cot(f*x+e)^3/(1+tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
405,1,13527,213,1.550000," ","int(cot(f*x+e)^5/(1+tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
406,1,326,239,0.234000," ","int(tan(f*x+e)^4/(1+tan(f*x+e))^(1/2),x)","\frac{2 \left(1+\tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}-\frac{4 \left(1+\tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2/5*(1+tan(f*x+e))^(5/2)/f-4/3*(1+tan(f*x+e))^(3/2)/f-1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/2/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/2/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","A"
407,1,311,195,0.251000," ","int(tan(f*x+e)^2/(1+tan(f*x+e))^(1/2),x)","\frac{2 \sqrt{1+\tan \left(f x +e \right)}}{f}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}-\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}"," ",0,"2*(1+tan(f*x+e))^(1/2)/f+1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/2/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/2/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","A"
408,1,296,180,0.175000," ","int(1/(1+tan(f*x+e))^(1/2),x)","-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}-\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}+\frac{\arctan \left(\frac{2 \sqrt{1+\tan \left(f x +e \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{4 f}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\sqrt{2}+\sqrt{2 \sqrt{2}+2}\, \sqrt{1+\tan \left(f x +e \right)}+\tan \left(f x +e \right)\right)}{8 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{2}+2}+2 \sqrt{1+\tan \left(f x +e \right)}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 f \sqrt{-2+2 \sqrt{2}}}"," ",0,"-1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)-(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/2/f/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+tan(f*x+e))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/4/f*(2*2^(1/2)+2)^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))-1/8/f*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+2^(1/2)+(2*2^(1/2)+2)^(1/2)*(1+tan(f*x+e))^(1/2)+tan(f*x+e))+1/2/f/(-2+2*2^(1/2))^(1/2)*arctan(((2*2^(1/2)+2)^(1/2)+2*(1+tan(f*x+e))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","A"
409,1,7175,216,1.735000," ","int(cot(f*x+e)^2/(1+tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
410,1,12089,263,1.789000," ","int(cot(f*x+e)^4/(1+tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
411,0,0,155,1.680000," ","int((d*tan(f*x+e))^n*(a+a*tan(f*x+e))^m,x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +a \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+a*tan(f*x+e))^m,x)","F"
412,1,99,85,0.019000," ","int(tan(d*x+c)^5*(a+b*tan(d*x+c)),x)","\frac{b \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{b \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b \tan \left(d x +c \right)}{d}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/5*b*tan(d*x+c)^5/d+1/4*a*tan(d*x+c)^4/d-1/3*b*tan(d*x+c)^3/d-1/2*a*tan(d*x+c)^2/d+b*tan(d*x+c)/d+1/2/d*a*ln(1+tan(d*x+c)^2)-1/d*b*arctan(tan(d*x+c))","A"
413,1,85,71,0.021000," ","int(tan(d*x+c)^4*(a+b*tan(d*x+c)),x)","\frac{b \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{b \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \tan \left(d x +c \right)}{d}+\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4*b*tan(d*x+c)^4/d+1/3*a*tan(d*x+c)^3/d-1/2*b*tan(d*x+c)^2/d-a*tan(d*x+c)/d+1/2/d*b*ln(1+tan(d*x+c)^2)+1/d*a*arctan(tan(d*x+c))","A"
414,1,71,56,0.021000," ","int(tan(d*x+c)^3*(a+b*tan(d*x+c)),x)","\frac{b \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \tan \left(d x +c \right)}{d}-\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/3*b*tan(d*x+c)^3/d+1/2*a*tan(d*x+c)^2/d-b*tan(d*x+c)/d-1/2/d*a*ln(1+tan(d*x+c)^2)+1/d*b*arctan(tan(d*x+c))","A"
415,1,57,42,0.022000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c)),x)","\frac{b \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \tan \left(d x +c \right)}{d}-\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2*b*tan(d*x+c)^2/d+a*tan(d*x+c)/d-1/2/d*b*ln(1+tan(d*x+c)^2)-1/d*a*arctan(tan(d*x+c))","A"
416,1,43,29,0.020000," ","int(tan(d*x+c)*(a+b*tan(d*x+c)),x)","\frac{b \tan \left(d x +c \right)}{d}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"b*tan(d*x+c)/d+1/2/d*a*ln(1+tan(d*x+c)^2)-1/d*b*arctan(tan(d*x+c))","A"
417,1,22,17,0.018000," ","int(a+b*tan(d*x+c),x)","a x +\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"a*x+1/2/d*b*ln(1+tan(d*x+c)^2)","A"
418,1,23,16,0.286000," ","int(cot(d*x+c)*(a+b*tan(d*x+c)),x)","b x +\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{b c}{d}"," ",0,"b*x+a*ln(sin(d*x+c))/d+b*c/d","A"
419,1,37,29,0.251000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c)),x)","-a x -\frac{a \cot \left(d x +c \right)}{d}+\frac{b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{c a}{d}"," ",0,"-a*x-a*cot(d*x+c)/d+b*ln(sin(d*x+c))/d-1/d*c*a","A"
420,1,52,44,0.336000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c)),x)","-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-b x -\frac{b \cot \left(d x +c \right)}{d}-\frac{b c}{d}"," ",0,"-1/2*a*cot(d*x+c)^2/d-a*ln(sin(d*x+c))/d-b*x-b*cot(d*x+c)/d-b*c/d","A"
421,1,63,56,0.272000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c)),x)","-\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cot \left(d x +c \right)}{d}+a x +\frac{c a}{d}-\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,"-1/3*a*cot(d*x+c)^3/d+a*cot(d*x+c)/d+a*x+1/d*c*a-1/2*b*cot(d*x+c)^2/d-b*ln(sin(d*x+c))/d","A"
422,1,76,69,0.306000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c)),x)","-\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{b \cot \left(d x +c \right)}{d}+b x +\frac{b c}{d}"," ",0,"-1/4*a*cot(d*x+c)^4/d+1/2*a*cot(d*x+c)^2/d+a*ln(sin(d*x+c))/d-1/3*b*cot(d*x+c)^3/d+b*cot(d*x+c)/d+b*x+b*c/d","A"
423,1,93,85,0.285000," ","int(cot(d*x+c)^6*(a+b*tan(d*x+c)),x)","-\frac{a \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \cot \left(d x +c \right)}{d}-a x -\frac{c a}{d}-\frac{b \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\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,"-1/5*a*cot(d*x+c)^5/d+1/3*a*cot(d*x+c)^3/d-a*cot(d*x+c)/d-a*x-1/d*c*a-1/4*b*cot(d*x+c)^4/d+1/2*b*cot(d*x+c)^2/d+b*ln(sin(d*x+c))/d","A"
424,1,153,114,0.021000," ","int(tan(d*x+c)^4*(a+b*tan(d*x+c))^2,x)","\frac{b^{2} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{a b \left(\tan^{4}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{\left(\tan^{3}\left(d x +c \right)\right) b^{2}}{3 d}-\frac{a b \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{a^{2} \tan \left(d x +c \right)}{d}+\frac{b^{2} \tan \left(d x +c \right)}{d}+\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}"," ",0,"1/5*b^2*tan(d*x+c)^5/d+1/2*a*b*tan(d*x+c)^4/d+1/3*a^2*tan(d*x+c)^3/d-1/3/d*tan(d*x+c)^3*b^2-a*b*tan(d*x+c)^2/d-a^2*tan(d*x+c)/d+b^2*tan(d*x+c)/d+1/d*a*b*ln(1+tan(d*x+c)^2)+1/d*arctan(tan(d*x+c))*a^2-1/d*arctan(tan(d*x+c))*b^2","A"
425,1,130,92,0.019000," ","int(tan(d*x+c)^3*(a+b*tan(d*x+c))^2,x)","\frac{b^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{2 a b \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{2 a b \tan \left(d x +c \right)}{d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2}}{2 d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d}+\frac{2 a b \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4*b^2*tan(d*x+c)^4/d+2/3*a*b*tan(d*x+c)^3/d+1/2*a^2*tan(d*x+c)^2/d-1/2/d*b^2*tan(d*x+c)^2-2*a*b*tan(d*x+c)/d-1/2/d*ln(1+tan(d*x+c)^2)*a^2+1/2/d*ln(1+tan(d*x+c)^2)*b^2+2/d*a*b*arctan(tan(d*x+c))","A"
426,1,106,61,0.020000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^2,x)","\frac{\left(\tan^{3}\left(d x +c \right)\right) b^{2}}{3 d}+\frac{a b \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{a^{2} \tan \left(d x +c \right)}{d}-\frac{b^{2} \tan \left(d x +c \right)}{d}-\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}"," ",0,"1/3/d*tan(d*x+c)^3*b^2+a*b*tan(d*x+c)^2/d+a^2*tan(d*x+c)/d-b^2*tan(d*x+c)/d-1/d*a*b*ln(1+tan(d*x+c)^2)-1/d*arctan(tan(d*x+c))*a^2+1/d*arctan(tan(d*x+c))*b^2","A"
427,1,83,56,0.019000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^2,x)","\frac{b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 a b \tan \left(d x +c \right)}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2}}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d}-\frac{2 a b \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*b^2*tan(d*x+c)^2+2*a*b*tan(d*x+c)/d+1/2/d*ln(1+tan(d*x+c)^2)*a^2-1/2/d*ln(1+tan(d*x+c)^2)*b^2-2/d*a*b*arctan(tan(d*x+c))","A"
428,1,61,39,0.020000," ","int((a+b*tan(d*x+c))^2,x)","\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}+\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{b^{2} \tan \left(d x +c \right)}{d}"," ",0,"1/d*arctan(tan(d*x+c))*a^2-1/d*arctan(tan(d*x+c))*b^2+1/d*a*b*ln(1+tan(d*x+c)^2)+b^2*tan(d*x+c)/d","A"
429,1,44,35,0.377000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^2,x)","2 a b x -\frac{b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{2 a b c}{d}"," ",0,"2*a*b*x-b^2*ln(cos(d*x+c))/d+a^2*ln(sin(d*x+c))/d+2/d*a*b*c","A"
430,1,58,41,0.260000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^2,x)","-a^{2} x +b^{2} x -\frac{a^{2} \cot \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} c}{d}+\frac{c \,b^{2}}{d}"," ",0,"-a^2*x+b^2*x-a^2*cot(d*x+c)/d+2*a*b*ln(sin(d*x+c))/d-1/d*a^2*c+1/d*c*b^2","A"
431,1,73,56,0.350000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-2 a b x -\frac{2 a b \cot \left(d x +c \right)}{d}-\frac{2 a b c}{d}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a^2*cot(d*x+c)^2/d-a^2*ln(sin(d*x+c))/d-2*a*b*x-2*a*b*cot(d*x+c)/d-2/d*a*b*c+1/d*b^2*ln(sin(d*x+c))","A"
432,1,102,76,0.302000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cot \left(d x +c \right)}{d}+a^{2} x +\frac{a^{2} c}{d}-\frac{a b \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{2 a b \ln \left(\sin \left(d x +c \right)\right)}{d}-b^{2} x -\frac{\cot \left(d x +c \right) b^{2}}{d}-\frac{c \,b^{2}}{d}"," ",0,"-1/3*a^2*cot(d*x+c)^3/d+a^2*cot(d*x+c)/d+a^2*x+1/d*a^2*c-a*b*cot(d*x+c)^2/d-2*a*b*ln(sin(d*x+c))/d-b^2*x-1/d*cot(d*x+c)*b^2-1/d*c*b^2","A"
433,1,120,92,0.337000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a b \cot \left(d x +c \right)}{d}+2 a b x +\frac{2 a b c}{d}-\frac{b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a^2*cot(d*x+c)^4/d+1/2*a^2*cot(d*x+c)^2/d+a^2*ln(sin(d*x+c))/d-2/3*a*b*cot(d*x+c)^3/d+2*a*b*cot(d*x+c)/d+2*a*b*x+2/d*a*b*c-1/2/d*b^2*cot(d*x+c)^2-1/d*b^2*ln(sin(d*x+c))","A"
434,1,148,114,0.326000," ","int(cot(d*x+c)^6*(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \cot \left(d x +c \right)}{d}-a^{2} x -\frac{a^{2} c}{d}-\frac{a b \left(\cot^{4}\left(d x +c \right)\right)}{2 d}+\frac{a b \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{2 a b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{\cot \left(d x +c \right) b^{2}}{d}+b^{2} x +\frac{c \,b^{2}}{d}"," ",0,"-1/5*a^2*cot(d*x+c)^5/d+1/3*a^2*cot(d*x+c)^3/d-a^2*cot(d*x+c)/d-a^2*x-1/d*a^2*c-1/2*a*b*cot(d*x+c)^4/d+a*b*cot(d*x+c)^2/d+2*a*b*ln(sin(d*x+c))/d-1/3/d*b^2*cot(d*x+c)^3+1/d*cot(d*x+c)*b^2+b^2*x+1/d*c*b^2","A"
435,1,198,139,0.019000," ","int(tan(d*x+c)^3*(a+b*tan(d*x+c))^3,x)","\frac{b^{3} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{3 b^{2} a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{\left(\tan^{3}\left(d x +c \right)\right) a^{2} b}{d}-\frac{b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 b^{2} a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b \tan \left(d x +c \right)}{d}+\frac{b^{3} \tan \left(d x +c \right)}{d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3}}{2 d}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} a}{2 d}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d}"," ",0,"1/5/d*b^3*tan(d*x+c)^5+3/4/d*b^2*a*tan(d*x+c)^4+1/d*tan(d*x+c)^3*a^2*b-1/3/d*b^3*tan(d*x+c)^3+1/2*a^3*tan(d*x+c)^2/d-3/2/d*b^2*a*tan(d*x+c)^2-3/d*a^2*b*tan(d*x+c)+1/d*b^3*tan(d*x+c)-1/2/d*ln(1+tan(d*x+c)^2)*a^3+3/2/d*ln(1+tan(d*x+c)^2)*b^2*a+3/d*arctan(tan(d*x+c))*a^2*b-1/d*arctan(tan(d*x+c))*b^3","A"
436,1,165,90,0.020000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^3,x)","\frac{b^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{\left(\tan^{3}\left(d x +c \right)\right) a \,b^{2}}{d}+\frac{3 a^{2} b \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \tan \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}-\frac{3 \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^{3}}{2 d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d}"," ",0,"1/4*b^3*tan(d*x+c)^4/d+1/d*tan(d*x+c)^3*a*b^2+3/2/d*a^2*b*tan(d*x+c)^2-1/2*b^3*tan(d*x+c)^2/d+a^3*tan(d*x+c)/d-3*a*b^2*tan(d*x+c)/d-3/2/d*ln(1+tan(d*x+c)^2)*a^2*b+1/2/d*ln(1+tan(d*x+c)^2)*b^3-1/d*arctan(tan(d*x+c))*a^3+3/d*arctan(tan(d*x+c))*a*b^2","A"
437,1,133,93,0.035000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^3,x)","\frac{b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{3 b^{2} a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{2} b \tan \left(d x +c \right)}{d}-\frac{b^{3} \tan \left(d x +c \right)}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3}}{2 d}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} a}{2 d}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d}"," ",0,"1/3/d*b^3*tan(d*x+c)^3+3/2/d*b^2*a*tan(d*x+c)^2+3/d*a^2*b*tan(d*x+c)-1/d*b^3*tan(d*x+c)+1/2/d*ln(1+tan(d*x+c)^2)*a^3-3/2/d*ln(1+tan(d*x+c)^2)*b^2*a-3/d*arctan(tan(d*x+c))*a^2*b+1/d*arctan(tan(d*x+c))*b^3","A"
438,1,102,70,0.029000," ","int((a+b*tan(d*x+c))^3,x)","\frac{b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{3 \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^{3}}{2 d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d}"," ",0,"1/2*b^3*tan(d*x+c)^2/d+3*a*b^2*tan(d*x+c)/d+3/2/d*ln(1+tan(d*x+c)^2)*a^2*b-1/2/d*ln(1+tan(d*x+c)^2)*b^3+1/d*arctan(tan(d*x+c))*a^3-3/d*arctan(tan(d*x+c))*a*b^2","A"
439,1,77,62,0.320000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^3,x)","3 a^{2} b x -b^{3} x +\frac{b^{3} \tan \left(d x +c \right)}{d}+\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b c}{d}-\frac{c \,b^{3}}{d}"," ",0,"3*a^2*b*x-b^3*x+1/d*b^3*tan(d*x+c)+a^3*ln(sin(d*x+c))/d-3*a*b^2*ln(cos(d*x+c))/d+3/d*a^2*b*c-1/d*c*b^3","A"
440,1,79,69,0.345000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^3,x)","-a^{3} x +3 b^{2} a x -\frac{a^{3} \cot \left(d x +c \right)}{d}+\frac{3 a^{2} b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{a^{3} c}{d}+\frac{3 a \,b^{2} c}{d}"," ",0,"-a^3*x+3*b^2*a*x-a^3*cot(d*x+c)/d+3*a^2*b*ln(sin(d*x+c))/d-b^3*ln(cos(d*x+c))/d-1/d*a^3*c+3/d*a*b^2*c","A"
441,1,94,79,0.433000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-3 a^{2} b x -\frac{3 a^{2} b \cot \left(d x +c \right)}{d}-\frac{3 a^{2} b c}{d}+\frac{3 b^{2} a \ln \left(\sin \left(d x +c \right)\right)}{d}+b^{3} x +\frac{c \,b^{3}}{d}"," ",0,"-1/2*a^3*cot(d*x+c)^2/d-a^3*ln(sin(d*x+c))/d-3*a^2*b*x-3*a^2*b*cot(d*x+c)/d-3/d*a^2*b*c+3/d*b^2*a*ln(sin(d*x+c))+b^3*x+1/d*c*b^3","A"
442,1,123,100,0.350000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \cot \left(d x +c \right)}{d}+a^{3} x +\frac{a^{3} c}{d}-\frac{3 a^{2} b \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b \ln \left(\sin \left(d x +c \right)\right)}{d}-3 b^{2} a x -\frac{3 \cot \left(d x +c \right) a \,b^{2}}{d}-\frac{3 a \,b^{2} c}{d}+\frac{b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/3*a^3*cot(d*x+c)^3/d+a^3*cot(d*x+c)/d+a^3*x+1/d*a^3*c-3/2*a^2*b*cot(d*x+c)^2/d-3*a^2*b*ln(sin(d*x+c))/d-3*b^2*a*x-3/d*cot(d*x+c)*a*b^2-3/d*a*b^2*c+1/d*b^3*ln(sin(d*x+c))","A"
443,1,159,124,0.358000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} b \left(\cot^{3}\left(d x +c \right)\right)}{d}+3 a^{2} b x +\frac{3 a^{2} b \cot \left(d x +c \right)}{d}+\frac{3 a^{2} b c}{d}-\frac{3 b^{2} a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 b^{2} a \ln \left(\sin \left(d x +c \right)\right)}{d}-b^{3} x -\frac{\cot \left(d x +c \right) b^{3}}{d}-\frac{c \,b^{3}}{d}"," ",0,"-1/4/d*a^3*cot(d*x+c)^4+1/2*a^3*cot(d*x+c)^2/d+a^3*ln(sin(d*x+c))/d-a^2*b*cot(d*x+c)^3/d+3*a^2*b*x+3*a^2*b*cot(d*x+c)/d+3/d*a^2*b*c-3/2/d*b^2*a*cot(d*x+c)^2-3/d*b^2*a*ln(sin(d*x+c))-b^3*x-1/d*cot(d*x+c)*b^3-1/d*c*b^3","A"
444,1,193,149,0.364000," ","int(cot(d*x+c)^6*(a+b*tan(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{3} \cot \left(d x +c \right)}{d}-a^{3} x -\frac{a^{3} c}{d}-\frac{3 a^{2} b \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{2} b \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{2} b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{2} a \left(\cot^{3}\left(d x +c \right)\right)}{d}+3 b^{2} a x +\frac{3 \cot \left(d x +c \right) a \,b^{2}}{d}+\frac{3 a \,b^{2} c}{d}-\frac{b^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/5*a^3*cot(d*x+c)^5/d+1/3*a^3*cot(d*x+c)^3/d-a^3*cot(d*x+c)/d-a^3*x-1/d*a^3*c-3/4*a^2*b*cot(d*x+c)^4/d+3/2*a^2*b*cot(d*x+c)^2/d+3*a^2*b*ln(sin(d*x+c))/d-1/d*b^2*a*cot(d*x+c)^3+3*b^2*a*x+3/d*cot(d*x+c)*a*b^2+3/d*a*b^2*c-1/2/d*b^3*cot(d*x+c)^2-1/d*b^3*ln(sin(d*x+c))","A"
445,1,277,171,0.022000," ","int(tan(d*x+c)^3*(a+b*tan(d*x+c))^4,x)","\frac{b^{4} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}+\frac{4 \left(\tan^{5}\left(d x +c \right)\right) a \,b^{3}}{5 d}+\frac{3 a^{2} b^{2} \left(\tan^{4}\left(d x +c \right)\right)}{2 d}-\frac{\left(\tan^{4}\left(d x +c \right)\right) b^{4}}{4 d}+\frac{4 \left(\tan^{3}\left(d x +c \right)\right) a^{3} b}{3 d}-\frac{4 \left(\tan^{3}\left(d x +c \right)\right) a \,b^{3}}{3 d}+\frac{a^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{b^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{4 a^{3} b \tan \left(d x +c \right)}{d}+\frac{4 a \,b^{3} \tan \left(d x +c \right)}{d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4}}{2 d}+\frac{3 \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^{4}}{2 d}+\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d}-\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d}"," ",0,"1/6/d*b^4*tan(d*x+c)^6+4/5/d*tan(d*x+c)^5*a*b^3+3/2/d*a^2*b^2*tan(d*x+c)^4-1/4/d*tan(d*x+c)^4*b^4+4/3/d*tan(d*x+c)^3*a^3*b-4/3/d*tan(d*x+c)^3*a*b^3+1/2*a^4*tan(d*x+c)^2/d-3/d*a^2*b^2*tan(d*x+c)^2+1/2/d*b^4*tan(d*x+c)^2-4/d*a^3*b*tan(d*x+c)+4*a*b^3*tan(d*x+c)/d-1/2/d*ln(1+tan(d*x+c)^2)*a^4+3/d*ln(1+tan(d*x+c)^2)*a^2*b^2-1/2/d*ln(1+tan(d*x+c)^2)*b^4+4/d*arctan(tan(d*x+c))*a^3*b-4/d*arctan(tan(d*x+c))*a*b^3","A"
446,1,234,124,0.025000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^4,x)","\frac{\left(\tan^{5}\left(d x +c \right)\right) b^{4}}{5 d}+\frac{a \,b^{3} \left(\tan^{4}\left(d x +c \right)\right)}{d}+\frac{2 \left(\tan^{3}\left(d x +c \right)\right) a^{2} b^{2}}{d}-\frac{b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{3} b \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 a \,b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{a^{4} \tan \left(d x +c \right)}{d}-\frac{6 a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{b^{4} \tan \left(d x +c \right)}{d}-\frac{2 \ln \left(1+\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) a \,b^{3}}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d}+\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d}"," ",0,"1/5/d*tan(d*x+c)^5*b^4+1/d*a*b^3*tan(d*x+c)^4+2/d*tan(d*x+c)^3*a^2*b^2-1/3*b^4*tan(d*x+c)^3/d+2/d*a^3*b*tan(d*x+c)^2-2*a*b^3*tan(d*x+c)^2/d+a^4*tan(d*x+c)/d-6*a^2*b^2*tan(d*x+c)/d+1/d*b^4*tan(d*x+c)-2/d*ln(1+tan(d*x+c)^2)*a^3*b+2/d*ln(1+tan(d*x+c)^2)*a*b^3-1/d*arctan(tan(d*x+c))*a^4+6/d*arctan(tan(d*x+c))*a^2*b^2-1/d*arctan(tan(d*x+c))*b^4","A"
447,1,192,124,0.021000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^4,x)","\frac{\left(\tan^{4}\left(d x +c \right)\right) b^{4}}{4 d}+\frac{4 \left(\tan^{3}\left(d x +c \right)\right) a \,b^{3}}{3 d}+\frac{3 a^{2} b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{b^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{4 a^{3} b \tan \left(d x +c \right)}{d}-\frac{4 a \,b^{3} \tan \left(d x +c \right)}{d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4}}{2 d}-\frac{3 \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^{4}}{2 d}-\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d}+\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d}"," ",0,"1/4/d*tan(d*x+c)^4*b^4+4/3/d*tan(d*x+c)^3*a*b^3+3/d*a^2*b^2*tan(d*x+c)^2-1/2/d*b^4*tan(d*x+c)^2+4/d*a^3*b*tan(d*x+c)-4*a*b^3*tan(d*x+c)/d+1/2/d*ln(1+tan(d*x+c)^2)*a^4-3/d*ln(1+tan(d*x+c)^2)*a^2*b^2+1/2/d*ln(1+tan(d*x+c)^2)*b^4-4/d*arctan(tan(d*x+c))*a^3*b+4/d*arctan(tan(d*x+c))*a*b^3","A"
448,1,152,101,0.021000," ","int((a+b*tan(d*x+c))^4,x)","\frac{b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a \,b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2} \tan \left(d x +c \right)}{d}-\frac{b^{4} \tan \left(d x +c \right)}{d}+\frac{2 \ln \left(1+\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) a \,b^{3}}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d}-\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d}"," ",0,"1/3*b^4*tan(d*x+c)^3/d+2*a*b^3*tan(d*x+c)^2/d+6*a^2*b^2*tan(d*x+c)/d-1/d*b^4*tan(d*x+c)+2/d*ln(1+tan(d*x+c)^2)*a^3*b-2/d*ln(1+tan(d*x+c)^2)*a*b^3+1/d*arctan(tan(d*x+c))*a^4-6/d*arctan(tan(d*x+c))*a^2*b^2+1/d*arctan(tan(d*x+c))*b^4","A"
449,1,113,90,0.375000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^4,x)","\frac{a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}+4 a^{3} b x +\frac{4 a^{3} b c}{d}-\frac{6 a^{2} b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}-4 a \,b^{3} x +\frac{4 a \,b^{3} \tan \left(d x +c \right)}{d}-\frac{4 a \,b^{3} c}{d}+\frac{b^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"a^4*ln(sin(d*x+c))/d+4*a^3*b*x+4/d*a^3*b*c-6/d*a^2*b^2*ln(cos(d*x+c))-4*a*b^3*x+4*a*b^3*tan(d*x+c)/d-4/d*a*b^3*c+1/2/d*b^4*tan(d*x+c)^2+b^4*ln(cos(d*x+c))/d","A"
450,1,112,97,0.308000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^4,x)","-a^{4} x +6 a^{2} b^{2} x -b^{4} x -\frac{4 a \,b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{a^{4} \cot \left(d x +c \right)}{d}+\frac{b^{4} \tan \left(d x +c \right)}{d}+\frac{4 a^{3} b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{4} c}{d}+\frac{6 a^{2} b^{2} c}{d}-\frac{b^{4} c}{d}"," ",0,"-a^4*x+6*a^2*b^2*x-b^4*x-4*a*b^3*ln(cos(d*x+c))/d-a^4*cot(d*x+c)/d+1/d*b^4*tan(d*x+c)+4*a^3*b*ln(sin(d*x+c))/d-1/d*a^4*c+6/d*a^2*b^2*c-1/d*b^4*c","A"
451,1,115,97,0.413000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-4 a^{3} b x -\frac{4 a^{3} b \cot \left(d x +c \right)}{d}-\frac{4 a^{3} b c}{d}+\frac{6 a^{2} b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+4 a \,b^{3} x +\frac{4 a \,b^{3} c}{d}-\frac{b^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a^4*cot(d*x+c)^2/d-a^4*ln(sin(d*x+c))/d-4*a^3*b*x-4*a^3*b*cot(d*x+c)/d-4/d*a^3*b*c+6/d*a^2*b^2*ln(sin(d*x+c))+4*a*b^3*x+4/d*a*b^3*c-b^4*ln(cos(d*x+c))/d","A"
452,1,144,111,0.333000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} \cot \left(d x +c \right)}{d}+a^{4} x +\frac{a^{4} c}{d}-\frac{2 a^{3} b \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{4 a^{3} b \ln \left(\sin \left(d x +c \right)\right)}{d}-6 a^{2} b^{2} x -\frac{6 \cot \left(d x +c \right) a^{2} b^{2}}{d}-\frac{6 a^{2} b^{2} c}{d}+\frac{4 a \,b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+b^{4} x +\frac{b^{4} c}{d}"," ",0,"-1/3*a^4*cot(d*x+c)^3/d+a^4*cot(d*x+c)/d+a^4*x+1/d*a^4*c-2*a^3*b*cot(d*x+c)^2/d-4*a^3*b*ln(sin(d*x+c))/d-6*a^2*b^2*x-6/d*cot(d*x+c)*a^2*b^2-6/d*a^2*b^2*c+4/d*a*b^3*ln(sin(d*x+c))+b^4*x+1/d*b^4*c","A"
453,1,180,135,0.387000," ","int(cot(d*x+c)^5*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 a^{3} b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{4 a^{3} b \cot \left(d x +c \right)}{d}+4 a^{3} b x +\frac{4 a^{3} b c}{d}-\frac{3 a^{2} b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{6 a^{2} b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-4 a \,b^{3} x -\frac{4 \cot \left(d x +c \right) a \,b^{3}}{d}-\frac{4 a \,b^{3} c}{d}+\frac{b^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a^4*cot(d*x+c)^4/d+1/2*a^4*cot(d*x+c)^2/d+a^4*ln(sin(d*x+c))/d-4/3*a^3*b*cot(d*x+c)^3/d+4*a^3*b*cot(d*x+c)/d+4*a^3*b*x+4/d*a^3*b*c-3/d*a^2*b^2*cot(d*x+c)^2-6/d*a^2*b^2*ln(sin(d*x+c))-4*a*b^3*x-4/d*cot(d*x+c)*a*b^3-4/d*a*b^3*c+1/d*b^4*ln(sin(d*x+c))","A"
454,1,232,164,0.377000," ","int(cot(d*x+c)^6*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{4} \cot \left(d x +c \right)}{d}-a^{4} x -\frac{a^{4} c}{d}-\frac{a^{3} b \left(\cot^{4}\left(d x +c \right)\right)}{d}+\frac{2 a^{3} b \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{4 a^{3} b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a^{2} b^{2} \left(\cot^{3}\left(d x +c \right)\right)}{d}+6 a^{2} b^{2} x +\frac{6 \cot \left(d x +c \right) a^{2} b^{2}}{d}+\frac{6 a^{2} b^{2} c}{d}-\frac{2 a \,b^{3} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{4 a \,b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-b^{4} x -\frac{\cot \left(d x +c \right) b^{4}}{d}-\frac{b^{4} c}{d}"," ",0,"-1/5*a^4*cot(d*x+c)^5/d+1/3*a^4*cot(d*x+c)^3/d-a^4*cot(d*x+c)/d-a^4*x-1/d*a^4*c-a^3*b*cot(d*x+c)^4/d+2*a^3*b*cot(d*x+c)^2/d+4*a^3*b*ln(sin(d*x+c))/d-2/d*a^2*b^2*cot(d*x+c)^3+6*a^2*b^2*x+6/d*cot(d*x+c)*a^2*b^2+6/d*a^2*b^2*c-2/d*a*b^3*cot(d*x+c)^2-4/d*a*b^3*ln(sin(d*x+c))-b^4*x-1/d*cot(d*x+c)*b^4-1/d*b^4*c","A"
455,1,267,188,0.403000," ","int(cot(d*x+c)^7*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \left(\cot^{6}\left(d x +c \right)\right)}{6 d}+\frac{a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 a^{3} b \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{4 a^{3} b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{4 a^{3} b \cot \left(d x +c \right)}{d}-4 a^{3} b x -\frac{4 a^{3} b c}{d}-\frac{3 a^{2} b^{2} \left(\cot^{4}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{2} b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 a \,b^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{4 \cot \left(d x +c \right) a \,b^{3}}{d}+4 a \,b^{3} x +\frac{4 a \,b^{3} c}{d}-\frac{b^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/6/d*a^4*cot(d*x+c)^6+1/4*a^4*cot(d*x+c)^4/d-1/2*a^4*cot(d*x+c)^2/d-a^4*ln(sin(d*x+c))/d-4/5*a^3*b*cot(d*x+c)^5/d+4/3*a^3*b*cot(d*x+c)^3/d-4*a^3*b*cot(d*x+c)/d-4*a^3*b*x-4/d*a^3*b*c-3/2/d*a^2*b^2*cot(d*x+c)^4+3/d*a^2*b^2*cot(d*x+c)^2+6/d*a^2*b^2*ln(sin(d*x+c))-4/3/d*a*b^3*cot(d*x+c)^3+4/d*cot(d*x+c)*a*b^3+4*a*b^3*x+4/d*a*b^3*c-1/2/d*b^4*cot(d*x+c)^2-1/d*b^4*ln(sin(d*x+c))","A"
456,1,179,148,0.182000," ","int(tan(d*x+c)^6/(a+b*tan(d*x+c)),x)","\frac{\tan^{4}\left(d x +c \right)}{4 b d}-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 b^{2} d}+\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d \,b^{3}}-\frac{\tan^{2}\left(d x +c \right)}{2 b d}-\frac{a^{3} \tan \left(d x +c \right)}{d \,b^{4}}+\frac{a \tan \left(d x +c \right)}{b^{2} d}+\frac{a^{6} \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{5} \left(a^{2}+b^{2}\right) d}+\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/4*tan(d*x+c)^4/b/d-1/3*a*tan(d*x+c)^3/b^2/d+1/2/d/b^3*a^2*tan(d*x+c)^2-1/2*tan(d*x+c)^2/b/d-1/d/b^4*a^3*tan(d*x+c)+a*tan(d*x+c)/b^2/d+a^6*ln(a+b*tan(d*x+c))/b^5/(a^2+b^2)/d+1/2/d/(a^2+b^2)*b*ln(1+tan(d*x+c)^2)-1/d/(a^2+b^2)*a*arctan(tan(d*x+c))","A"
457,1,143,121,0.196000," ","int(tan(d*x+c)^5/(a+b*tan(d*x+c)),x)","\frac{\tan^{3}\left(d x +c \right)}{3 b d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 b^{2} d}+\frac{a^{2} \tan \left(d x +c \right)}{d \,b^{3}}-\frac{\tan \left(d x +c \right)}{b d}-\frac{a^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{4} \left(a^{2}+b^{2}\right) d}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/3*tan(d*x+c)^3/b/d-1/2*a*tan(d*x+c)^2/b^2/d+1/d/b^3*a^2*tan(d*x+c)-tan(d*x+c)/b/d-a^5*ln(a+b*tan(d*x+c))/b^4/(a^2+b^2)/d+1/2/d/(a^2+b^2)*a*ln(1+tan(d*x+c)^2)+1/d/(a^2+b^2)*b*arctan(tan(d*x+c))","A"
458,1,110,95,0.162000," ","int(tan(d*x+c)^4/(a+b*tan(d*x+c)),x)","\frac{\tan^{2}\left(d x +c \right)}{2 b d}-\frac{a \tan \left(d x +c \right)}{b^{2} d}+\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{3} \left(a^{2}+b^{2}\right) d}-\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/2*tan(d*x+c)^2/b/d-a*tan(d*x+c)/b^2/d+a^4*ln(a+b*tan(d*x+c))/b^3/(a^2+b^2)/d-1/2/d/(a^2+b^2)*b*ln(1+tan(d*x+c)^2)+1/d/(a^2+b^2)*a*arctan(tan(d*x+c))","A"
459,1,94,79,0.184000," ","int(tan(d*x+c)^3/(a+b*tan(d*x+c)),x)","\frac{\tan \left(d x +c \right)}{b d}-\frac{a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{2} \left(a^{2}+b^{2}\right) d}-\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"tan(d*x+c)/b/d-a^3*ln(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d-1/2/d/(a^2+b^2)*a*ln(1+tan(d*x+c)^2)-1/d/(a^2+b^2)*b*arctan(tan(d*x+c))","A"
460,1,80,66,0.159000," ","int(tan(d*x+c)^2/(a+b*tan(d*x+c)),x)","\frac{a^{2} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right) b}+\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/d*a^2/(a^2+b^2)/b*ln(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)*b*ln(1+tan(d*x+c)^2)-1/d/(a^2+b^2)*a*arctan(tan(d*x+c))","A"
461,1,75,46,0.149000," ","int(tan(d*x+c)/(a+b*tan(d*x+c)),x)","-\frac{a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"-1/d*a/(a^2+b^2)*ln(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)*a*ln(1+tan(d*x+c)^2)+1/d/(a^2+b^2)*b*arctan(tan(d*x+c))","A"
462,1,74,45,0.163000," ","int(1/(a+b*tan(d*x+c)),x)","\frac{b \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}-\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/d*b/(a^2+b^2)*ln(a+b*tan(d*x+c))-1/2/d/(a^2+b^2)*b*ln(1+tan(d*x+c)^2)+1/d/(a^2+b^2)*a*arctan(tan(d*x+c))","A"
463,1,95,66,0.472000," ","int(cot(d*x+c)/(a+b*tan(d*x+c)),x)","-\frac{b^{2} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right) a}+\frac{\ln \left(\tan \left(d x +c \right)\right)}{d a}-\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"-1/d*b^2/(a^2+b^2)/a*ln(a+b*tan(d*x+c))+1/d/a*ln(tan(d*x+c))-1/2/d/(a^2+b^2)*a*ln(1+tan(d*x+c)^2)-1/d/(a^2+b^2)*b*arctan(tan(d*x+c))","A"
464,1,112,81,0.423000," ","int(cot(d*x+c)^2/(a+b*tan(d*x+c)),x)","\frac{b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right) a^{2}}-\frac{1}{d a \tan \left(d x +c \right)}-\frac{b \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}+\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/d*b^3/(a^2+b^2)/a^2*ln(a+b*tan(d*x+c))-1/d/a/tan(d*x+c)-b*ln(tan(d*x+c))/a^2/d+1/2/d/(a^2+b^2)*b*ln(1+tan(d*x+c)^2)-1/d/(a^2+b^2)*a*arctan(tan(d*x+c))","A"
465,1,144,105,0.523000," ","int(cot(d*x+c)^3/(a+b*tan(d*x+c)),x)","-\frac{b^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right) a^{3}}-\frac{1}{2 d a \tan \left(d x +c \right)^{2}}-\frac{\ln \left(\tan \left(d x +c \right)\right)}{d a}+\frac{\ln \left(\tan \left(d x +c \right)\right) b^{2}}{d \,a^{3}}+\frac{b}{d \,a^{2} \tan \left(d x +c \right)}+\frac{a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"-1/d*b^4/(a^2+b^2)/a^3*ln(a+b*tan(d*x+c))-1/2/d/a/tan(d*x+c)^2-1/d/a*ln(tan(d*x+c))+1/d/a^3*ln(tan(d*x+c))*b^2+1/d*b/a^2/tan(d*x+c)+1/2/d/(a^2+b^2)*a*ln(1+tan(d*x+c)^2)+1/d/(a^2+b^2)*b*arctan(tan(d*x+c))","A"
466,1,179,129,0.484000," ","int(cot(d*x+c)^4/(a+b*tan(d*x+c)),x)","\frac{b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right) a^{4}}-\frac{1}{3 d a \tan \left(d x +c \right)^{3}}+\frac{1}{d a \tan \left(d x +c \right)}-\frac{b^{2}}{d \,a^{3} \tan \left(d x +c \right)}+\frac{b \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}-\frac{b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{4}}+\frac{b}{2 d \,a^{2} \tan \left(d x +c \right)^{2}}-\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/d*b^5/(a^2+b^2)/a^4*ln(a+b*tan(d*x+c))-1/3/d/a/tan(d*x+c)^3+1/d/a/tan(d*x+c)-1/d/a^3/tan(d*x+c)*b^2+b*ln(tan(d*x+c))/a^2/d-1/d/a^4*b^3*ln(tan(d*x+c))+1/2/d*b/a^2/tan(d*x+c)^2-1/2/d/(a^2+b^2)*b*ln(1+tan(d*x+c)^2)+1/d/(a^2+b^2)*a*arctan(tan(d*x+c))","A"
467,1,233,237,0.190000," ","int(tan(d*x+c)^6/(a+b*tan(d*x+c))^2,x)","\frac{\tan^{3}\left(d x +c \right)}{3 b^{2} d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{b^{3} d}+\frac{3 a^{2} \tan \left(d x +c \right)}{d \,b^{4}}-\frac{\tan \left(d x +c \right)}{b^{2} d}-\frac{a^{6}}{d \,b^{5} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{4 a^{7} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{5} \left(a^{2}+b^{2}\right)^{2}}-\frac{6 a^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/3*tan(d*x+c)^3/b^2/d-a*tan(d*x+c)^2/b^3/d+3/d/b^4*a^2*tan(d*x+c)-tan(d*x+c)/b^2/d-1/d/b^5*a^6/(a^2+b^2)/(a+b*tan(d*x+c))-4/d/b^5*a^7/(a^2+b^2)^2*ln(a+b*tan(d*x+c))-6/d/b^3*a^5/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+1/d/(a^2+b^2)^2*a*b*ln(1+tan(d*x+c)^2)-1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^2+1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*b^2","A"
468,1,205,195,0.196000," ","int(tan(d*x+c)^5/(a+b*tan(d*x+c))^2,x)","\frac{\tan^{2}\left(d x +c \right)}{2 d \,b^{2}}-\frac{2 a \tan \left(d x +c \right)}{d \,b^{3}}+\frac{3 a^{6} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{4} \left(a^{2}+b^{2}\right)^{2}}+\frac{5 a^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{a^{5}}{d \,b^{4} \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}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{2 a b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/2/d/b^2*tan(d*x+c)^2-2/d/b^3*a*tan(d*x+c)+3/d/b^4*a^6/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+5/d/b^2*a^4/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+1/d/b^4*a^5/(a^2+b^2)/(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2+2/d/(a^2+b^2)^2*a*b*arctan(tan(d*x+c))","A"
469,1,183,155,0.180000," ","int(tan(d*x+c)^4/(a+b*tan(d*x+c))^2,x)","\frac{\tan \left(d x +c \right)}{b^{2} d}-\frac{a^{4}}{d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 a^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{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)}{d b \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"tan(d*x+c)/b^2/d-1/d/b^3*a^4/(a^2+b^2)/(a+b*tan(d*x+c))-2/d/b^3*a^5/(a^2+b^2)^2*ln(a+b*tan(d*x+c))-4/d/b*a^3/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^2-1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*b^2-1/d/(a^2+b^2)^2*a*b*ln(1+tan(d*x+c)^2)","A"
470,1,170,114,0.209000," ","int(tan(d*x+c)^3/(a+b*tan(d*x+c))^2,x)","\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{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)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a^{3}}{b^{2} \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 a b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d/b^2*a^4/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+3/d*a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+a^3/b^2/(a^2+b^2)/d/(a+b*tan(d*x+c))-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2-2/d/(a^2+b^2)^2*a*b*arctan(tan(d*x+c))","A"
471,1,134,88,0.197000," ","int(tan(d*x+c)^2/(a+b*tan(d*x+c))^2,x)","-\frac{a^{2}}{b \left(a^{2}+b^{2}\right) d \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)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-a^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))-2/d*a*b/(a^2+b^2)^2*ln(a+b*tan(d*x+c))-1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^2+1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*b^2+1/d/(a^2+b^2)^2*a*b*ln(1+tan(d*x+c)^2)","A"
472,1,162,82,0.158000," ","int(tan(d*x+c)/(a+b*tan(d*x+c))^2,x)","\frac{a}{\left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{2} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{2 a b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"a/(a^2+b^2)/d/(a+b*tan(d*x+c))-1/d*a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+1/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*b^2+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2+2/d/(a^2+b^2)^2*a*b*arctan(tan(d*x+c))","A"
473,1,130,82,0.157000," ","int(1/(a+b*tan(d*x+c))^2,x)","-\frac{b}{\left(a^{2}+b^{2}\right) d \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)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-b/(a^2+b^2)/d/(a+b*tan(d*x+c))+2/d*a*b/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^2-1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*b^2-1/d/(a^2+b^2)^2*a*b*ln(1+tan(d*x+c)^2)","A"
474,1,185,107,0.484000," ","int(cot(d*x+c)/(a+b*tan(d*x+c))^2,x)","\frac{b^{2}}{a \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 \ln \left(a +b \tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} a^{2}}+\frac{\ln \left(\tan \left(d x +c \right)\right)}{d \,a^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 a b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"b^2/a/(a^2+b^2)/d/(a+b*tan(d*x+c))-3/d/(a^2+b^2)^2*ln(a+b*tan(d*x+c))*b^2-1/d*b^4/(a^2+b^2)^2/a^2*ln(a+b*tan(d*x+c))+1/d/a^2*ln(tan(d*x+c))-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2-2/d/(a^2+b^2)^2*a*b*arctan(tan(d*x+c))","A"
475,1,201,150,0.501000," ","int(cot(d*x+c)^2/(a+b*tan(d*x+c))^2,x)","-\frac{b^{3}}{d \left(a^{2}+b^{2}\right) a^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} a}+\frac{2 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} a^{3}}-\frac{1}{d \,a^{2} \tan \left(d x +c \right)}-\frac{2 b \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-1/d*b^3/(a^2+b^2)/a^2/(a+b*tan(d*x+c))+4/d*b^3/(a^2+b^2)^2/a*ln(a+b*tan(d*x+c))+2/d*b^5/(a^2+b^2)^2/a^3*ln(a+b*tan(d*x+c))-1/d/a^2/tan(d*x+c)-2*b*ln(tan(d*x+c))/a^3/d-1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^2+1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*b^2+1/d/(a^2+b^2)^2*a*b*ln(1+tan(d*x+c)^2)","A"
476,1,240,185,0.563000," ","int(cot(d*x+c)^3/(a+b*tan(d*x+c))^2,x)","\frac{b^{4}}{d \left(a^{2}+b^{2}\right) a^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{5 b^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} a^{2}}-\frac{3 b^{6} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} a^{4}}-\frac{1}{2 d \,a^{2} \tan \left(d x +c \right)^{2}}-\frac{\ln \left(\tan \left(d x +c \right)\right)}{d \,a^{2}}+\frac{3 \ln \left(\tan \left(d x +c \right)\right) b^{2}}{d \,a^{4}}+\frac{2 b}{d \,a^{3} \tan \left(d x +c \right)}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{2 a b \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d*b^4/(a^2+b^2)/a^3/(a+b*tan(d*x+c))-5/d*b^4/(a^2+b^2)^2/a^2*ln(a+b*tan(d*x+c))-3/d*b^6/(a^2+b^2)^2/a^4*ln(a+b*tan(d*x+c))-1/2/d/a^2/tan(d*x+c)^2-1/d/a^2*ln(tan(d*x+c))+3/d/a^4*ln(tan(d*x+c))*b^2+2/d/a^3*b/tan(d*x+c)+1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*b^2+2/d/(a^2+b^2)^2*a*b*arctan(tan(d*x+c))","A"
477,1,328,279,0.195000," ","int(tan(d*x+c)^6/(a+b*tan(d*x+c))^3,x)","\frac{\tan^{2}\left(d x +c \right)}{2 b^{3} d}-\frac{3 a \tan \left(d x +c \right)}{b^{4} d}-\frac{a^{6}}{2 d \,b^{5} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{6 a^{8} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{5} \left(a^{2}+b^{2}\right)^{3}}+\frac{17 a^{6} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{15 a^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{d b \left(a^{2}+b^{2}\right)^{3}}+\frac{4 a^{7}}{d \,b^{5} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{6 a^{5}}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/2*tan(d*x+c)^2/b^3/d-3*a*tan(d*x+c)/b^4/d-1/2/d/b^5*a^6/(a^2+b^2)/(a+b*tan(d*x+c))^2+6/d/b^5*a^8/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+17/d/b^3*a^6/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+15/d/b*a^4/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+4/d/b^5*a^7/(a^2+b^2)^2/(a+b*tan(d*x+c))+6/d/b^3*a^5/(a^2+b^2)^2/(a+b*tan(d*x+c))+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3-1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^3+3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a*b^2","A"
478,1,307,235,0.214000," ","int(tan(d*x+c)^5/(a+b*tan(d*x+c))^3,x)","\frac{\tan \left(d x +c \right)}{d \,b^{3}}-\frac{3 a^{6}}{d \,b^{4} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{5 a^{4}}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{5}}{2 d \,b^{4} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 a^{7} \ln \left(a +b \tan \left(d x +c \right)\right)}{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)}{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)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} a}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/d/b^3*tan(d*x+c)-3/d/b^4*a^6/(a^2+b^2)^2/(a+b*tan(d*x+c))-5/d/b^2*a^4/(a^2+b^2)^2/(a+b*tan(d*x+c))+1/2/d/b^4*a^5/(a^2+b^2)/(a+b*tan(d*x+c))^2-3/d/b^4*a^7/(a^2+b^2)^3*ln(a+b*tan(d*x+c))-9/d/b^2*a^5/(a^2+b^2)^3*ln(a+b*tan(d*x+c))-10/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^3-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^2*a+3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^2*b-1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*b^3","A"
479,1,293,181,0.206000," ","int(tan(d*x+c)^4/(a+b*tan(d*x+c))^3,x)","-\frac{a^{4}}{2 d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{6} \ln \left(a +b \tan \left(d x +c \right)\right)}{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)}{d b \left(a^{2}+b^{2}\right)^{3}}+\frac{6 a^{2} b \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{2 a^{5}}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 a^{3}}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \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^4/b^3/(a^2+b^2)/(a+b*tan(d*x+c))^2+1/d/b^3*a^6/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+3/d/b*a^4/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+6/d*a^2/(a^2+b^2)^3*b*ln(a+b*tan(d*x+c))+2/d/b^3*a^5/(a^2+b^2)^2/(a+b*tan(d*x+c))+4/d*a^3/b/(a^2+b^2)^2/(a+b*tan(d*x+c))-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3+1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^3-3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a*b^2","A"
480,1,256,145,0.223000," ","int(tan(d*x+c)^3/(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a \ln \left(a +b \tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{a^{4}}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{2}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{3}}{2 d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} a}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{3}}{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))-3/d*a/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*b^2-1/d/b^2*a^4/(a^2+b^2)^2/(a+b*tan(d*x+c))-3/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))+1/2/d/b^2*a^3/(a^2+b^2)/(a+b*tan(d*x+c))^2-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^3+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^2*a-3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^2*b+1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*b^3","A"
481,1,224,127,0.200000," ","int(tan(d*x+c)^2/(a+b*tan(d*x+c))^3,x)","-\frac{a^{2}}{2 b \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{2 a b}{\left(a^{2}+b^{2}\right)^{2} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{2} b \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/2*a^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+2*a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))-3/d*a^2/(a^2+b^2)^3*b*ln(a+b*tan(d*x+c))+1/d*b^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3-1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^3+3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a*b^2","A"
482,1,249,127,0.201000," ","int(tan(d*x+c)/(a+b*tan(d*x+c))^3,x)","\frac{a}{2 \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{2}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{2}}{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)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 a \ln \left(a +b \tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} a}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/2*a/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+1/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))-1/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*b^2-1/d*a^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+3/d*a/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*b^2+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^3-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^2*a+3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^2*b-1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*b^3","A"
483,1,219,120,0.166000," ","int(1/(a+b*tan(d*x+c))^3,x)","-\frac{b}{2 \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a^{2} b \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{2 a b}{\left(a^{2}+b^{2}\right)^{2} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/2*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+3/d*a^2/(a^2+b^2)^3*b*ln(a+b*tan(d*x+c))-1/d*b^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))-2*a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))-3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b+1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3+1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^3-3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a*b^2","A"
484,1,304,166,0.603000," ","int(cot(d*x+c)/(a+b*tan(d*x+c))^3,x)","\frac{b^{2}}{2 a \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{4}}{d \left(a^{2}+b^{2}\right)^{2} a^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{6 a \ln \left(a +b \tan \left(d x +c \right)\right) 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)}{d \left(a^{2}+b^{2}\right)^{3} a}-\frac{b^{6} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3} a^{3}}+\frac{\ln \left(\tan \left(d x +c \right)\right)}{d \,a^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{2} a}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/2*b^2/a/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+3/d/(a^2+b^2)^2/(a+b*tan(d*x+c))*b^2+1/d*b^4/(a^2+b^2)^2/a^2/(a+b*tan(d*x+c))-6/d*a/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*b^2-3/d*b^4/(a^2+b^2)^3/a*ln(a+b*tan(d*x+c))-1/d*b^6/(a^2+b^2)^3/a^3*ln(a+b*tan(d*x+c))+1/d/a^3*ln(tan(d*x+c))-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^3+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^2*a-3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^2*b+1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*b^3","A"
485,1,326,209,0.506000," ","int(cot(d*x+c)^2/(a+b*tan(d*x+c))^3,x)","-\frac{b^{3}}{2 d \left(a^{2}+b^{2}\right) a^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{10 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{9 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3} a^{2}}+\frac{3 b^{7} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3} a^{4}}-\frac{4 b^{3}}{d \left(a^{2}+b^{2}\right)^{2} a \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 b^{5}}{d \left(a^{2}+b^{2}\right)^{2} a^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{1}{d \,a^{3} \tan \left(d x +c \right)}-\frac{3 b \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/2/d*b^3/(a^2+b^2)/a^2/(a+b*tan(d*x+c))^2+10/d*b^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+9/d*b^5/(a^2+b^2)^3/a^2*ln(a+b*tan(d*x+c))+3/d*b^7/(a^2+b^2)^3/a^4*ln(a+b*tan(d*x+c))-4/d*b^3/(a^2+b^2)^2/a/(a+b*tan(d*x+c))-2/d*b^5/(a^2+b^2)^2/a^3/(a+b*tan(d*x+c))-1/d/a^3/tan(d*x+c)-3*b*ln(tan(d*x+c))/a^4/d+3/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^2*b-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*b^3-1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^3+3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a*b^2","A"
486,1,462,311,0.229000," ","int(tan(d*x+c)^6/(a+b*tan(d*x+c))^4,x)","\frac{\tan \left(d x +c \right)}{d \,b^{4}}-\frac{a^{6}}{3 d \,b^{5} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{6 a^{8}}{d \,b^{5} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{17 a^{6}}{d \,b^{3} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{15 a^{4}}{d b \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{4 a^{9} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{5} \left(a^{2}+b^{2}\right)^{4}}-\frac{16 a^{7} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{3} \left(a^{2}+b^{2}\right)^{4}}-\frac{24 a^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d b \left(a^{2}+b^{2}\right)^{4}}-\frac{20 b \,a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{2 a^{7}}{d \,b^{5} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a^{5}}{d \,b^{3} \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^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"1/d/b^4*tan(d*x+c)-1/3/d/b^5*a^6/(a^2+b^2)/(a+b*tan(d*x+c))^3-6/d/b^5*a^8/(a^2+b^2)^3/(a+b*tan(d*x+c))-17/d/b^3*a^6/(a^2+b^2)^3/(a+b*tan(d*x+c))-15/d/b*a^4/(a^2+b^2)^3/(a+b*tan(d*x+c))-4/d/b^5*a^9/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-16/d/b^3*a^7/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-24/d/b*a^5/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-20/d*b*a^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))+2/d/b^5*a^7/(a^2+b^2)^2/(a+b*tan(d*x+c))^2+3/d/b^3*a^5/(a^2+b^2)^2/(a+b*tan(d*x+c))^2+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^3*b-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a*b^3-1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^4+6/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^2*b^2-1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^4","A"
487,1,448,252,0.233000," ","int(tan(d*x+c)^5/(a+b*tan(d*x+c))^4,x)","\frac{a^{8} \ln \left(a +b \tan \left(d x +c \right)\right)}{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)}{d \left(a^{2}+b^{2}\right)^{4} b^{2}}+\frac{5 a^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{10 a^{2} b^{2} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{3 a^{6}}{2 d \,b^{4} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{5 a^{4}}{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}}{3 d \,b^{4} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{3 a^{7}}{d \,b^{4} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{9 a^{5}}{d \,b^{2} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{10 a^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) 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^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"1/d*a^8/(a^2+b^2)^4/b^4*ln(a+b*tan(d*x+c))+4/d*a^6/(a^2+b^2)^4/b^2*ln(a+b*tan(d*x+c))+5/d*a^4/(a^2+b^2)^4*ln(a+b*tan(d*x+c))+10/d*a^2/(a^2+b^2)^4*b^2*ln(a+b*tan(d*x+c))-3/2/d*a^6/b^4/(a^2+b^2)^2/(a+b*tan(d*x+c))^2-5/2/d*a^4/b^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2+1/3/d*a^5/b^4/(a^2+b^2)/(a+b*tan(d*x+c))^3+3/d*a^7/b^4/(a^2+b^2)^3/(a+b*tan(d*x+c))+9/d*a^5/b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))+10/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^4-3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^2+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*b^4+4/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^3*b-4/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a*b^3","A"
488,1,380,202,0.210000," ","int(tan(d*x+c)^4/(a+b*tan(d*x+c))^4,x)","-\frac{a^{4}}{3 d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{a^{6}}{d \,b^{3} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{4}}{d b \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{6 a^{2} b}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 b \,a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 a \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{a^{5}}{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}}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) 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 \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/3/d*a^4/b^3/(a^2+b^2)/(a+b*tan(d*x+c))^3-1/d/b^3*a^6/(a^2+b^2)^3/(a+b*tan(d*x+c))-3/d/b*a^4/(a^2+b^2)^3/(a+b*tan(d*x+c))-6/d*a^2/(a^2+b^2)^3*b/(a+b*tan(d*x+c))+4/d*b*a^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-4/d*a*b^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))+1/d/b^3*a^5/(a^2+b^2)^2/(a+b*tan(d*x+c))^2+2/d*a^3/b/(a^2+b^2)^2/(a+b*tan(d*x+c))^2+1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^4-6/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^2*b^2+1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^4-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^3*b+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a*b^3","A"
489,1,376,185,0.242000," ","int(tan(d*x+c)^3/(a+b*tan(d*x+c))^4,x)","\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{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)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{a^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{4}}{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}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{3}}{3 d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) 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^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"1/d*a^4/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-6/d*a^2/(a^2+b^2)^4*b^2*ln(a+b*tan(d*x+c))+1/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*b^4-1/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))+3/d*a/(a^2+b^2)^3/(a+b*tan(d*x+c))*b^2-1/2/d*a^4/b^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2-3/2/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2+1/3/d/b^2*a^3/(a^2+b^2)/(a+b*tan(d*x+c))^3-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^4+3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^2-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*b^4-4/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^3*b+4/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a*b^3","B"
490,1,311,167,0.211000," ","int(tan(d*x+c)^2/(a+b*tan(d*x+c))^4,x)","-\frac{a^{2}}{3 b \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{a b}{\left(a^{2}+b^{2}\right)^{2} d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a^{2} b}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{4 b \,a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 a \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) 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 \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/3*a^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^3+a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2+3/d*a^2/(a^2+b^2)^3*b/(a+b*tan(d*x+c))-1/d*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))-4/d*b*a^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))+4/d*a*b^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^4+6/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^2*b^2-1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^4+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^3*b-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a*b^3","A"
491,1,369,168,0.224000," ","int(tan(d*x+c)/(a+b*tan(d*x+c))^4,x)","\frac{a}{3 \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{a^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{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)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(a +b \tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) 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^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"1/3*a/(a^2+b^2)/d/(a+b*tan(d*x+c))^3-1/d*a^4/(a^2+b^2)^4*ln(a+b*tan(d*x+c))+6/d*a^2/(a^2+b^2)^4*b^2*ln(a+b*tan(d*x+c))-1/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*b^4+1/2/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^2-1/2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*b^2+1/d*a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))-3/d*a/(a^2+b^2)^3/(a+b*tan(d*x+c))*b^2+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^4-3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^2+1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*b^4+4/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^3*b-4/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a*b^3","B"
492,1,304,163,0.184000," ","int(1/(a+b*tan(d*x+c))^4,x)","-\frac{b}{3 \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{3 a^{2} b}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a b}{\left(a^{2}+b^{2}\right)^{2} d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{4 b \,a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 a \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) 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 \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/3*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^3-3/d*a^2/(a^2+b^2)^3*b/(a+b*tan(d*x+c))+1/d*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))-a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2+4/d*b*a^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-4/d*a*b^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))+1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^4-6/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^2*b^2+1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^4-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^3*b+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a*b^3","A"
493,1,460,222,0.615000," ","int(cot(d*x+c)/(a+b*tan(d*x+c))^4,x)","\frac{b^{2}}{3 a \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{3 b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{b^{4}}{2 d \left(a^{2}+b^{2}\right)^{2} a^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{6 a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 b^{4}}{d \left(a^{2}+b^{2}\right)^{3} a \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{6}}{d \left(a^{2}+b^{2}\right)^{3} a^{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)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{5 \ln \left(a +b \tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 b^{6} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4} a^{2}}-\frac{b^{8} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4} a^{4}}+\frac{\ln \left(\tan \left(d x +c \right)\right)}{d \,a^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) 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^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"1/3*b^2/a/(a^2+b^2)/d/(a+b*tan(d*x+c))^3+3/2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))^2*b^2+1/2/d*b^4/(a^2+b^2)^2/a^2/(a+b*tan(d*x+c))^2+6/d*a/(a^2+b^2)^3/(a+b*tan(d*x+c))*b^2+3/d*b^4/(a^2+b^2)^3/a/(a+b*tan(d*x+c))+1/d*b^6/(a^2+b^2)^3/a^3/(a+b*tan(d*x+c))-10/d*a^2/(a^2+b^2)^4*b^2*ln(a+b*tan(d*x+c))-5/d/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*b^4-4/d*b^6/(a^2+b^2)^4/a^2*ln(a+b*tan(d*x+c))-1/d*b^8/(a^2+b^2)^4/a^4*ln(a+b*tan(d*x+c))+1/d/a^4*ln(tan(d*x+c))-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^4+3/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^2-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*b^4-4/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^3*b+4/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a*b^3","B"
494,1,478,276,0.534000," ","int(cot(d*x+c)^2/(a+b*tan(d*x+c))^4,x)","-\frac{b^{3}}{3 d \left(a^{2}+b^{2}\right) a^{2} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{10 b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{9 b^{5}}{d \left(a^{2}+b^{2}\right)^{3} a^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 b^{7}}{d \left(a^{2}+b^{2}\right)^{3} a^{4} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 b^{3}}{d \left(a^{2}+b^{2}\right)^{2} a \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b^{5}}{d \left(a^{2}+b^{2}\right)^{2} a^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{20 a \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{24 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4} a}+\frac{16 b^{7} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4} a^{3}}+\frac{4 b^{9} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4} a^{5}}-\frac{1}{d \,a^{4} \tan \left(d x +c \right)}-\frac{4 b \ln \left(\tan \left(d x +c \right)\right)}{a^{5} d}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) 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 \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/3/d*b^3/(a^2+b^2)/a^2/(a+b*tan(d*x+c))^3-10/d*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))-9/d*b^5/(a^2+b^2)^3/a^2/(a+b*tan(d*x+c))-3/d*b^7/(a^2+b^2)^3/a^4/(a+b*tan(d*x+c))-2/d*b^3/(a^2+b^2)^2/a/(a+b*tan(d*x+c))^2-1/d*b^5/(a^2+b^2)^2/a^3/(a+b*tan(d*x+c))^2+20/d*a*b^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))+24/d*b^5/(a^2+b^2)^4/a*ln(a+b*tan(d*x+c))+16/d*b^7/(a^2+b^2)^4/a^3*ln(a+b*tan(d*x+c))+4/d*b^9/(a^2+b^2)^4/a^5*ln(a+b*tan(d*x+c))-1/d/a^4/tan(d*x+c)-4*b*ln(tan(d*x+c))/a^5/d+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^3*b-2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a*b^3-1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^4+6/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^2*b^2-1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^4","A"
495,1,46,27,0.172000," ","int(1/(3+5*tan(d*x+c)),x)","\frac{5 \ln \left(3+5 \tan \left(d x +c \right)\right)}{34 d}-\frac{5 \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{68 d}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right)}{34 d}"," ",0,"5/34/d*ln(3+5*tan(d*x+c))-5/68/d*ln(1+tan(d*x+c)^2)+3/34/d*arctan(tan(d*x+c))","A"
496,1,63,44,0.148000," ","int(1/(3+5*tan(d*x+c))^2,x)","-\frac{5}{34 d \left(3+5 \tan \left(d x +c \right)\right)}+\frac{15 \ln \left(3+5 \tan \left(d x +c \right)\right)}{578 d}-\frac{15 \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{1156 d}-\frac{4 \arctan \left(\tan \left(d x +c \right)\right)}{289 d}"," ",0,"-5/34/d/(3+5*tan(d*x+c))+15/578/d*ln(3+5*tan(d*x+c))-15/1156/d*ln(1+tan(d*x+c)^2)-4/289/d*arctan(tan(d*x+c))","A"
497,1,80,61,0.162000," ","int(1/(3+5*tan(d*x+c))^3,x)","-\frac{5}{68 d \left(3+5 \tan \left(d x +c \right)\right)^{2}}-\frac{15}{578 d \left(3+5 \tan \left(d x +c \right)\right)}+\frac{5 \ln \left(3+5 \tan \left(d x +c \right)\right)}{19652 d}-\frac{5 \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{39304 d}-\frac{99 \arctan \left(\tan \left(d x +c \right)\right)}{19652 d}"," ",0,"-5/68/d/(3+5*tan(d*x+c))^2-15/578/d/(3+5*tan(d*x+c))+5/19652/d*ln(3+5*tan(d*x+c))-5/39304/d*ln(1+tan(d*x+c)^2)-99/19652/d*arctan(tan(d*x+c))","A"
498,1,97,78,0.169000," ","int(1/(3+5*tan(d*x+c))^4,x)","-\frac{5}{102 d \left(3+5 \tan \left(d x +c \right)\right)^{3}}-\frac{15}{1156 d \left(3+5 \tan \left(d x +c \right)\right)^{2}}-\frac{5}{19652 d \left(3+5 \tan \left(d x +c \right)\right)}-\frac{60 \ln \left(3+5 \tan \left(d x +c \right)\right)}{83521 d}+\frac{30 \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{83521 d}-\frac{161 \arctan \left(\tan \left(d x +c \right)\right)}{334084 d}"," ",0,"-5/102/d/(3+5*tan(d*x+c))^3-15/1156/d/(3+5*tan(d*x+c))^2-5/19652/d/(3+5*tan(d*x+c))-60/83521/d*ln(3+5*tan(d*x+c))+30/83521/d*ln(1+tan(d*x+c)^2)-161/334084/d*arctan(tan(d*x+c))","A"
499,1,46,27,0.164000," ","int(1/(5+3*tan(d*x+c)),x)","-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{68 d}+\frac{5 \arctan \left(\tan \left(d x +c \right)\right)}{34 d}+\frac{3 \ln \left(5+3 \tan \left(d x +c \right)\right)}{34 d}"," ",0,"-3/68/d*ln(1+tan(d*x+c)^2)+5/34/d*arctan(tan(d*x+c))+3/34/d*ln(5+3*tan(d*x+c))","A"
500,1,63,44,0.176000," ","int(1/(5+3*tan(d*x+c))^2,x)","-\frac{15 \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{1156 d}+\frac{4 \arctan \left(\tan \left(d x +c \right)\right)}{289 d}-\frac{3}{34 d \left(5+3 \tan \left(d x +c \right)\right)}+\frac{15 \ln \left(5+3 \tan \left(d x +c \right)\right)}{578 d}"," ",0,"-15/1156/d*ln(1+tan(d*x+c)^2)+4/289/d*arctan(tan(d*x+c))-3/34/d/(5+3*tan(d*x+c))+15/578/d*ln(5+3*tan(d*x+c))","A"
501,1,80,61,0.165000," ","int(1/(5+3*tan(d*x+c))^3,x)","-\frac{99 \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{39304 d}-\frac{5 \arctan \left(\tan \left(d x +c \right)\right)}{19652 d}-\frac{3}{68 d \left(5+3 \tan \left(d x +c \right)\right)^{2}}-\frac{15}{578 d \left(5+3 \tan \left(d x +c \right)\right)}+\frac{99 \ln \left(5+3 \tan \left(d x +c \right)\right)}{19652 d}"," ",0,"-99/39304/d*ln(1+tan(d*x+c)^2)-5/19652/d*arctan(tan(d*x+c))-3/68/d/(5+3*tan(d*x+c))^2-15/578/d/(5+3*tan(d*x+c))+99/19652/d*ln(5+3*tan(d*x+c))","A"
502,1,97,78,0.166000," ","int(1/(5+3*tan(d*x+c))^4,x)","-\frac{30 \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{83521 d}-\frac{161 \arctan \left(\tan \left(d x +c \right)\right)}{334084 d}-\frac{1}{34 d \left(5+3 \tan \left(d x +c \right)\right)^{3}}-\frac{15}{1156 d \left(5+3 \tan \left(d x +c \right)\right)^{2}}-\frac{99}{19652 d \left(5+3 \tan \left(d x +c \right)\right)}+\frac{60 \ln \left(5+3 \tan \left(d x +c \right)\right)}{83521 d}"," ",0,"-30/83521/d*ln(1+tan(d*x+c)^2)-161/334084/d*arctan(tan(d*x+c))-1/34/d/(5+3*tan(d*x+c))^3-15/1156/d/(5+3*tan(d*x+c))^2-99/19652/d/(5+3*tan(d*x+c))+60/83521/d*ln(5+3*tan(d*x+c))","A"
503,1,556,373,0.385000," ","int((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^4,x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d \,b^{3}}-\frac{4 \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5 d \,b^{3}}+\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3 d \,b^{3}}-\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 b d}+\frac{\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 b}-\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)}{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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\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 b}+\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)}{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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/7/d/b^3*(a+b*tan(d*x+c))^(7/2)-4/5/d/b^3*(a+b*tan(d*x+c))^(5/2)*a+2/3/d/b^3*(a+b*tan(d*x+c))^(3/2)*a^2-2/3*(a+b*tan(d*x+c))^(3/2)/b/d+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))-1/4/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/(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*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^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/(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"
504,1,519,133,0.321000," ","int((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^3,x)","\frac{2 \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 b^{2} d}-\frac{2 \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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{\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) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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{\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) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/5/d/b^2*(a+b*tan(d*x+c))^(5/2)-2/3*a*(a+b*tan(d*x+c))^(3/2)/b^2/d-2*(a+b*tan(d*x+c))^(1/2)/d+1/4/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/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+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^2+b^2)^(1/2)-1/4/d*(2*(a^2+b^2)^(1/2)+2*a)^(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/(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))*(a^2+b^2)^(1/2)","B"
505,1,499,307,0.272000," ","int((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^2,x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 b d}-\frac{\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 b}+\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)}{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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\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 b d}-\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)}{4 b 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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/3*(a+b*tan(d*x+c))^(3/2)/b/d-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))+1/4/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/(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/b/d*(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))-1/4/b/d*(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))+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))","A"
506,1,478,88,0.225000," ","int((a+b*tan(d*x+c))^(1/2)*tan(d*x+c),x)","\frac{2 \sqrt{a +b \tan \left(d x +c \right)}}{d}-\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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{\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) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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{\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) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2*(a+b*tan(d*x+c))^(1/2)/d-1/4/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/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-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^2+b^2)^(1/2)+1/4/d*(2*(a^2+b^2)^(1/2)+2*a)^(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/(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))*(a^2+b^2)^(1/2)","B"
507,1,654,287,0.288000," ","int((a+b*tan(d*x+c))^(1/2),x)","\frac{\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 b}-\frac{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{\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 b}+\frac{\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{\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 b d}+\frac{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{\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 b d}-\frac{\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*(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))+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))-1/4/b/d*(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/b/d*(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*(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"
508,1,15731,94,2.357000," ","int(cot(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"
509,1,26752,336,1.750000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
510,1,45073,157,2.357000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
511,1,906,177,0.270000," ","int(tan(d*x+c)^4*(a+b*tan(d*x+c))^(3/2),x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{9}{2}}}{9 d \,b^{3}}-\frac{4 a \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d \,b^{3}}+\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}} a^{2}}{5 d \,b^{3}}-\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 b d}+\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) \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{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}}{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}{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}}}{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}{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{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}}{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}{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}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/9/d/b^3*(a+b*tan(d*x+c))^(9/2)-4/7/d/b^3*a*(a+b*tan(d*x+c))^(7/2)+2/5/d/b^3*(a+b*tan(d*x+c))^(5/2)*a^2-2/5*(a+b*tan(d*x+c))^(5/2)/b/d+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))*(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^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)+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-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)+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^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)-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+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)","B"
512,1,863,151,0.239000," ","int(tan(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d \,b^{2}}-\frac{2 a \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 b^{2} d}-\frac{2 \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)}}{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}}}{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}{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) a^{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)}{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) \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) \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) \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) a^{2}}{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)}{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) \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/7/d/b^2*(a+b*tan(d*x+c))^(7/2)-2/5*a*(a+b*tan(d*x+c))^(5/2)/b^2/d-2/3*(a+b*tan(d*x+c))^(3/2)/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))*(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))*(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^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))+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^2+b^2)^(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))*(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))*(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^2-1/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))-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^2+b^2)^(1/2)*a","B"
513,1,842,111,0.267000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 b d}-\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) \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{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}}{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}{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}}}{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}{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{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}}{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}{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}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/5*(a+b*tan(d*x+c))^(5/2)/b/d-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))*(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^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)-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+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)-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^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)+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-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)","B"
514,1,831,106,0.170000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^(3/2),x)","\frac{2 \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)}}{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}}}{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}{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) \left(a^{2}+b^{2}\right)}{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) \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{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^{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}}}{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}{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) \left(a^{2}+b^{2}\right)}{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) \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{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^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/3*(a+b*tan(d*x+c))^(3/2)/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))*(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))*(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^2+b^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^2+b^2)^(1/2)*a+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^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))*(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))*(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^2+b^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^2+b^2)^(1/2)*a-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^2","B"
515,1,822,91,0.199000," ","int((a+b*tan(d*x+c))^(3/2),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) \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{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}}{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}{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}}}{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}{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{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}}{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}{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}}}{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))*(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^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)+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-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)+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^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)-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+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)","B"
516,1,22251,94,1.851000," ","int(cot(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"
517,1,35888,123,2.190000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
518,1,54149,157,2.476000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
519,1,1240,177,0.283000," ","int(tan(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{9}{2}}}{9 d \,b^{2}}-\frac{2 a \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 b^{2} d}-\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}-\frac{2 a \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{2 a^{2} \sqrt{a +b \tan \left(d x +c \right)}}{d}+\frac{2 b^{2} \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}{2 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 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) \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^{3}}{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}{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) \sqrt{a^{2}+b^{2}}\, a^{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) \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}{2 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 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^{3}}{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}{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) \sqrt{a^{2}+b^{2}}\, a^{2}}{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) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/9/d/b^2*(a+b*tan(d*x+c))^(9/2)-2/7*a*(a+b*tan(d*x+c))^(7/2)/b^2/d-2/5*(a+b*tan(d*x+c))^(5/2)/d-2/3*a*(a+b*tan(d*x+c))^(3/2)/d-2/d*a^2*(a+b*tan(d*x+c))^(1/2)+2*b^2*(a+b*tan(d*x+c))^(1/2)/d-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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*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))*(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^3+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))*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^2+b^2)^(1/2)*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^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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^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))*(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^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^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/(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^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^2)^(1/2)","B"
520,1,1194,130,0.257000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 b d}-\frac{2 b \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{4 a 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{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) \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 b d}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 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) 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)}{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) \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 b 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}\, \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 b 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 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^{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)}{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) \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/7*(a+b*tan(d*x+c))^(7/2)/b/d-2/3*b*(a+b*tan(d*x+c))^(3/2)/d-4*a*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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+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))*(2*(a^2+b^2)^(1/2)+2*a)^(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))*a^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))+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))*(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))*(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))*(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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-3/4*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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+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))*a^2-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))-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))*(a^2+b^2)^(1/2)*a","B"
521,1,1361,132,0.206000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^(5/2),x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 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) a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{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) \left(a^{2}+b^{2}\right) 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{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) \left(a^{2}+b^{2}\right) 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) \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) \sqrt{a^{2}+b^{2}}\, a^{2}}{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) \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, 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) \sqrt{a^{2}+b^{2}}\, a^{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) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{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^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{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^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{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{3}{2}}}{3 d}+\frac{2 a^{2} \sqrt{a +b \tan \left(d x +c \right)}}{d}"," ",0,"2/5*(a+b*tan(d*x+c))^(5/2)/d+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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+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-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^2+b^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))*a+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^2+b^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))*(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^2+b^2)^(1/2)*a^2-1/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^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))*(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^2+b^2)^(1/2)*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^2+b^2)^(1/2)+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))*a^3-3/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))*a^3-2*b^2*(a+b*tan(d*x+c))^(1/2)/d+2/3*a*(a+b*tan(d*x+c))^(3/2)/d+2/d*a^2*(a+b*tan(d*x+c))^(1/2)","B"
522,1,1174,110,0.190000," ","int((a+b*tan(d*x+c))^(5/2),x)","\frac{2 b \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{4 a 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{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) \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 b d}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 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) 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)}{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) \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 b 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}\, \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 b 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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 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^{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)}{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) \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/3*b*(a+b*tan(d*x+c))^(3/2)/d+4*a*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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-3/4*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))*(2*(a^2+b^2)^(1/2)+2*a)^(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))*a^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))-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))*(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))*(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))*(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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+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))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-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))*a^2+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))+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))*(a^2+b^2)^(1/2)*a","B"
523,1,28373,114,2.499000," ","int(cot(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"
524,1,45707,125,2.227000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
525,1,66439,160,3.058000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
526,1,88284,199,3.443000," ","int(cot(d*x+c)^4*(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
527,1,1552,139,0.224000," ","int((a+b*tan(d*x+c))^(7/2),x)","\frac{2 b \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}-\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{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 \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{4 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{4 a b \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{6 b \,a^{2} \sqrt{a +b \tan \left(d x +c \right)}}{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}\, \sqrt{a^{2}+b^{2}}\, a^{3}}{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{3}}{4 d b}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 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) \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d}-\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 \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}}+\frac{4 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{\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{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 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) \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{3} \sqrt{a +b \tan \left(d x +c \right)}}{d}+\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}"," ",0,"2/5*b*(a+b*tan(d*x+c))^(5/2)/d-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)+4/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+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)-4/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+4/3*a*b*(a+b*tan(d*x+c))^(3/2)/d+6/d*b*a^2*(a+b*tan(d*x+c))^(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(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^4-3/2/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^2-1/4/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+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))*(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+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+3/2/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^2-4/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^3-1/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)+4/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((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*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/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^2-2/d*b^3*(a+b*tan(d*x+c))^(1/2)+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)","B"
528,1,607,197,0.324000," ","int(tan(d*x+c)^5/(a+b*tan(d*x+c))^(1/2),x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d \,b^{4}}-\frac{6 \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}} a}{5 d \,b^{4}}+\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{d \,b^{4}}-\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d \,b^{2}}-\frac{2 a^{3} \sqrt{a +b \tan \left(d x +c \right)}}{d \,b^{4}}+\frac{2 a \sqrt{a +b \tan \left(d x +c \right)}}{b^{2} d}-\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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 \sqrt{a^{2}+b^{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}{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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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 \sqrt{a^{2}+b^{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}{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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/7/d/b^4*(a+b*tan(d*x+c))^(7/2)-6/5/d/b^4*(a+b*tan(d*x+c))^(5/2)*a+2/d/b^4*(a+b*tan(d*x+c))^(3/2)*a^2-2/3/d/b^2*(a+b*tan(d*x+c))^(3/2)-2/d/b^4*a^3*(a+b*tan(d*x+c))^(1/2)+2*a*(a+b*tan(d*x+c))^(1/2)/b^2/d-1/4/d/(a^2+b^2)^(1/2)*(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/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/(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/(a^2+b^2)^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(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/(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/(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"
529,1,1641,409,0.292000," ","int(tan(d*x+c)^4/(a+b*tan(d*x+c))^(1/2),x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d \,b^{3}}-\frac{4 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{3 d \,b^{3}}+\frac{2 a^{2} \sqrt{a +b \tan \left(d x +c \right)}}{d \,b^{3}}-\frac{2 \sqrt{a +b \tan \left(d x +c \right)}}{b 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^{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) \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) \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) \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^{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)}{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^{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) 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)}{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^{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) \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) \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) \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^{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)}{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^{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) 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)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/5/d/b^3*(a+b*tan(d*x+c))^(5/2)-4/3/d/b^3*(a+b*tan(d*x+c))^(3/2)*a+2/d/b^3*a^2*(a+b*tan(d*x+c))^(1/2)-2*(a+b*tan(d*x+c))^(1/2)/b/d+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^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))*(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))*(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))*(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^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))+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+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+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))-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^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)+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^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))*(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^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))-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^4-3/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^2-2/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"
530,1,520,116,0.266000," ","int(tan(d*x+c)^3/(a+b*tan(d*x+c))^(1/2),x)","\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d \,b^{2}}-\frac{2 a \sqrt{a +b \tan \left(d x +c \right)}}{b^{2} d}+\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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 \sqrt{a^{2}+b^{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}{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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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 \sqrt{a^{2}+b^{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}{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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2/3/d/b^2*(a+b*tan(d*x+c))^(3/2)-2*a*(a+b*tan(d*x+c))^(1/2)/b^2/d+1/4/d/(a^2+b^2)^(1/2)*(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/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/(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/(a^2+b^2)^(1/2)*(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/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/(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"
531,1,1577,343,0.243000," ","int(tan(d*x+c)^2/(a+b*tan(d*x+c))^(1/2),x)","\frac{2 \sqrt{a +b \tan \left(d x +c \right)}}{b 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^{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) \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) \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) \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^{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)}{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^{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) 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)}{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^{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) \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) \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) \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^{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)}{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^{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) 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)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"2*(a+b*tan(d*x+c))^(1/2)/b/d-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^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))*(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))*(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))*(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^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))-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^4-3/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^2-2/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))+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^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)-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^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))*(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^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))+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+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+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"
532,1,479,71,0.293000," ","int(tan(d*x+c)/(a+b*tan(d*x+c))^(1/2),x)","-\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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 \sqrt{a^{2}+b^{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}{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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 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 \sqrt{a^{2}+b^{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}{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)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-1/4/d/(a^2+b^2)^(1/2)*(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/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/(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/(a^2+b^2)^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(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/(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/(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"
533,1,1557,323,0.212000," ","int(1/(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^{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) \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) \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) \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^{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)}{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^{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) 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)}{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^{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) \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) \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) \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^{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)}{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^{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) 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)}{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^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))*(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))*(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))*(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^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))+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+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+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))-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^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)+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^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))*(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^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))-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^4-3/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^2-2/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"
534,1,20194,94,1.748000," ","int(cot(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"
535,1,39033,374,2.200000," ","int(cot(d*x+c)^2/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
536,1,58397,162,2.717000," ","int(cot(d*x+c)^3/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
537,1,1836,252,0.325000," ","int(tan(d*x+c)^5/(a+b*tan(d*x+c))^(3/2),x)","-\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}} a}{d \,b^{4}}+\frac{6 a^{2} \sqrt{a +b \tan \left(d x +c \right)}}{d \,b^{4}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{2 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^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{2 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^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \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 \left(a^{2}+b^{2}\right)^{2} \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 \left(a^{2}+b^{2}\right)^{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^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d \,b^{4}}-\frac{2 \sqrt{a +b \tan \left(d x +c \right)}}{d \,b^{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 \left(a^{2}+b^{2}\right)^{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^{3}}{2 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^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{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^{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^{2}}{4 d \left(a^{2}+b^{2}\right)^{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 \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b^{4} \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{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)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{4} \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{2 a^{5}}{d \,b^{4} \left(a^{2}+b^{2}\right) \sqrt{a +b \tan \left(d x +c \right)}}-\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^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\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)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-2/d/b^4*(a+b*tan(d*x+c))^(3/2)*a+6/d/b^4*a^2*(a+b*tan(d*x+c))^(1/2)-1/2/d*b^2/(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+2/d*b^2/(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+1/2/d*b^2/(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-2/d*b^2/(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+1/d*b^2/(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-1/d*b^2/(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-1/4/d/(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^2+2/5/d/b^4*(a+b*tan(d*x+c))^(5/2)-2/d/b^2*(a+b*tan(d*x+c))^(1/2)-1/d/(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/(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+1/2/d/(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/(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/(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^2+1/d/(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+2/d*b^4/(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))+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))-2/d*b^4/(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))+2/d/b^4*a^5/(a^2+b^2)/(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+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^2/(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^2/(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^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))","B"
538,1,1978,198,0.263000," ","int(tan(d*x+c)^4/(a+b*tan(d*x+c))^(3/2),x)","\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{5}{2}} \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{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{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{5}{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 \left(a^{2}+b^{2}\right)^{\frac{3}{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 \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^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \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{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{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^{3}}{4 d b \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 d \left(a^{2}+b^{2}\right)^{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^{2}}{d \left(a^{2}+b^{2}\right)^{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)^{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 d \left(a^{2}+b^{2}\right)^{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)^{\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^{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}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 a \sqrt{a +b \tan \left(d x +c \right)}}{d \,b^{3}}+\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d \,b^{3}}+\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)^{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{5}{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{5}{2}}}-\frac{2 a^{4}}{d \,b^{3} \left(a^{2}+b^{2}\right) \sqrt{a +b \tan \left(d x +c \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 \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^{3}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"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+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+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^3+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^4+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^3+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-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^5-3/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-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^3+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^3+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-1/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^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^3-1/4/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-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^4+1/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^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-4/d/b^3*a*(a+b*tan(d*x+c))^(1/2)+2/3/d/b^3*(a+b*tan(d*x+c))^(3/2)+1/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))+1/4/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)-1/4/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)-2/d/b^3/(a^2+b^2)*a^4/(a+b*tan(d*x+c))^(1/2)-1/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))-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^3","B"
539,1,1772,145,0.244000," ","int(tan(d*x+c)^3/(a+b*tan(d*x+c))^(3/2),x)","\frac{2 \sqrt{a +b \tan \left(d x +c \right)}}{d \,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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d \left(a^{2}+b^{2}\right)^{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{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^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{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^{2}}{d \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^{3}}{d \left(a^{2}+b^{2}\right)^{2} \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)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \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 \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 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^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{4} \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{\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}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{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^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{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^{2}}{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^{3}}{d \left(a^{2}+b^{2}\right)^{2} \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)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \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 \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 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^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b^{4} \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{2 a^{3}}{d \,b^{2} \left(a^{2}+b^{2}\right) \sqrt{a +b \tan \left(d x +c \right)}}"," ",0,"2/d/b^2*(a+b*tan(d*x+c))^(1/2)-1/4/d/(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^2-1/4/d*b^2/(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)+1/2/d/(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+1/2/d*b^2/(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/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^2-1/d/(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^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))-1/d*b^2/(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^2/(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^2-2/d*b^4/(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))+1/4/d/(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^2+1/4/d*b^2/(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)-1/2/d/(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^3-1/2/d*b^2/(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/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^2+1/d/(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/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))+1/d*b^2/(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^2/(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+2/d*b^4/(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))+2/d/b^2*a^3/(a^2+b^2)/(a+b*tan(d*x+c))^(1/2)","B"
540,1,1937,105,0.239000," ","int(tan(d*x+c)^2/(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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \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 d \left(a^{2}+b^{2}\right)^{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)^{\frac{5}{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{5}{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 \left(a^{2}+b^{2}\right)^{\frac{3}{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 \left(a^{2}+b^{2}\right)^{\frac{3}{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)^{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^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{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)^{2} \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{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{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)^{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 d \left(a^{2}+b^{2}\right)^{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^{4}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{5}{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{5}{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 \left(a^{2}+b^{2}\right)^{\frac{3}{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 \left(a^{2}+b^{2}\right)^{\frac{3}{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)^{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^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{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)^{2} \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{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 a^{2}}{b \left(a^{2}+b^{2}\right) d \sqrt{a +b \tan \left(d x +c \right)}}"," ",0,"-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^3-1/4/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+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^4-1/4/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)+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^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))*a+1/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^2-1/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+1/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))-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-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^3+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^3+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-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^4+1/4/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)-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^3-1/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-1/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^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^5-1/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))+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+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^3-2*a^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(1/2)","B"
541,1,1747,98,0.201000," ","int(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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d \left(a^{2}+b^{2}\right)^{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{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^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{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^{2}}{d \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^{3}}{d \left(a^{2}+b^{2}\right)^{2} \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)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \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 \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 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^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b^{4} \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{\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}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{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^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{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^{2}}{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^{3}}{d \left(a^{2}+b^{2}\right)^{2} \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)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \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 \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 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^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{4} \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{2 a}{\left(a^{2}+b^{2}\right) d \sqrt{a +b \tan \left(d x +c \right)}}"," ",0,"1/4/d/(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^2+1/4/d*b^2/(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)-1/2/d/(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^3-1/2/d*b^2/(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/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^2+1/d/(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^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))+1/d*b^2/(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^2/(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+2/d*b^4/(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))-1/4/d/(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^2-1/4/d*b^2/(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)+1/2/d/(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+1/2/d*b^2/(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/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^2-1/d/(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/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))-1/d*b^2/(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^2/(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^2-2/d*b^4/(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))+2*a/(a^2+b^2)/d/(a+b*tan(d*x+c))^(1/2)","B"
542,1,1932,100,0.201000," ","int(1/(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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \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 d \left(a^{2}+b^{2}\right)^{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)^{\frac{5}{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{5}{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 \left(a^{2}+b^{2}\right)^{\frac{3}{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 \left(a^{2}+b^{2}\right)^{\frac{3}{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)^{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^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{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)^{2} \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{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{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)^{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 d \left(a^{2}+b^{2}\right)^{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^{4}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{5}{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{5}{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 \left(a^{2}+b^{2}\right)^{\frac{3}{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 \left(a^{2}+b^{2}\right)^{\frac{3}{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)^{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^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{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)^{2} \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{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b}{\left(a^{2}+b^{2}\right) d \sqrt{a +b \tan \left(d x +c \right)}}"," ",0,"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^3+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-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^4+1/4/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)-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^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))*a-1/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^2+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^5-1/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))+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+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^3-1/4/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^3-1/4/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+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^4-1/4/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)+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^3+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+1/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^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^5+1/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))-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-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^3-2*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(1/2)","B"
543,1,39358,126,2.382000," ","int(cot(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"
544,1,60231,164,3.216000," ","int(cot(d*x+c)^2/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
545,1,93020,205,4.017000," ","int(cot(d*x+c)^3/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
546,1,2209,261,0.339000," ","int(tan(d*x+c)^5/(a+b*tan(d*x+c))^(5/2),x)","-\frac{6 a \sqrt{a +b \tan \left(d x +c \right)}}{d \,b^{4}}+\frac{2 a^{5}}{3 d \,b^{4} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{2 \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d \,b^{4}}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)^{\frac{7}{2}}}+\frac{2 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 \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{5 b^{4} \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{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{6 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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{2}} \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{3}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{5 b^{4} \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{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{6 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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{6 a^{6}}{d \,b^{4} \left(a^{2}+b^{2}\right)^{2} \sqrt{a +b \tan \left(d x +c \right)}}-\frac{b^{4} \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)^{3} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{4} \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)^{3} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{10 a^{4}}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \sqrt{a +b \tan \left(d x +c \right)}}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d \left(a^{2}+b^{2}\right)^{\frac{7}{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^{5}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{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^{5}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{4} \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{7}{2}}}-\frac{b^{4} \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{7}{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 \left(a^{2}+b^{2}\right)^{3} \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^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\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 \left(a^{2}+b^{2}\right)^{3} \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}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d \left(a^{2}+b^{2}\right)^{\frac{7}{2}}}-\frac{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)^{\frac{7}{2}}}-\frac{2 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 \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-6/d/b^4*a*(a+b*tan(d*x+c))^(1/2)+2/3/d/b^4*a^5/(a^2+b^2)/(a+b*tan(d*x+c))^(3/2)+2/3/d/b^4*(a+b*tan(d*x+c))^(3/2)+1/2/d*b^2/(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^2/(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/d*b^4/(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+6/d*b^2/(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+1/2/d*b^2/(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-1/2/d*b^2/(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/d*b^4/(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-6/d*b^2/(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^3-6/d/b^4*a^6/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)-1/d*b^4/(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))+1/d*b^4/(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))-10/d/b^2*a^4/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)+3/4/d/(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^4-1/d/(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+1/d/(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^4/(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)-1/4/d*b^4/(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/d/(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/(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/d/(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^4-1/2/d/(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+2/d/(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^3-3/4/d/(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/(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^3-1/2/d*b^2/(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^2-2/d*b^2/(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","B"
547,1,2379,196,0.289000," ","int(tan(d*x+c)^4/(a+b*tan(d*x+c))^(5/2),x)","-\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)^{3} \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{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{4 a^{5}}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \sqrt{a +b \tan \left(d x +c \right)}}-\frac{2 a^{4}}{3 d \,b^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\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)^{3}}-\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)^{3}}+\frac{8 a^{3}}{d b \left(a^{2}+b^{2}\right)^{2} \sqrt{a +b \tan \left(d x +c \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 \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{7}{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{7}{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^{4}}{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{7}{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) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{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^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{7}{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{7}{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^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{7}{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{7}{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 \left(a^{2}+b^{2}\right)^{\frac{5}{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{7}{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{7}{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) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{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{7}{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{7}{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{7}{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)^{3}}+\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)^{3} \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)^{3} \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)^{3} \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)^{3}}+\frac{2 \sqrt{a +b \tan \left(d x +c \right)}}{d \,b^{3}}"," ",0,"-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-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))+4/d/b^3*a^5/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)-2/3/d/b^3*a^4/(a^2+b^2)/(a+b*tan(d*x+c))^(3/2)+1/4/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)-1/4/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)+8/d/b*a^3/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)+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))-2/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))+2/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))+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^4-4/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^4-1/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^2+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^5-1/4/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^5+1/2/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^3+3/4/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-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^4+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^6+4/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^4+1/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^2-1/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^6-1/2/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^3-3/4/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+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^4+2/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^3-2/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^3+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-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^4+2/d/b^3*(a+b*tan(d*x+c))^(1/2)","B"
548,1,2165,148,0.280000," ","int(tan(d*x+c)^3/(a+b*tan(d*x+c))^(5/2),x)","-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)^{\frac{7}{2}}}-\frac{2 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 \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{5 b^{4} \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{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{6 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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{2}} \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{3}}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{5 b^{4} \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{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{6 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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 a^{3}}{3 d \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{b^{4} \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)^{3} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{4} \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)^{3} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 a^{4}}{d \,b^{2} \left(a^{2}+b^{2}\right)^{2} \sqrt{a +b \tan \left(d x +c \right)}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d \left(a^{2}+b^{2}\right)^{\frac{7}{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^{5}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{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^{5}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{4} \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{7}{2}}}+\frac{b^{4} \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{7}{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 \left(a^{2}+b^{2}\right)^{3} \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^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\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 \left(a^{2}+b^{2}\right)^{3} \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}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d \left(a^{2}+b^{2}\right)^{\frac{7}{2}}}+\frac{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{6 a^{2}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a +b \tan \left(d x +c \right)}}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)^{\frac{7}{2}}}+\frac{2 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 \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-1/2/d*b^2/(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^2/(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/d*b^4/(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-6/d*b^2/(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^3-1/2/d*b^2/(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+1/2/d*b^2/(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/d*b^4/(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+6/d*b^2/(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+2/3/d/b^2*a^3/(a^2+b^2)/(a+b*tan(d*x+c))^(3/2)+1/d*b^4/(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))-1/d*b^4/(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))-2/d/b^2*a^4/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)-3/4/d/(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+1/d/(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^5-1/d/(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^4/(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)+1/4/d*b^4/(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/d/(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/(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/d/(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+1/2/d/(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^3-2/d/(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+3/4/d/(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/(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^3-6/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)+1/2/d*b^2/(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+2/d*b^2/(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","B"
549,1,2323,133,0.240000," ","int(tan(d*x+c)^2/(a+b*tan(d*x+c))^(5/2),x)","\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)^{3} \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{5}{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)^{3}}+\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)^{3}}-\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{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{7}{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{7}{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^{4}}{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{7}{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) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{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^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{7}{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{7}{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^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{7}{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{7}{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 \left(a^{2}+b^{2}\right)^{\frac{5}{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{7}{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{7}{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) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{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{7}{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{7}{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{7}{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)^{3}}-\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)^{3} \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)^{3} \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)^{3} \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)^{3}}+\frac{4 a b}{\left(a^{2}+b^{2}\right)^{2} d \sqrt{a +b \tan \left(d x +c \right)}}-\frac{2 a^{2}}{3 b \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"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+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))-1/4/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)+1/4/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)-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))+2/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))-2/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))-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^4+4/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^4+1/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^2-1/4/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^5+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^5-1/2/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^3-3/4/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+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^4-1/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^6-4/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^4-1/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^2+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^6+1/2/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^3+3/4/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-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^4-2/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^3+2/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^3-2/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+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^4+4*a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^(1/2)-2/3*a^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)","B"
550,1,2157,133,0.209000," ","int(tan(d*x+c)/(a+b*tan(d*x+c))^(5/2),x)","\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)^{\frac{7}{2}}}+\frac{2 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 \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{5 b^{4} \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{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{6 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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{2}} \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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{3}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{5 b^{4} \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{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{6 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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{4} \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)^{3} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{4} \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)^{3} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d \left(a^{2}+b^{2}\right)^{\frac{7}{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^{5}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{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^{5}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{4} \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{7}{2}}}-\frac{b^{4} \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{7}{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 \left(a^{2}+b^{2}\right)^{3} \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^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\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 \left(a^{2}+b^{2}\right)^{3} \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}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d \left(a^{2}+b^{2}\right)^{\frac{7}{2}}}-\frac{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^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a +b \tan \left(d x +c \right)}}+\frac{2 a^{2}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a +b \tan \left(d x +c \right)}}-\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) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)^{\frac{7}{2}}}-\frac{2 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 \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 a}{3 \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/2/d*b^2/(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^2/(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/d*b^4/(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+6/d*b^2/(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+1/2/d*b^2/(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-1/2/d*b^2/(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/d*b^4/(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-6/d*b^2/(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^3-1/d*b^4/(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))+1/d*b^4/(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))+3/4/d/(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^4-1/d/(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+1/d/(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^4/(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)-1/4/d*b^4/(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/d/(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/(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/d/(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^4-1/2/d/(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+2/d/(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^3-3/4/d/(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/(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^3-2/d/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)*b^2+2/d*a^2/(a^2+b^2)^2/(a+b*tan(d*x+c))^(1/2)-1/2/d*b^2/(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^2-2/d*b^2/(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+2/3*a/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)","B"
551,1,2318,128,0.222000," ","int(1/(a+b*tan(d*x+c))^(5/2),x)","-\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)^{3} \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{5}{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)^{3}}-\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)^{3}}+\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{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{7}{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{7}{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^{4}}{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{7}{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) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{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^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{7}{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{7}{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^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{7}{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{7}{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 \left(a^{2}+b^{2}\right)^{\frac{5}{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{7}{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{7}{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) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{7}{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{7}{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{7}{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{7}{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)^{3}}+\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)^{3} \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)^{3} \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)^{3} \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)^{3}}-\frac{2 b}{3 \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{4 a b}{\left(a^{2}+b^{2}\right)^{2} d \sqrt{a +b \tan \left(d x +c \right)}}"," ",0,"-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-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))+1/4/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)-1/4/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)+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))-2/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))+2/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))+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^4-4/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^4-1/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^2+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^5-1/4/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^5+1/2/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^3+3/4/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-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^4+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^6+4/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^4+1/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^2-1/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^6-1/2/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^3-3/4/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+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^4+2/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^3-2/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^3+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-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^4-2/3*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-4*a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^(1/2)","B"
552,1,115830,167,5.232000," ","int(cot(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"
553,1,175534,213,10.127000," ","int(cot(d*x+c)^2/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
554,1,3073,166,0.244000," ","int(1/(a+b*tan(d*x+c))^(7/2),x)","\text{output too large to display}"," ",0,"-2/d*b^3/(a^2+b^2)^4/(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)^4*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)^4*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-1/2/d*b/(a^2+b^2)^4*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^3-6/d*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^(1/2)*a^2+1/d*b^5/(a^2+b^2)^4/(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^5/(a^2+b^2)^4/(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^5/(a^2+b^2)^(9/2)*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^5/(a^2+b^2)^(9/2)*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)+2/d*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^(1/2)-3/d*b/(a^2+b^2)^4/(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)^(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+3/d*b/(a^2+b^2)^(9/2)/(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)^(9/2)/(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^3-7/d*b^5/(a^2+b^2)^(9/2)/(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+1/4/d/b/(a^2+b^2)^(9/2)*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)^(9/2)*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/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/d/b/(a^2+b^2)^(9/2)/(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^7-5/d*b^3/(a^2+b^2)^(9/2)/(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^3-7/d*b^5/(a^2+b^2)^(9/2)/(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/(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+3/d*b/(a^2+b^2)^(9/2)/(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^5-5/4/d*b/(a^2+b^2)^(9/2)*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+5/4/d*b/(a^2+b^2)^(9/2)*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+3/4/d*b^3/(a^2+b^2)^4*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)^4/(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)^4*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+1/d/b/(a^2+b^2)^(9/2)/(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^7-2/5*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(5/2)-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^5+3/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/d*b/(a^2+b^2)^4/(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^4-1/4/d/b/(a^2+b^2)^(9/2)*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+1/2/d*b/(a^2+b^2)^4*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+3/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+5/4/d*b^3/(a^2+b^2)^(9/2)*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^2-4/3*a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^(3/2)","B"
555,1,248,164,0.108000," ","int(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x)","\frac{2 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)}{3 d}-\frac{2 b \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{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)}{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{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)}{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)}{4 d}"," ",0,"2/5*b*tan(d*x+c)^(5/2)/d+2/3*a*tan(d*x+c)^(3/2)/d-2*b*tan(d*x+c)^(1/2)/d+1/2/d*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))+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)))-1/2/d*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))-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"
556,1,234,150,0.093000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x)","\frac{2 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)}{d}-\frac{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)}{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)}{4 d}-\frac{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)}{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+2*a*tan(d*x+c)^(1/2)/d-1/2/d*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))-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)))-1/2/d*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))-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"
557,1,220,136,0.087000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c)),x)","\frac{2 b \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{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)}{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{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)}{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)}{4 d}"," ",0,"2*b*tan(d*x+c)^(1/2)/d-1/2/d*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))-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)))+1/2/d*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))+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"
558,1,206,122,0.094000," ","int((a+b*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\frac{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)}{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)}{4 d}+\frac{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)}{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,"1/2/d*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))+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)))+1/2/d*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))+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"
559,1,220,136,0.092000," ","int((a+b*tan(d*x+c))/tan(d*x+c)^(3/2),x)","-\frac{2 a}{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)}{2 d}+\frac{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)}{4 d}-\frac{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)}{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)}{4 d}"," ",0,"-2*a/d/tan(d*x+c)^(1/2)+1/2/d*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))+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)))-1/2/d*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))-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"
560,1,234,150,0.102000," ","int((a+b*tan(d*x+c))/tan(d*x+c)^(5/2),x)","-\frac{2 a}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 b}{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)}{2 d}-\frac{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)}{4 d}-\frac{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)}{4 d}-\frac{b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{2 d}"," ",0,"-2/3*a/d/tan(d*x+c)^(3/2)-2*b/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))-1/2/d*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)))-1/2/d*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)))-1/2/d*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","A"
561,1,248,164,0.094000," ","int((a+b*tan(d*x+c))/tan(d*x+c)^(7/2),x)","-\frac{2 a}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{2 b}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 a}{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)}{2 d}-\frac{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)}{4 d}+\frac{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)}{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)}{4 d}"," ",0,"-2/5*a/d/tan(d*x+c)^(5/2)-2/3*b/d/tan(d*x+c)^(3/2)+2*a/d/tan(d*x+c)^(1/2)-1/2/d*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))-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)))+1/2/d*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))+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"
562,1,399,226,0.096000," ","int(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x)","\frac{2 b^{2} \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}+\frac{4 a b \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{2 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a^{2}}{3 d}-\frac{2 b^{2} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}-\frac{4 a b \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)}{d}+\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{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)}{2 d}-\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}"," ",0,"2/7*b^2*tan(d*x+c)^(7/2)/d+4/5*a*b*tan(d*x+c)^(5/2)/d+2/3/d*tan(d*x+c)^(3/2)*a^2-2/3*b^2*tan(d*x+c)^(3/2)/d-4*a*b*tan(d*x+c)^(1/2)/d+1/d*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/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)*ln((1+2^(1/2)*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*2^(1/2)*ln((1-2^(1/2)*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*2^(1/2)*ln((1-2^(1/2)*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2","A"
563,1,386,211,0.086000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x)","\frac{2 b^{2} \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{4 a b \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{2} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 b^{2} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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 b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{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)}{2 d}"," ",0,"2/5*b^2*tan(d*x+c)^(5/2)/d+4/3*a*b*tan(d*x+c)^(3/2)/d+2/d*a^2*tan(d*x+c)^(1/2)-2*b^2*tan(d*x+c)^(1/2)/d-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/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^2+1/4/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)))*b^2-1/d*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/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)*ln((1-2^(1/2)*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"
564,1,354,189,0.092000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2,x)","\frac{2 b^{2} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{4 a b \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)}{d}-\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{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)}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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}"," ",0,"2/3*b^2*tan(d*x+c)^(3/2)/d+4*a*b*tan(d*x+c)^(1/2)/d-1/d*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/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)*ln((1+2^(1/2)*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/4/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^2-1/4/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)))*b^2","A"
565,1,337,174,0.093000," ","int((a+b*tan(d*x+c))^2/tan(d*x+c)^(1/2),x)","\frac{2 b^{2} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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 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 b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"2*b^2*tan(d*x+c)^(1/2)/d+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/4/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^2-1/4/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)))*b^2+1/2/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/d*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","A"
566,1,337,174,0.097000," ","int((a+b*tan(d*x+c))^2/tan(d*x+c)^(3/2),x)","-\frac{2 a^{2}}{d \sqrt{\tan \left(d x +c \right)}}+\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{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)}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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}"," ",0,"-2*a^2/d/tan(d*x+c)^(1/2)+1/d*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/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)*ln((1+2^(1/2)*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/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^2+1/4/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)))*b^2","A"
567,1,354,189,0.102000," ","int((a+b*tan(d*x+c))^2/tan(d*x+c)^(5/2),x)","-\frac{2 a^{2}}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{4 a b}{d \sqrt{\tan \left(d x +c \right)}}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}-\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{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)}{2 d}-\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}"," ",0,"-2/3*a^2/d/tan(d*x+c)^(3/2)-4*a*b/d/tan(d*x+c)^(1/2)-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/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^2+1/4/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)))*b^2-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/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/d*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","A"
568,1,386,211,0.100000," ","int((a+b*tan(d*x+c))^2/tan(d*x+c)^(7/2),x)","-\frac{2 a^{2}}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}+\frac{2 a^{2}}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 b^{2}}{d \sqrt{\tan \left(d x +c \right)}}-\frac{4 a b}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\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)}{2 d}-\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}-\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d}+\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{2}}{2 d}"," ",0,"-2/5*a^2/d/tan(d*x+c)^(5/2)+2*a^2/d/tan(d*x+c)^(1/2)-2/d/tan(d*x+c)^(1/2)*b^2-4/3*a*b/d/tan(d*x+c)^(3/2)-1/2/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/d*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/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^2-1/4/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)))*b^2+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2","A"
569,1,572,282,0.096000," ","int(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x)","\frac{2 \left(\tan^{\frac{9}{2}}\left(d x +c \right)\right) b^{3}}{9 d}+\frac{6 a \,b^{2} \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right)}{7 d}+\frac{6 \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right) a^{2} b}{5 d}-\frac{2 b^{3} \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{2 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a^{3}}{3 d}-\frac{2 a \,b^{2} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{d}-\frac{6 a^{2} b \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{2 b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}"," ",0,"2/9/d*tan(d*x+c)^(9/2)*b^3+6/7*a*b^2*tan(d*x+c)^(7/2)/d+6/5/d*tan(d*x+c)^(5/2)*a^2*b-2/5/d*b^3*tan(d*x+c)^(5/2)+2/3/d*tan(d*x+c)^(3/2)*a^3-2*a*b^2*tan(d*x+c)^(3/2)/d-6/d*a^2*b*tan(d*x+c)^(1/2)+2/d*b^3*tan(d*x+c)^(1/2)+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/4/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^2*b-1/4/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)))*b^3+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/4/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^3+3/4/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*b^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2","B"
570,1,539,257,0.103000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x)","\frac{2 \left(\tan^{\frac{7}{2}}\left(d x +c \right)\right) b^{3}}{7 d}+\frac{6 a \,b^{2} \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{2 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) a^{2} b}{d}-\frac{2 b^{3} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{3} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{6 a \,b^{2} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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}"," ",0,"2/7/d*tan(d*x+c)^(7/2)*b^3+6/5*a*b^2*tan(d*x+c)^(5/2)/d+2/d*tan(d*x+c)^(3/2)*a^2*b-2/3/d*b^3*tan(d*x+c)^(3/2)+2/d*a^3*tan(d*x+c)^(1/2)-6*a*b^2*tan(d*x+c)^(1/2)/d-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/4/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^3+3/4/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*b^2-3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/4/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^2*b+1/4/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)))*b^3","B"
571,1,506,234,0.090000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3,x)","\frac{2 b^{3} \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 d}+\frac{2 a \,b^{2} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{d}+\frac{6 a^{2} b \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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,"2/5/d*b^3*tan(d*x+c)^(5/2)+2*a*b^2*tan(d*x+c)^(3/2)/d+6/d*a^2*b*tan(d*x+c)^(1/2)-2/d*b^3*tan(d*x+c)^(1/2)-3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/4/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^2*b+1/4/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)))*b^3+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/4/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^3-3/4/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*b^2","B"
572,1,473,209,0.093000," ","int((a+b*tan(d*x+c))^3/tan(d*x+c)^(1/2),x)","\frac{2 b^{3} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d}+\frac{6 a \,b^{2} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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}"," ",0,"2/3/d*b^3*tan(d*x+c)^(3/2)+6*a*b^2*tan(d*x+c)^(1/2)/d+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/4/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^3-3/4/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*b^2+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/4/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^2*b-1/4/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)))*b^3","B"
573,1,472,213,0.092000," ","int((a+b*tan(d*x+c))^3/tan(d*x+c)^(3/2),x)","\frac{2 b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d}-\frac{2 a^{3}}{d \sqrt{\tan \left(d x +c \right)}}+\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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,"2/d*b^3*tan(d*x+c)^(1/2)-2/d*a^3/tan(d*x+c)^(1/2)+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/4/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^2*b-1/4/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)))*b^3-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/4/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^3+3/4/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*b^2","B"
574,1,473,209,0.107000," ","int((a+b*tan(d*x+c))^3/tan(d*x+c)^(5/2),x)","-\frac{2 a^{3}}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{6 a^{2} b}{d \sqrt{\tan \left(d x +c \right)}}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}"," ",0,"-2/3/d*a^3/tan(d*x+c)^(3/2)-6*a^2*b/d/tan(d*x+c)^(1/2)-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/4/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^3+3/4/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*b^2-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-3/4/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^2*b+1/4/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)))*b^3-3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3","B"
575,1,506,232,0.100000," ","int((a+b*tan(d*x+c))^3/tan(d*x+c)^(7/2),x)","-\frac{2 a^{3}}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}+\frac{2 a^{3}}{d \sqrt{\tan \left(d x +c \right)}}-\frac{6 a \,b^{2}}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 a^{2} b}{d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}-\frac{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}"," ",0,"-2/5/d*a^3/tan(d*x+c)^(5/2)+2/d*a^3/tan(d*x+c)^(1/2)-6/d*a/tan(d*x+c)^(1/2)*b^2-2*a^2*b/d/tan(d*x+c)^(3/2)-3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/4/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^2*b+1/4/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)))*b^3-3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+1/4/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^3-3/4/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*b^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2","B"
576,1,539,257,0.098000," ","int((a+b*tan(d*x+c))^3/tan(d*x+c)^(9/2),x)","-\frac{2 a^{3}}{7 d \tan \left(d x +c \right)^{\frac{7}{2}}}+\frac{2 a^{3}}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 a \,b^{2}}{d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{6 a^{2} b}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}+\frac{6 a^{2} b}{d \sqrt{\tan \left(d x +c \right)}}-\frac{2 b^{3}}{d \sqrt{\tan \left(d x +c \right)}}+\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}-\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}+\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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}"," ",0,"-2/7/d*a^3/tan(d*x+c)^(7/2)+2/3/d*a^3/tan(d*x+c)^(3/2)-2/d*a/tan(d*x+c)^(3/2)*b^2-6/5*a^2*b/d/tan(d*x+c)^(5/2)+6*a^2*b/d/tan(d*x+c)^(1/2)-2/d*b^3/tan(d*x+c)^(1/2)+1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/4/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^3-3/4/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*b^2+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/4/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^2*b-1/4/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)))*b^3","B"
577,1,572,280,0.097000," ","int((a+b*tan(d*x+c))^3/tan(d*x+c)^(11/2),x)","-\frac{2 a^{3}}{9 d \tan \left(d x +c \right)^{\frac{9}{2}}}-\frac{2 a^{3}}{d \sqrt{\tan \left(d x +c \right)}}+\frac{6 a \,b^{2}}{d \sqrt{\tan \left(d x +c \right)}}+\frac{2 a^{3}}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{6 a \,b^{2}}{5 d \tan \left(d x +c \right)^{\frac{5}{2}}}-\frac{6 a^{2} b}{7 d \tan \left(d x +c \right)^{\frac{7}{2}}}+\frac{2 a^{2} b}{d \tan \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 b^{3}}{3 d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{2} b}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) b^{3}}{2 d}+\frac{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{\sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a^{3}}{2 d}+\frac{3 \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right) a \,b^{2}}{2 d}-\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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,"-2/9/d*a^3/tan(d*x+c)^(9/2)-2/d*a^3/tan(d*x+c)^(1/2)+6/d*a/tan(d*x+c)^(1/2)*b^2+2/5/d*a^3/tan(d*x+c)^(5/2)-6/5/d*a/tan(d*x+c)^(5/2)*b^2-6/7*a^2*b/d/tan(d*x+c)^(7/2)+2*a^2*b/d/tan(d*x+c)^(3/2)-2/3/d*b^3/tan(d*x+c)^(3/2)+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2*b-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/4/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^2*b-1/4/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)))*b^3-1/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/4/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^3+3/4/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*b^2","B"
578,1,206,122,0.089000," ","int((a+b*tan(d*x+c))/tan(d*x+c)^(1/2),x)","\frac{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)}{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)}{4 d}+\frac{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)}{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,"1/2/d*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))+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)))+1/2/d*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))+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"
579,1,230,134,0.193000," ","int((a+b*tan(d*x+c))/(-tan(d*x+c))^(1/2),x)","-\frac{a \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \sqrt{-\tan \left(d x +c \right)}\right)}{2 d}-\frac{a \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \sqrt{-\tan \left(d x +c \right)}-\tan \left(d x +c \right)}{1-\sqrt{2}\, \sqrt{-\tan \left(d x +c \right)}-\tan \left(d x +c \right)}\right)}{4 d}-\frac{a \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \sqrt{-\tan \left(d x +c \right)}\right)}{2 d}+\frac{b \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \sqrt{-\tan \left(d x +c \right)}-\tan \left(d x +c \right)}{1+\sqrt{2}\, \sqrt{-\tan \left(d x +c \right)}-\tan \left(d x +c \right)}\right)}{4 d}+\frac{b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \sqrt{-\tan \left(d x +c \right)}\right)}{2 d}+\frac{b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \sqrt{-\tan \left(d x +c \right)}\right)}{2 d}"," ",0,"-1/2/d*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)))-1/2/d*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)))+1/2/d*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))","A"
580,1,327,161,0.231000," ","int((a+b*tan(d*x+c))/(e*tan(d*x+c))^(1/2),x)","\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \tan \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \tan \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \tan \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \tan \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}+\frac{b \sqrt{2}\, \ln \left(\frac{e \tan \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \tan \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \tan \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \tan \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"1/4/d*a/e*(e^2)^(1/4)*2^(1/2)*ln((e*tan(d*x+c)+(e^2)^(1/4)*(e*tan(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*tan(d*x+c)-(e^2)^(1/4)*(e*tan(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d*a/e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*tan(d*x+c))^(1/2)+1)-1/2/d*a/e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*tan(d*x+c))^(1/2)+1)+1/4/d*b/(e^2)^(1/4)*2^(1/2)*ln((e*tan(d*x+c)-(e^2)^(1/4)*(e*tan(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*tan(d*x+c)+(e^2)^(1/4)*(e*tan(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*tan(d*x+c))^(1/2)+1)-1/2/d*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*tan(d*x+c))^(1/2)+1)","B"
581,1,339,167,0.196000," ","int((a+b*tan(d*x+c))/(-e*tan(d*x+c))^(1/2),x)","-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{-e \tan \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{-e \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{-e \tan \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{-e \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{-e \tan \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{-e \tan \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}+\frac{b \sqrt{2}\, \ln \left(\frac{-e \tan \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{-e \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{-e \tan \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{-e \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{-e \tan \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{-e \tan \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/4/d*a/e*(e^2)^(1/4)*2^(1/2)*ln((-e*tan(d*x+c)+(e^2)^(1/4)*(-e*tan(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(-e*tan(d*x+c)-(e^2)^(1/4)*(-e*tan(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2/d*a/e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(-e*tan(d*x+c))^(1/2)+1)+1/2/d*a/e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(-e*tan(d*x+c))^(1/2)+1)+1/4/d*b/(e^2)^(1/4)*2^(1/2)*ln((-e*tan(d*x+c)-(e^2)^(1/4)*(-e*tan(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(-e*tan(d*x+c)+(e^2)^(1/4)*(-e*tan(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(-e*tan(d*x+c))^(1/2)+1)-1/2/d*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(-e*tan(d*x+c))^(1/2)+1)","B"
582,1,369,252,0.242000," ","int(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c)),x)","\frac{2 \left(\tan^{\frac{5}{2}}\left(d x +c \right)\right)}{5 b d}-\frac{2 a \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 b^{2} d}+\frac{2 a^{2} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,b^{3}}-\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{b d}-\frac{2 a^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \,b^{3} \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)}{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)}{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)}{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)}{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)}{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)}{4 d \left(a^{2}+b^{2}\right)}"," ",0,"2/5*tan(d*x+c)^(5/2)/b/d-2/3*a*tan(d*x+c)^(3/2)/b^2/d+2/d/b^3*a^2*tan(d*x+c)^(1/2)-2*tan(d*x+c)^(1/2)/b/d-2/d/b^3*a^5/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(-1+2^(1/2)*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)))+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(1+2^(1/2)*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))+1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+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"
583,1,334,227,0.298000," ","int(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x)","\frac{2 \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)}{b^{2} d}+\frac{2 a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \,b^{2} \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)}{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)}{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)}{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)}{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)}{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)}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"2/3*tan(d*x+c)^(3/2)/b/d-2*a*tan(d*x+c)^(1/2)/b^2/d+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))+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)))+1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(-1+2^(1/2)*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))-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)))-1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","A"
584,1,317,210,0.253000," ","int(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x)","\frac{2 \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)}{d b \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)}{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)}{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)}{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)}{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)}{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)}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"2*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))-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)))-1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-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)))-1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(-1+2^(1/2)*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"
585,1,298,194,0.250000," ","int(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x)","\frac{2 a^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{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)}{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)}{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)}{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)}{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)}{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)}{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))-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)))-1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(1+2^(1/2)*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))+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)))+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","A"
586,1,297,194,0.291000," ","int(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x)","-\frac{2 b a \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{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)}{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)}{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)}{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)}{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)}{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)}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"-2/d*b*a/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(-1+2^(1/2)*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)))+1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+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)))+1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","A"
587,1,298,194,0.245000," ","int(1/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)}{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)}{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)}{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)}{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)}{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)}{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)}{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))+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)))+1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(-1+2^(1/2)*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))-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)))-1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","A"
588,1,317,210,0.200000," ","int(1/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)}{d a \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{2}{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)}{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)}{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)}{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)}{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)}{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)}{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))-2/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)))-1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-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)))-1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(-1+2^(1/2)*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"
589,1,334,227,0.232000," ","int(1/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)}{d \,a^{2} \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{2}{3 a d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 b}{a^{2} 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)}{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)}{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)}{4 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)}{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)}{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)}{2 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))-2/3/a/d/tan(d*x+c)^(3/2)+2*b/a^2/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))-1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-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)))+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)))+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","A"
590,1,369,252,0.226000," ","int(1/tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x)","-\frac{2 b^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \,a^{3} \left(a^{2}+b^{2}\right) \sqrt{a b}}-\frac{2}{5 a d \tan \left(d x +c \right)^{\frac{5}{2}}}+\frac{2}{a d \sqrt{\tan \left(d x +c \right)}}-\frac{2 b^{2}}{d \,a^{3} \sqrt{\tan \left(d x +c \right)}}+\frac{2 b}{3 a^{2} d \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{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)}{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)}{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)}{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)}{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)}{4 d \left(a^{2}+b^{2}\right)}"," ",0,"-2/d/a^3*b^5/(a^2+b^2)/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))-2/5/a/d/tan(d*x+c)^(5/2)+2/a/d/tan(d*x+c)^(1/2)-2/d/a^3/tan(d*x+c)^(1/2)*b^2+2/3*b/a^2/d/tan(d*x+c)^(3/2)+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d/(a^2+b^2)*b*2^(1/2)*arctan(-1+2^(1/2)*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)))+1/2/d/(a^2+b^2)*a*2^(1/2)*arctan(1+2^(1/2)*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))+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"
591,1,597,353,0.294000," ","int(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^2,x)","\frac{2 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d \,b^{2}}-\frac{4 a \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,b^{3}}-\frac{a^{6} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{4} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{5 a^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \,b^{3} \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{9 a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d b \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\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)}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\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{\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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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{\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}}"," ",0,"2/3/d/b^2*tan(d*x+c)^(3/2)-4/d/b^3*a*tan(d*x+c)^(1/2)-1/d*a^6/b^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))-1/d*a^4/b/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))+5/d*a^6/b^3/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))+9/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))+1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d/(a^2+b^2)^2*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^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/4/d/(a^2+b^2)^2*2^(1/2)*ln((1-2^(1/2)*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*2^(1/2)*ln((1-2^(1/2)*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2","A"
592,1,574,316,0.273000," ","int(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x)","\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,b^{2}}+\frac{a^{5} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} b^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a^{3} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} b^{2} \sqrt{a b}}-\frac{7 a^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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{\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{\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{\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 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 \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"2/d/b^2*tan(d*x+c)^(1/2)+1/d*a^5/(a^2+b^2)^2/b^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))+1/d*a^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))-3/d*a^5/(a^2+b^2)^2/b^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))-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))+1/4/d/(a^2+b^2)^2*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*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*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)^2*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","A"
593,1,561,278,0.258000," ","int(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x)","-\frac{a^{4} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d b \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{2} b \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \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)}{d b \left(a^{2}+b^{2}\right)^{2} \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)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\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)}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\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{\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{\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{\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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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}}"," ",0,"-1/d*a^4/b/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))-1/d*a^2/(a^2+b^2)^2*b*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))+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))+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))-1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d/(a^2+b^2)^2*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/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/d/(a^2+b^2)^2*2^(1/2)*ln((1-2^(1/2)*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*2^(1/2)*ln((1-2^(1/2)*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"
594,1,551,272,0.271000," ","int(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x)","\frac{a^{3} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{a \left(\sqrt{\tan}\left(d x +c \right)\right) b^{2}}{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)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{3 a \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)^{2} \sqrt{a b}}-\frac{\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{\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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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{\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 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 \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d*a^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))+1/d*a/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*b^2+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))-3/d*a/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/d/(a^2+b^2)^2*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*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*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)^2*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))","B"
595,1,553,276,0.287000," ","int(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} b \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right)}{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)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\frac{b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}+\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)}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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{\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{\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{\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}}"," ",0,"-1/d*a^2/(a^2+b^2)^2*b*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))-1/d*b^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))-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))+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))+1/2/d/(a^2+b^2)^2*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/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/4/d/(a^2+b^2)^2*2^(1/2)*ln((1-2^(1/2)*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*2^(1/2)*ln((1-2^(1/2)*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2","A"
596,1,559,277,0.246000," ","int(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x)","\frac{a \left(\sqrt{\tan}\left(d x +c \right)\right) 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)}{d \left(a^{2}+b^{2}\right)^{2} a \left(a +b \tan \left(d x +c \right)\right)}+\frac{5 a \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)^{2} \sqrt{a b}}+\frac{b^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} a \sqrt{a b}}+\frac{\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{\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{\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{\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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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 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 \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d*a/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))*b^2+1/d*b^4/(a^2+b^2)^2/a*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))+5/d*a/(a^2+b^2)^2/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*b^2+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))+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/4/d/(a^2+b^2)^2*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*ln((1+2^(1/2)*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*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/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))","B"
597,1,576,315,0.233000," ","int(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x)","-\frac{b^{3} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{5} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} a^{2} \left(a +b \tan \left(d x +c \right)\right)}-\frac{7 b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{3 b^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} a^{2} \sqrt{a b}}-\frac{2}{d \,a^{2} \sqrt{\tan \left(d x +c \right)}}-\frac{a b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\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)}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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{\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{\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{\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}}"," ",0,"-1/d*b^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))-1/d*b^5/(a^2+b^2)^2/a^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))-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))-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))-2/d/a^2/tan(d*x+c)^(1/2)-1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))-1/2/d/(a^2+b^2)^2*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/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))-1/4/d/(a^2+b^2)^2*2^(1/2)*ln((1-2^(1/2)*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*2^(1/2)*ln((1-2^(1/2)*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2","A"
598,1,595,351,0.230000," ","int(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x)","\frac{b^{4} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2} a \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{6} \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,a^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{9 b^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} a \sqrt{a b}}+\frac{5 b^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{d \,a^{3} \left(a^{2}+b^{2}\right)^{2} \sqrt{a b}}-\frac{2}{3 d \,a^{2} \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{4 b}{d \,a^{3} \sqrt{\tan \left(d x +c \right)}}-\frac{\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{\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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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{\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 b \sqrt{2}\, \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \sqrt{2}\, \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\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)}{2 d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d*b^4/(a^2+b^2)^2/a*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))+1/d*b^6/a^3/(a^2+b^2)^2*tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))+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))+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))-2/3/d/a^2/tan(d*x+c)^(3/2)+4/d/a^3*b/tan(d*x+c)^(1/2)-1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^2-1/4/d/(a^2+b^2)^2*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^2+1/2/d/(a^2+b^2)^2*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^2+1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))+1/d/(a^2+b^2)^2*a*b*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))+1/2/d/(a^2+b^2)^2*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)))","A"
599,1,936,437,0.352000," ","int(tan(d*x+c)^(11/2)/(a+b*tan(d*x+c))^3,x)","\frac{2 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{3 d \,b^{3}}-\frac{6 a \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,b^{4}}-\frac{13 a^{8} \left(\tan^{\frac{3}{2}}\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{17 a^{6} \left(\tan^{\frac{3}{2}}\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{21 a^{4} b \left(\tan^{\frac{3}{2}}\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{11 a^{9} \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \,b^{4} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{15 a^{7} \left(\sqrt{\tan}\left(d x +c \right)\right)}{2 d \,b^{2} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{19 a^{5} \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{35 a^{8} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{4 d \,b^{4} \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{51 a^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{2 d \,b^{2} \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{99 a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{\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 \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{\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 \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \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{\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{3 \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{\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}}"," ",0,"2/3/d/b^3*tan(d*x+c)^(3/2)-6/d/b^4*a*tan(d*x+c)^(1/2)-13/4/d*a^8/b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)-17/2/d*a^6/b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)-21/4/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)-11/4/d*a^9/b^4/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)-15/2/d*a^7/b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)-19/4/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)+35/4/d*a^8/b^4/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))+51/2/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))+99/4/d*a^4/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))-1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*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*2^(1/2)*ln((1+2^(1/2)*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+3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*ln((1-2^(1/2)*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-1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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+3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3","B"
600,1,920,392,0.335000," ","int(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^3,x)","\frac{2 \left(\sqrt{\tan}\left(d x +c \right)\right)}{d \,b^{3}}+\frac{9 a^{7} \left(\tan^{\frac{3}{2}}\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{13 a^{5} \left(\tan^{\frac{3}{2}}\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{17 a^{3} b^{2} \left(\tan^{\frac{3}{2}}\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{7 a^{8} \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{11 a^{6} \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{15 a^{4} 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{15 a^{7} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{4 d \,b^{3} \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{23 a^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{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)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{3 \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{\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{3 \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{\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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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 \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{\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 \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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}}"," ",0,"2/d/b^3*tan(d*x+c)^(1/2)+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)+13/2/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)+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)+7/4/d*a^8/b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)+11/2/d*a^6/b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)+15/4/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)-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))-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))-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))+3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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-1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d/(a^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d/(a^2+b^2)^3*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*2^(1/2)*ln((1-2^(1/2)*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^3-3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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"
601,1,903,348,0.321000," ","int(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x)","-\frac{5 a^{6} \left(\tan^{\frac{3}{2}}\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{9 a^{4} b \left(\tan^{\frac{3}{2}}\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{13 a^{2} b^{3} \left(\tan^{\frac{3}{2}}\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^{7} \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{7 a^{5} \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{11 a^{3} b^{2} \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)}{4 d \,b^{2} \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{3 a^{4} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{35 a^{2} b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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 \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{\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 \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 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \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{\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{3 \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{\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}}"," ",0,"-5/4/d*a^6/b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)-9/2/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)-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)-3/4/d*a^7/b^2/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)-7/2/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)-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)+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))+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))+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))+1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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^3-3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d/(a^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d/(a^2+b^2)^3*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*2^(1/2)*ln((1-2^(1/2)*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+1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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^3-3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3","B"
602,1,900,342,0.314000," ","int(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x)","\frac{a^{5} \left(\tan^{\frac{3}{2}}\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{5 a^{3} b^{2} \left(\tan^{\frac{3}{2}}\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{9 a \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{6} \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(\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{7 a^{2} b^{3} \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^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{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)}{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)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{3 \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{\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{3 \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{\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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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 \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{\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 \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}}"," ",0,"1/4/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)+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)+9/4/d*a/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*b^4-1/4/d*a^6/b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)+3/2/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)+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)+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))+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))-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))-3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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+1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*ln((1-2^(1/2)*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+3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2","B"
603,1,895,337,0.350000," ","int(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x)","\frac{3 a^{4} b \left(\tan^{\frac{3}{2}}\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^{2} b^{3} \left(\tan^{\frac{3}{2}}\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{5 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{5}}{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)}{4 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)}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 \left(\sqrt{\tan}\left(d x +c \right)\right) a \,b^{4}}{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)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{13 a^{2} b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{3 \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) b^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{\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 \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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 \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 \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{\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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \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{\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}}"," ",0,"3/4/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)-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)-5/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*b^5+5/4/d*a^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)+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)-3/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*a*b^4+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))-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))+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^4-1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*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*2^(1/2)*ln((1+2^(1/2)*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+3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*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*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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-1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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+3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3","B"
604,1,900,341,0.347000," ","int(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x)","-\frac{7 a^{3} b^{2} \left(\tan^{\frac{3}{2}}\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 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{4}}{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)}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} a}-\frac{9 a^{4} 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{5 a^{2} b^{3} \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{b^{5} \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{15 a^{3} b \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{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)}{2 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)}{4 d \left(a^{2}+b^{2}\right)^{3} a \sqrt{a b}}+\frac{3 \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{\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{3 \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{\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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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 \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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 \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}}"," ",0,"-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)-3/2/d*a/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*b^4+1/4/d*b^6/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/a*tan(d*x+c)^(3/2)-9/4/d*a^4*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)-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)-1/4/d*b^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)-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))+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))+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))+3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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-1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d/(a^2+b^2)^3*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*2^(1/2)*ln((1-2^(1/2)*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^3-3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2","B"
605,1,903,348,0.372000," ","int(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x)","\frac{11 a^{2} b^{3} \left(\tan^{\frac{3}{2}}\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{7 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{5}}{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)}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} a^{2}}+\frac{13 a^{3} b^{2} \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{9 \left(\sqrt{\tan}\left(d x +c \right)\right) a \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{5 b^{6} \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} a}+\frac{35 a^{2} b^{2} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{3 \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{3 b^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} a^{2} \sqrt{a b}}+\frac{\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 \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{\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 \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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 \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{\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{3 \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{\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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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,"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)+7/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*b^5+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)+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)+9/2/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*a*b^4+5/4/d*b^6/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/a*tan(d*x+c)^(1/2)+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))+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+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))+1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d/(a^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2+1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3-3/2/d/(a^2+b^2)^3*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*2^(1/2)*ln((1+2^(1/2)*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^3-3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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+1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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","B"
606,1,920,392,0.313000," ","int(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x)","-\frac{15 a \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{4}}{4 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)}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2} a}-\frac{7 b^{8} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{4 d \left(a^{2}+b^{2}\right)^{3} a^{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)}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{13 b^{5} \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{9 b^{7} \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{63 a \,b^{3} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{23 b^{5} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{2 d \left(a^{2}+b^{2}\right)^{3} a \sqrt{a b}}-\frac{15 b^{7} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} a^{3} \sqrt{a b}}-\frac{2}{d \,a^{3} \sqrt{\tan \left(d x +c \right)}}-\frac{3 \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{\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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \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{\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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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 \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{\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 \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}}"," ",0,"-15/4/d*a/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*b^4-11/2/d*b^6/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/a*tan(d*x+c)^(3/2)-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)-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)-13/2/d*b^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)-9/4/d*b^7/(a^2+b^2)^3/a^2/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)-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))-23/2/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))-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))-2/d/a^3/tan(d*x+c)^(1/2)-3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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+1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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^3-3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3-1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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+3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2-1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a*b^2","B"
607,1,936,437,0.346000," ","int(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x)","\frac{19 \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) b^{5}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{15 b^{7} \left(\tan^{\frac{3}{2}}\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} a^{2}}+\frac{11 b^{9} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)}{4 d \,a^{4} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{21 \left(\sqrt{\tan}\left(d x +c \right)\right) a \,b^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{17 b^{6} \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} a}+\frac{13 b^{8} \left(\sqrt{\tan}\left(d x +c \right)\right)}{4 d \,a^{3} \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{99 \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right) b^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}+\frac{51 b^{6} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{2 d \left(a^{2}+b^{2}\right)^{3} a^{2} \sqrt{a b}}+\frac{35 b^{8} \arctan \left(\frac{\left(\sqrt{\tan}\left(d x +c \right)\right) b}{\sqrt{a b}}\right)}{4 d \,a^{4} \left(a^{2}+b^{2}\right)^{3} \sqrt{a b}}-\frac{2}{3 d \,a^{3} \tan \left(d x +c \right)^{\frac{3}{2}}}+\frac{6 b}{d \,a^{4} \sqrt{\tan \left(d x +c \right)}}-\frac{\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 \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{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{3 \sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\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 \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 \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{\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{3 \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{\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{3 \sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(d x +c \right)\right)+\tan \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,"19/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)*b^5+15/2/d*b^7/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/a^2*tan(d*x+c)^(3/2)+11/4/d*b^9/a^4/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(3/2)+21/4/d/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)*a*b^4+17/2/d*b^6/(a^2+b^2)^3/(a+b*tan(d*x+c))^2/a*tan(d*x+c)^(1/2)+13/4/d*b^8/a^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2*tan(d*x+c)^(1/2)+99/4/d/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))*b^4+51/2/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))+35/4/d*b^8/a^4/(a^2+b^2)^3/(a*b)^(1/2)*arctan(tan(d*x+c)^(1/2)*b/(a*b)^(1/2))-2/3/d/a^3/tan(d*x+c)^(3/2)+6/d/a^4*b/tan(d*x+c)^(1/2)-1/2/d/(a^2+b^2)^3*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*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*2^(1/2)*ln((1+2^(1/2)*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+3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1+2^(1/2)*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^2+b^2)^3*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*a^3+3/2/d/(a^2+b^2)^3*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*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*2^(1/2)*arctan(-1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/2/d/(a^2+b^2)^3*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*2^(1/2)*arctan(1+2^(1/2)*tan(d*x+c)^(1/2))*b^3+3/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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-1/4/d/(a^2+b^2)^3*2^(1/2)*ln((1-2^(1/2)*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","B"
608,1,1092021,189,1.344000," ","int(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
609,1,1090637,150,1.058000," ","int(tan(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","B"
610,1,1089481,123,0.699000," ","int(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"
611,1,1084638,93,0.730000," ","int((a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
612,1,1089777,115,0.643000," ","int((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"
613,1,1090457,147,0.710000," ","int((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"
614,1,1091469,183,0.686000," ","int((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"
615,1,1347974,230,0.761000," ","int(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"
616,1,1346578,184,0.849000," ","int(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"
617,1,1345539,152,0.925000," ","int(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"
618,1,1343726,124,0.758000," ","int((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
619,1,1343523,119,0.778000," ","int((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
620,1,1345207,141,0.921000," ","int((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
621,1,1346038,184,0.796000," ","int((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
622,1,1347641,222,0.949000," ","int((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
623,1,1347722,278,0.826000," ","int(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"
624,1,1310426,227,0.793000," ","int(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"
625,1,1345303,189,0.781000," ","int(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"
626,1,1308863,154,0.776000," ","int((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
627,1,1343532,151,0.820000," ","int((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
628,1,1307424,148,0.768000," ","int((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
629,1,1344685,181,0.740000," ","int((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
630,1,1309621,224,0.792000," ","int((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
631,1,1347695,268,0.964000," ","int((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(11/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
632,1,946413,190,0.707000," ","int(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
633,1,945569,154,0.777000," ","int(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
634,1,943897,124,0.682000," ","int(tan(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","B"
635,1,940034,93,0.767000," ","int(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"
636,1,939795,89,0.702000," ","int(1/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"
637,1,944396,121,0.782000," ","int(1/tan(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","B"
638,1,944677,148,0.653000," ","int(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
639,1,946581,189,0.749000," ","int(1/tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
640,1,763794,212,1.088000," ","int(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
641,1,798946,163,1.054000," ","int(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"
642,1,761722,128,1.027000," ","int(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"
643,1,797813,125,1.075000," ","int(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"
644,1,761738,133,1.059000," ","int(1/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"
645,1,798721,165,1.045000," ","int(1/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"
646,1,763924,201,1.436000," ","int(1/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"
647,1,1492208,271,1.417000," ","int(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
648,1,1490358,213,1.293000," ","int(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
649,1,1488448,180,1.355000," ","int(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"
650,1,1488163,167,1.739000," ","int(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"
651,1,1488472,177,1.704000," ","int(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"
652,1,1488187,180,1.750000," ","int(1/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"
653,1,1489984,227,1.418000," ","int(1/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"
654,1,1489930,256,1.353000," ","int(1/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"
655,1,480,73,0.561000," ","int(1/tan(d*x+c)^(1/2)/(2+3*tan(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right) \left(3 \sqrt{13}\, \sqrt{2 \sqrt{13}+6}\, \arctan \left(\frac{\sqrt{\frac{\left(11 \sqrt{13}-39\right) \tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right) \left(39+11 \sqrt{13}\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-6+2 \sqrt{13}}\, \left(11+3 \sqrt{13}\right) \left(\sqrt{13}+3-2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)}{416 \tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}\right) \sqrt{-6+2 \sqrt{13}}-11 \sqrt{2 \sqrt{13}+6}\, \arctan \left(\frac{\sqrt{\frac{\left(11 \sqrt{13}-39\right) \tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right) \left(39+11 \sqrt{13}\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-6+2 \sqrt{13}}\, \left(11+3 \sqrt{13}\right) \left(\sqrt{13}+3-2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)}{416 \tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}\right) \sqrt{-6+2 \sqrt{13}}+4 \arctanh \left(\frac{4 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right) \sqrt{13}-12 \arctanh \left(\frac{4 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{2+3 \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+6}\, \left(11 \sqrt{13}-39\right)}"," ",0,"1/2/d*(tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)*(13^(1/2)-3+2*tan(d*x+c))*(3*13^(1/2)*(2*13^(1/2)+6)^(1/2)*arctan(1/416*((11*13^(1/2)-39)*tan(d*x+c)*(2+3*tan(d*x+c))*(39+11*13^(1/2))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)*(-6+2*13^(1/2))^(1/2)*(11+3*13^(1/2))*(13^(1/2)+3-2*tan(d*x+c))*(11*13^(1/2)-39)*(13^(1/2)-3+2*tan(d*x+c))/tan(d*x+c)/(2+3*tan(d*x+c)))*(-6+2*13^(1/2))^(1/2)-11*(2*13^(1/2)+6)^(1/2)*arctan(1/416*((11*13^(1/2)-39)*tan(d*x+c)*(2+3*tan(d*x+c))*(39+11*13^(1/2))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)*(-6+2*13^(1/2))^(1/2)*(11+3*13^(1/2))*(13^(1/2)+3-2*tan(d*x+c))*(11*13^(1/2)-39)*(13^(1/2)-3+2*tan(d*x+c))/tan(d*x+c)/(2+3*tan(d*x+c)))*(-6+2*13^(1/2))^(1/2)+4*arctanh(4*13^(1/2)*(tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2))*13^(1/2)-12*arctanh(4*13^(1/2)*(tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2)))/tan(d*x+c)^(1/2)/(2+3*tan(d*x+c))^(1/2)/(2*13^(1/2)+6)^(1/2)/(11*13^(1/2)-39)","B"
656,1,480,73,0.335000," ","int(1/tan(d*x+c)^(1/2)/(-2+3*tan(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right) \left(3 \sqrt{-6+2 \sqrt{13}}\, \sqrt{13}\, \sqrt{2 \sqrt{13}+6}\, \arctan \left(\frac{\sqrt{\frac{\left(11 \sqrt{13}-39\right) \tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right) \left(39+11 \sqrt{13}\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-6+2 \sqrt{13}}\, \left(11+3 \sqrt{13}\right) \left(\sqrt{13}+3+2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)}{416 \tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}\right)-11 \sqrt{-6+2 \sqrt{13}}\, \sqrt{2 \sqrt{13}+6}\, \arctan \left(\frac{\sqrt{\frac{\left(11 \sqrt{13}-39\right) \tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right) \left(39+11 \sqrt{13}\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-6+2 \sqrt{13}}\, \left(11+3 \sqrt{13}\right) \left(\sqrt{13}+3+2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)}{416 \tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}\right)+4 \arctanh \left(\frac{4 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right) \sqrt{13}-12 \arctanh \left(\frac{4 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{-2+3 \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+6}\, \left(11 \sqrt{13}-39\right)}"," ",0,"-1/2/d*(tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)*(13^(1/2)-3-2*tan(d*x+c))*(3*(-6+2*13^(1/2))^(1/2)*13^(1/2)*(2*13^(1/2)+6)^(1/2)*arctan(1/416*((11*13^(1/2)-39)*tan(d*x+c)*(-2+3*tan(d*x+c))*(39+11*13^(1/2))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)*(-6+2*13^(1/2))^(1/2)*(11+3*13^(1/2))*(13^(1/2)+3+2*tan(d*x+c))*(11*13^(1/2)-39)*(13^(1/2)-3-2*tan(d*x+c))/tan(d*x+c)/(-2+3*tan(d*x+c)))-11*(-6+2*13^(1/2))^(1/2)*(2*13^(1/2)+6)^(1/2)*arctan(1/416*((11*13^(1/2)-39)*tan(d*x+c)*(-2+3*tan(d*x+c))*(39+11*13^(1/2))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)*(-6+2*13^(1/2))^(1/2)*(11+3*13^(1/2))*(13^(1/2)+3+2*tan(d*x+c))*(11*13^(1/2)-39)*(13^(1/2)-3-2*tan(d*x+c))/tan(d*x+c)/(-2+3*tan(d*x+c)))+4*arctanh(4*13^(1/2)*(tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2))*13^(1/2)-12*arctanh(4*13^(1/2)*(tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2)))/tan(d*x+c)^(1/2)/(-2+3*tan(d*x+c))^(1/2)/(2*13^(1/2)+6)^(1/2)/(11*13^(1/2)-39)","B"
657,1,435,73,0.289000," ","int(1/(2-3*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x)","\frac{\sqrt{2-3 \tan \left(d x +c \right)}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right) \left(3 \arctanh \left(\frac{\left(\sqrt{13}+3\right) \left(\sqrt{13}+3+2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \sqrt{13}}{52 \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right) \sqrt{-6+2 \sqrt{13}}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}\right) \sqrt{13}\, \sqrt{2 \sqrt{13}+6}\, \sqrt{-6+2 \sqrt{13}}-11 \arctanh \left(\frac{\left(\sqrt{13}+3\right) \left(\sqrt{13}+3+2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \sqrt{13}}{52 \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right) \sqrt{-6+2 \sqrt{13}}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}\right) \sqrt{2 \sqrt{13}+6}\, \sqrt{-6+2 \sqrt{13}}-4 \arctan \left(\frac{4 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right) \sqrt{13}+12 \arctan \left(\frac{4 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \left(-2+3 \tan \left(d x +c \right)\right) \sqrt{2 \sqrt{13}+6}\, \left(11 \sqrt{13}-39\right)}"," ",0,"1/2/d*(2-3*tan(d*x+c))^(1/2)*(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)*(13^(1/2)-3-2*tan(d*x+c))*(3*arctanh(1/52*(13^(1/2)+3)*(13^(1/2)+3+2*tan(d*x+c))*(11*13^(1/2)-39)/(13^(1/2)-3-2*tan(d*x+c))/(-6+2*13^(1/2))^(1/2)*13^(1/2)/(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2))*13^(1/2)*(2*13^(1/2)+6)^(1/2)*(-6+2*13^(1/2))^(1/2)-11*arctanh(1/52*(13^(1/2)+3)*(13^(1/2)+3+2*tan(d*x+c))*(11*13^(1/2)-39)/(13^(1/2)-3-2*tan(d*x+c))/(-6+2*13^(1/2))^(1/2)*13^(1/2)/(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2))*(2*13^(1/2)+6)^(1/2)*(-6+2*13^(1/2))^(1/2)-4*arctan(4*13^(1/2)*(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2))*13^(1/2)+12*arctan(4*13^(1/2)*(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2)))/tan(d*x+c)^(1/2)/(-2+3*tan(d*x+c))/(2*13^(1/2)+6)^(1/2)/(11*13^(1/2)-39)","B"
658,1,435,73,0.301000," ","int(1/(-2-3*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x)","-\frac{\sqrt{-2-3 \tan \left(d x +c \right)}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right) \left(3 \sqrt{-6+2 \sqrt{13}}\, \sqrt{13}\, \sqrt{2 \sqrt{13}+6}\, \arctanh \left(\frac{\left(\sqrt{13}+3\right) \left(\sqrt{13}+3-2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \sqrt{13}}{52 \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right) \sqrt{-6+2 \sqrt{13}}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}\right)-11 \sqrt{-6+2 \sqrt{13}}\, \sqrt{2 \sqrt{13}+6}\, \arctanh \left(\frac{\left(\sqrt{13}+3\right) \left(\sqrt{13}+3-2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \sqrt{13}}{52 \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right) \sqrt{-6+2 \sqrt{13}}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}\right)-4 \arctan \left(\frac{4 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right) \sqrt{13}+12 \arctan \left(\frac{4 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \left(2+3 \tan \left(d x +c \right)\right) \sqrt{2 \sqrt{13}+6}\, \left(11 \sqrt{13}-39\right)}"," ",0,"-1/2/d*(-2-3*tan(d*x+c))^(1/2)*(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)*(13^(1/2)-3+2*tan(d*x+c))*(3*(-6+2*13^(1/2))^(1/2)*13^(1/2)*(2*13^(1/2)+6)^(1/2)*arctanh(1/52*(13^(1/2)+3)*(13^(1/2)+3-2*tan(d*x+c))*(11*13^(1/2)-39)/(13^(1/2)-3+2*tan(d*x+c))/(-6+2*13^(1/2))^(1/2)*13^(1/2)/(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2))-11*(-6+2*13^(1/2))^(1/2)*(2*13^(1/2)+6)^(1/2)*arctanh(1/52*(13^(1/2)+3)*(13^(1/2)+3-2*tan(d*x+c))*(11*13^(1/2)-39)/(13^(1/2)-3+2*tan(d*x+c))/(-6+2*13^(1/2))^(1/2)*13^(1/2)/(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2))-4*arctan(4*13^(1/2)*(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2))*13^(1/2)+12*arctan(4*13^(1/2)*(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2)))/tan(d*x+c)^(1/2)/(2+3*tan(d*x+c))/(2*13^(1/2)+6)^(1/2)/(11*13^(1/2)-39)","B"
659,1,480,73,0.571000," ","int(1/tan(d*x+c)^(1/2)/(3+2*tan(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right) \left(4 \sqrt{-4+2 \sqrt{13}}\, \sqrt{13}\, \sqrt{2 \sqrt{13}+4}\, \arctan \left(\frac{\sqrt{\frac{\left(17 \sqrt{13}-52\right) \tan \left(d x +c \right) \left(52+17 \sqrt{13}\right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-4+2 \sqrt{13}}\, \left(4 \sqrt{13}+17\right) \left(\sqrt{13}+2-3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)}{56862 \tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}\right)-17 \sqrt{-4+2 \sqrt{13}}\, \sqrt{2 \sqrt{13}+4}\, \arctan \left(\frac{\sqrt{\frac{\left(17 \sqrt{13}-52\right) \tan \left(d x +c \right) \left(52+17 \sqrt{13}\right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-4+2 \sqrt{13}}\, \left(4 \sqrt{13}+17\right) \left(\sqrt{13}+2-3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)}{56862 \tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}\right)+18 \arctanh \left(\frac{6 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right) \sqrt{13}-36 \arctanh \left(\frac{6 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{3+2 \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+4}\, \left(17 \sqrt{13}-52\right)}"," ",0,"1/2/d*(tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)*(13^(1/2)-2+3*tan(d*x+c))*(4*(-4+2*13^(1/2))^(1/2)*13^(1/2)*(2*13^(1/2)+4)^(1/2)*arctan(1/56862*((17*13^(1/2)-52)*tan(d*x+c)*(52+17*13^(1/2))*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)*(-4+2*13^(1/2))^(1/2)*(4*13^(1/2)+17)*(13^(1/2)+2-3*tan(d*x+c))*(17*13^(1/2)-52)*(13^(1/2)-2+3*tan(d*x+c))/tan(d*x+c)/(3+2*tan(d*x+c)))-17*(-4+2*13^(1/2))^(1/2)*(2*13^(1/2)+4)^(1/2)*arctan(1/56862*((17*13^(1/2)-52)*tan(d*x+c)*(52+17*13^(1/2))*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)*(-4+2*13^(1/2))^(1/2)*(4*13^(1/2)+17)*(13^(1/2)+2-3*tan(d*x+c))*(17*13^(1/2)-52)*(13^(1/2)-2+3*tan(d*x+c))/tan(d*x+c)/(3+2*tan(d*x+c)))+18*arctanh(6*13^(1/2)*(tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2))*13^(1/2)-36*arctanh(6*13^(1/2)*(tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2)))/tan(d*x+c)^(1/2)/(3+2*tan(d*x+c))^(1/2)/(2*13^(1/2)+4)^(1/2)/(17*13^(1/2)-52)","B"
660,1,435,73,0.309000," ","int(1/(3-2*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x)","\frac{\sqrt{3-2 \tan \left(d x +c \right)}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right) \left(4 \sqrt{-4+2 \sqrt{13}}\, \arctanh \left(\frac{\left(\sqrt{13}+2\right) \left(\sqrt{13}+2+3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \sqrt{13}}{351 \sqrt{-4+2 \sqrt{13}}\, \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right) \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}\right) \sqrt{13}\, \sqrt{2 \sqrt{13}+4}-17 \sqrt{-4+2 \sqrt{13}}\, \arctanh \left(\frac{\left(\sqrt{13}+2\right) \left(\sqrt{13}+2+3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \sqrt{13}}{351 \sqrt{-4+2 \sqrt{13}}\, \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right) \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}\right) \sqrt{2 \sqrt{13}+4}-18 \arctan \left(\frac{6 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right) \sqrt{13}+36 \arctan \left(\frac{6 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+4}\, \left(-3+2 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right)}"," ",0,"1/2/d*(3-2*tan(d*x+c))^(1/2)*(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)*(13^(1/2)-2-3*tan(d*x+c))*(4*(-4+2*13^(1/2))^(1/2)*arctanh(1/351*(13^(1/2)+2)*(13^(1/2)+2+3*tan(d*x+c))*(17*13^(1/2)-52)/(-4+2*13^(1/2))^(1/2)/(13^(1/2)-2-3*tan(d*x+c))*13^(1/2)/(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2))*13^(1/2)*(2*13^(1/2)+4)^(1/2)-17*(-4+2*13^(1/2))^(1/2)*arctanh(1/351*(13^(1/2)+2)*(13^(1/2)+2+3*tan(d*x+c))*(17*13^(1/2)-52)/(-4+2*13^(1/2))^(1/2)/(13^(1/2)-2-3*tan(d*x+c))*13^(1/2)/(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2))*(2*13^(1/2)+4)^(1/2)-18*arctan(6*13^(1/2)*(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2))*13^(1/2)+36*arctan(6*13^(1/2)*(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2)))/tan(d*x+c)^(1/2)/(2*13^(1/2)+4)^(1/2)/(-3+2*tan(d*x+c))/(17*13^(1/2)-52)","B"
661,1,480,73,0.303000," ","int(1/tan(d*x+c)^(1/2)/(-3+2*tan(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right) \left(4 \sqrt{13}\, \sqrt{2 \sqrt{13}+4}\, \arctan \left(\frac{\sqrt{\frac{\left(17 \sqrt{13}-52\right) \tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right) \left(52+17 \sqrt{13}\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-4+2 \sqrt{13}}\, \left(4 \sqrt{13}+17\right) \left(\sqrt{13}+2+3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)}{56862 \tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}\right) \sqrt{-4+2 \sqrt{13}}-17 \sqrt{2 \sqrt{13}+4}\, \arctan \left(\frac{\sqrt{\frac{\left(17 \sqrt{13}-52\right) \tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right) \left(52+17 \sqrt{13}\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-4+2 \sqrt{13}}\, \left(4 \sqrt{13}+17\right) \left(\sqrt{13}+2+3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)}{56862 \tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}\right) \sqrt{-4+2 \sqrt{13}}+18 \arctanh \left(\frac{6 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right) \sqrt{13}-36 \arctanh \left(\frac{6 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{-3+2 \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+4}\, \left(17 \sqrt{13}-52\right)}"," ",0,"-1/2/d*(tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)*(13^(1/2)-2-3*tan(d*x+c))*(4*13^(1/2)*(2*13^(1/2)+4)^(1/2)*arctan(1/56862*((17*13^(1/2)-52)*tan(d*x+c)*(-3+2*tan(d*x+c))*(52+17*13^(1/2))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)*(-4+2*13^(1/2))^(1/2)*(4*13^(1/2)+17)*(13^(1/2)+2+3*tan(d*x+c))*(17*13^(1/2)-52)*(13^(1/2)-2-3*tan(d*x+c))/tan(d*x+c)/(-3+2*tan(d*x+c)))*(-4+2*13^(1/2))^(1/2)-17*(2*13^(1/2)+4)^(1/2)*arctan(1/56862*((17*13^(1/2)-52)*tan(d*x+c)*(-3+2*tan(d*x+c))*(52+17*13^(1/2))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)*(-4+2*13^(1/2))^(1/2)*(4*13^(1/2)+17)*(13^(1/2)+2+3*tan(d*x+c))*(17*13^(1/2)-52)*(13^(1/2)-2-3*tan(d*x+c))/tan(d*x+c)/(-3+2*tan(d*x+c)))*(-4+2*13^(1/2))^(1/2)+18*arctanh(6*13^(1/2)*(tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2))*13^(1/2)-36*arctanh(6*13^(1/2)*(tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2)))/tan(d*x+c)^(1/2)/(-3+2*tan(d*x+c))^(1/2)/(2*13^(1/2)+4)^(1/2)/(17*13^(1/2)-52)","B"
662,1,435,73,0.269000," ","int(1/(-3-2*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x)","-\frac{\sqrt{-3-2 \tan \left(d x +c \right)}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right) \left(4 \sqrt{-4+2 \sqrt{13}}\, \sqrt{13}\, \sqrt{2 \sqrt{13}+4}\, \arctanh \left(\frac{\left(\sqrt{13}+2\right) \left(\sqrt{13}+2-3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \sqrt{13}}{351 \sqrt{-4+2 \sqrt{13}}\, \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right) \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}\right)-17 \sqrt{-4+2 \sqrt{13}}\, \sqrt{2 \sqrt{13}+4}\, \arctanh \left(\frac{\left(\sqrt{13}+2\right) \left(\sqrt{13}+2-3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \sqrt{13}}{351 \sqrt{-4+2 \sqrt{13}}\, \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right) \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}\right)-18 \arctan \left(\frac{6 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right) \sqrt{13}+36 \arctan \left(\frac{6 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+4}\, \left(3+2 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right)}"," ",0,"-1/2/d*(-3-2*tan(d*x+c))^(1/2)*(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)*(13^(1/2)-2+3*tan(d*x+c))*(4*(-4+2*13^(1/2))^(1/2)*13^(1/2)*(2*13^(1/2)+4)^(1/2)*arctanh(1/351*(13^(1/2)+2)*(13^(1/2)+2-3*tan(d*x+c))*(17*13^(1/2)-52)/(-4+2*13^(1/2))^(1/2)/(13^(1/2)-2+3*tan(d*x+c))*13^(1/2)/(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2))-17*(-4+2*13^(1/2))^(1/2)*(2*13^(1/2)+4)^(1/2)*arctanh(1/351*(13^(1/2)+2)*(13^(1/2)+2-3*tan(d*x+c))*(17*13^(1/2)-52)/(-4+2*13^(1/2))^(1/2)/(13^(1/2)-2+3*tan(d*x+c))*13^(1/2)/(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2))-18*arctan(6*13^(1/2)*(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2))*13^(1/2)+36*arctan(6*13^(1/2)*(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2)))/tan(d*x+c)^(1/2)/(2*13^(1/2)+4)^(1/2)/(3+2*tan(d*x+c))/(17*13^(1/2)-52)","B"
663,1,479,77,0.247000," ","int(tan(d*x+c)^(1/2)/(2+3*tan(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right) \left(\sqrt{13}\, \sqrt{2 \sqrt{13}+6}\, \arctan \left(\frac{\sqrt{\frac{\left(11 \sqrt{13}-39\right) \tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right) \left(39+11 \sqrt{13}\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-6+2 \sqrt{13}}\, \left(11+3 \sqrt{13}\right) \left(\sqrt{13}+3-2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)}{416 \tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}\right) \sqrt{-6+2 \sqrt{13}}-3 \sqrt{2 \sqrt{13}+6}\, \arctan \left(\frac{\sqrt{\frac{\left(11 \sqrt{13}-39\right) \tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right) \left(39+11 \sqrt{13}\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-6+2 \sqrt{13}}\, \left(11+3 \sqrt{13}\right) \left(\sqrt{13}+3-2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)}{416 \tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}\right) \sqrt{-6+2 \sqrt{13}}-12 \arctanh \left(\frac{4 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right) \sqrt{13}+44 \arctanh \left(\frac{4 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{2+3 \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+6}\, \left(11 \sqrt{13}-39\right)}"," ",0,"-1/2/d*(tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)*(13^(1/2)-3+2*tan(d*x+c))*(13^(1/2)*(2*13^(1/2)+6)^(1/2)*arctan(1/416*((11*13^(1/2)-39)*tan(d*x+c)*(2+3*tan(d*x+c))*(39+11*13^(1/2))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)*(-6+2*13^(1/2))^(1/2)*(11+3*13^(1/2))*(13^(1/2)+3-2*tan(d*x+c))*(11*13^(1/2)-39)*(13^(1/2)-3+2*tan(d*x+c))/tan(d*x+c)/(2+3*tan(d*x+c)))*(-6+2*13^(1/2))^(1/2)-3*(2*13^(1/2)+6)^(1/2)*arctan(1/416*((11*13^(1/2)-39)*tan(d*x+c)*(2+3*tan(d*x+c))*(39+11*13^(1/2))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)*(-6+2*13^(1/2))^(1/2)*(11+3*13^(1/2))*(13^(1/2)+3-2*tan(d*x+c))*(11*13^(1/2)-39)*(13^(1/2)-3+2*tan(d*x+c))/tan(d*x+c)/(2+3*tan(d*x+c)))*(-6+2*13^(1/2))^(1/2)-12*arctanh(4*13^(1/2)*(tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2))*13^(1/2)+44*arctanh(4*13^(1/2)*(tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2)))/tan(d*x+c)^(1/2)/(2+3*tan(d*x+c))^(1/2)/(2*13^(1/2)+6)^(1/2)/(11*13^(1/2)-39)","B"
664,1,479,77,0.256000," ","int(tan(d*x+c)^(1/2)/(-2+3*tan(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right) \left(\sqrt{-6+2 \sqrt{13}}\, \sqrt{13}\, \sqrt{2 \sqrt{13}+6}\, \arctan \left(\frac{\sqrt{\frac{\left(11 \sqrt{13}-39\right) \tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right) \left(39+11 \sqrt{13}\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-6+2 \sqrt{13}}\, \left(11+3 \sqrt{13}\right) \left(\sqrt{13}+3+2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)}{416 \tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}\right)-3 \sqrt{-6+2 \sqrt{13}}\, \sqrt{2 \sqrt{13}+6}\, \arctan \left(\frac{\sqrt{\frac{\left(11 \sqrt{13}-39\right) \tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right) \left(39+11 \sqrt{13}\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-6+2 \sqrt{13}}\, \left(11+3 \sqrt{13}\right) \left(\sqrt{13}+3+2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)}{416 \tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}\right)-12 \arctanh \left(\frac{4 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right) \sqrt{13}+44 \arctanh \left(\frac{4 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{-2+3 \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+6}\, \left(11 \sqrt{13}-39\right)}"," ",0,"-1/2/d*(tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)*(13^(1/2)-3-2*tan(d*x+c))*((-6+2*13^(1/2))^(1/2)*13^(1/2)*(2*13^(1/2)+6)^(1/2)*arctan(1/416*((11*13^(1/2)-39)*tan(d*x+c)*(-2+3*tan(d*x+c))*(39+11*13^(1/2))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)*(-6+2*13^(1/2))^(1/2)*(11+3*13^(1/2))*(13^(1/2)+3+2*tan(d*x+c))*(11*13^(1/2)-39)*(13^(1/2)-3-2*tan(d*x+c))/tan(d*x+c)/(-2+3*tan(d*x+c)))-3*(-6+2*13^(1/2))^(1/2)*(2*13^(1/2)+6)^(1/2)*arctan(1/416*((11*13^(1/2)-39)*tan(d*x+c)*(-2+3*tan(d*x+c))*(39+11*13^(1/2))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)*(-6+2*13^(1/2))^(1/2)*(11+3*13^(1/2))*(13^(1/2)+3+2*tan(d*x+c))*(11*13^(1/2)-39)*(13^(1/2)-3-2*tan(d*x+c))/tan(d*x+c)/(-2+3*tan(d*x+c)))-12*arctanh(4*13^(1/2)*(tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2))*13^(1/2)+44*arctanh(4*13^(1/2)*(tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2)))/tan(d*x+c)^(1/2)/(-2+3*tan(d*x+c))^(1/2)/(2*13^(1/2)+6)^(1/2)/(11*13^(1/2)-39)","B"
665,1,434,77,0.243000," ","int(tan(d*x+c)^(1/2)/(2-3*tan(d*x+c))^(1/2),x)","\frac{\sqrt{2-3 \tan \left(d x +c \right)}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right) \left(\arctanh \left(\frac{\left(\sqrt{13}+3\right) \left(\sqrt{13}+3+2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \sqrt{13}}{52 \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right) \sqrt{-6+2 \sqrt{13}}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}\right) \sqrt{13}\, \sqrt{2 \sqrt{13}+6}\, \sqrt{-6+2 \sqrt{13}}-3 \arctanh \left(\frac{\left(\sqrt{13}+3\right) \left(\sqrt{13}+3+2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \sqrt{13}}{52 \left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right) \sqrt{-6+2 \sqrt{13}}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}\right) \sqrt{2 \sqrt{13}+6}\, \sqrt{-6+2 \sqrt{13}}+12 \arctan \left(\frac{4 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right) \sqrt{13}-44 \arctan \left(\frac{4 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3-2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \left(-2+3 \tan \left(d x +c \right)\right) \sqrt{2 \sqrt{13}+6}\, \left(11 \sqrt{13}-39\right)}"," ",0,"1/2/d*(2-3*tan(d*x+c))^(1/2)*(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)*(13^(1/2)-3-2*tan(d*x+c))*(arctanh(1/52*(13^(1/2)+3)*(13^(1/2)+3+2*tan(d*x+c))*(11*13^(1/2)-39)/(13^(1/2)-3-2*tan(d*x+c))/(-6+2*13^(1/2))^(1/2)*13^(1/2)/(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2))*13^(1/2)*(2*13^(1/2)+6)^(1/2)*(-6+2*13^(1/2))^(1/2)-3*arctanh(1/52*(13^(1/2)+3)*(13^(1/2)+3+2*tan(d*x+c))*(11*13^(1/2)-39)/(13^(1/2)-3-2*tan(d*x+c))/(-6+2*13^(1/2))^(1/2)*13^(1/2)/(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2))*(2*13^(1/2)+6)^(1/2)*(-6+2*13^(1/2))^(1/2)+12*arctan(4*13^(1/2)*(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2))*13^(1/2)-44*arctan(4*13^(1/2)*(-tan(d*x+c)*(-2+3*tan(d*x+c))/(13^(1/2)-3-2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2)))/tan(d*x+c)^(1/2)/(-2+3*tan(d*x+c))/(2*13^(1/2)+6)^(1/2)/(11*13^(1/2)-39)","B"
666,1,434,77,0.270000," ","int(tan(d*x+c)^(1/2)/(-2-3*tan(d*x+c))^(1/2),x)","\frac{\sqrt{-2-3 \tan \left(d x +c \right)}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right) \left(\sqrt{-6+2 \sqrt{13}}\, \sqrt{13}\, \sqrt{2 \sqrt{13}+6}\, \arctanh \left(\frac{\left(\sqrt{13}+3\right) \left(\sqrt{13}+3-2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \sqrt{13}}{52 \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right) \sqrt{-6+2 \sqrt{13}}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}\right)-3 \sqrt{-6+2 \sqrt{13}}\, \sqrt{2 \sqrt{13}+6}\, \arctanh \left(\frac{\left(\sqrt{13}+3\right) \left(\sqrt{13}+3-2 \tan \left(d x +c \right)\right) \left(11 \sqrt{13}-39\right) \sqrt{13}}{52 \left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right) \sqrt{-6+2 \sqrt{13}}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}\right)+12 \arctan \left(\frac{4 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right) \sqrt{13}-44 \arctan \left(\frac{4 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(2+3 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-3+2 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+78}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \left(2+3 \tan \left(d x +c \right)\right) \sqrt{2 \sqrt{13}+6}\, \left(11 \sqrt{13}-39\right)}"," ",0,"1/2/d*(-2-3*tan(d*x+c))^(1/2)*(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)*(13^(1/2)-3+2*tan(d*x+c))*((-6+2*13^(1/2))^(1/2)*13^(1/2)*(2*13^(1/2)+6)^(1/2)*arctanh(1/52*(13^(1/2)+3)*(13^(1/2)+3-2*tan(d*x+c))*(11*13^(1/2)-39)/(13^(1/2)-3+2*tan(d*x+c))/(-6+2*13^(1/2))^(1/2)*13^(1/2)/(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2))-3*(-6+2*13^(1/2))^(1/2)*(2*13^(1/2)+6)^(1/2)*arctanh(1/52*(13^(1/2)+3)*(13^(1/2)+3-2*tan(d*x+c))*(11*13^(1/2)-39)/(13^(1/2)-3+2*tan(d*x+c))/(-6+2*13^(1/2))^(1/2)*13^(1/2)/(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2))+12*arctan(4*13^(1/2)*(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2))*13^(1/2)-44*arctan(4*13^(1/2)*(-tan(d*x+c)*(2+3*tan(d*x+c))/(13^(1/2)-3+2*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+78)^(1/2)))/tan(d*x+c)^(1/2)/(2+3*tan(d*x+c))/(2*13^(1/2)+6)^(1/2)/(11*13^(1/2)-39)","B"
667,1,479,77,0.243000," ","int(tan(d*x+c)^(1/2)/(3+2*tan(d*x+c))^(1/2),x)","-\frac{3 \sqrt{\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right) \left(\sqrt{-4+2 \sqrt{13}}\, \sqrt{13}\, \sqrt{2 \sqrt{13}+4}\, \arctan \left(\frac{\sqrt{\frac{\left(17 \sqrt{13}-52\right) \tan \left(d x +c \right) \left(52+17 \sqrt{13}\right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-4+2 \sqrt{13}}\, \left(4 \sqrt{13}+17\right) \left(\sqrt{13}+2-3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)}{56862 \tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}\right)-2 \sqrt{-4+2 \sqrt{13}}\, \sqrt{2 \sqrt{13}+4}\, \arctan \left(\frac{\sqrt{\frac{\left(17 \sqrt{13}-52\right) \tan \left(d x +c \right) \left(52+17 \sqrt{13}\right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-4+2 \sqrt{13}}\, \left(4 \sqrt{13}+17\right) \left(\sqrt{13}+2-3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)}{56862 \tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}\right)-8 \arctanh \left(\frac{6 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right) \sqrt{13}+34 \arctanh \left(\frac{6 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{3+2 \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+4}\, \left(17 \sqrt{13}-52\right)}"," ",0,"-3/2/d*(tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)*(13^(1/2)-2+3*tan(d*x+c))*((-4+2*13^(1/2))^(1/2)*13^(1/2)*(2*13^(1/2)+4)^(1/2)*arctan(1/56862*((17*13^(1/2)-52)*tan(d*x+c)*(52+17*13^(1/2))*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)*(-4+2*13^(1/2))^(1/2)*(4*13^(1/2)+17)*(13^(1/2)+2-3*tan(d*x+c))*(17*13^(1/2)-52)*(13^(1/2)-2+3*tan(d*x+c))/tan(d*x+c)/(3+2*tan(d*x+c)))-2*(-4+2*13^(1/2))^(1/2)*(2*13^(1/2)+4)^(1/2)*arctan(1/56862*((17*13^(1/2)-52)*tan(d*x+c)*(52+17*13^(1/2))*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)*(-4+2*13^(1/2))^(1/2)*(4*13^(1/2)+17)*(13^(1/2)+2-3*tan(d*x+c))*(17*13^(1/2)-52)*(13^(1/2)-2+3*tan(d*x+c))/tan(d*x+c)/(3+2*tan(d*x+c)))-8*arctanh(6*13^(1/2)*(tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2))*13^(1/2)+34*arctanh(6*13^(1/2)*(tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2)))/tan(d*x+c)^(1/2)/(3+2*tan(d*x+c))^(1/2)/(2*13^(1/2)+4)^(1/2)/(17*13^(1/2)-52)","B"
668,1,434,77,0.253000," ","int(tan(d*x+c)^(1/2)/(3-2*tan(d*x+c))^(1/2),x)","\frac{3 \sqrt{3-2 \tan \left(d x +c \right)}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right) \left(\sqrt{-4+2 \sqrt{13}}\, \arctanh \left(\frac{\left(\sqrt{13}+2\right) \left(\sqrt{13}+2+3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \sqrt{13}}{351 \sqrt{-4+2 \sqrt{13}}\, \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right) \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}\right) \sqrt{13}\, \sqrt{2 \sqrt{13}+4}-2 \sqrt{-4+2 \sqrt{13}}\, \arctanh \left(\frac{\left(\sqrt{13}+2\right) \left(\sqrt{13}+2+3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \sqrt{13}}{351 \sqrt{-4+2 \sqrt{13}}\, \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right) \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}\right) \sqrt{2 \sqrt{13}+4}+8 \arctan \left(\frac{6 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right) \sqrt{13}-34 \arctan \left(\frac{6 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+4}\, \left(-3+2 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right)}"," ",0,"3/2/d*(3-2*tan(d*x+c))^(1/2)*(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)*(13^(1/2)-2-3*tan(d*x+c))*((-4+2*13^(1/2))^(1/2)*arctanh(1/351*(13^(1/2)+2)*(13^(1/2)+2+3*tan(d*x+c))*(17*13^(1/2)-52)/(-4+2*13^(1/2))^(1/2)/(13^(1/2)-2-3*tan(d*x+c))*13^(1/2)/(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2))*13^(1/2)*(2*13^(1/2)+4)^(1/2)-2*(-4+2*13^(1/2))^(1/2)*arctanh(1/351*(13^(1/2)+2)*(13^(1/2)+2+3*tan(d*x+c))*(17*13^(1/2)-52)/(-4+2*13^(1/2))^(1/2)/(13^(1/2)-2-3*tan(d*x+c))*13^(1/2)/(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2))*(2*13^(1/2)+4)^(1/2)+8*arctan(6*13^(1/2)*(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2))*13^(1/2)-34*arctan(6*13^(1/2)*(-tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2)))/tan(d*x+c)^(1/2)/(2*13^(1/2)+4)^(1/2)/(-3+2*tan(d*x+c))/(17*13^(1/2)-52)","B"
669,1,479,77,0.236000," ","int(tan(d*x+c)^(1/2)/(-3+2*tan(d*x+c))^(1/2),x)","-\frac{3 \sqrt{\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right) \left(\sqrt{13}\, \sqrt{2 \sqrt{13}+4}\, \arctan \left(\frac{\sqrt{\frac{\left(17 \sqrt{13}-52\right) \tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right) \left(52+17 \sqrt{13}\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-4+2 \sqrt{13}}\, \left(4 \sqrt{13}+17\right) \left(\sqrt{13}+2+3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)}{56862 \tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}\right) \sqrt{-4+2 \sqrt{13}}-2 \sqrt{2 \sqrt{13}+4}\, \arctan \left(\frac{\sqrt{\frac{\left(17 \sqrt{13}-52\right) \tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right) \left(52+17 \sqrt{13}\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}\, \sqrt{-4+2 \sqrt{13}}\, \left(4 \sqrt{13}+17\right) \left(\sqrt{13}+2+3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)}{56862 \tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}\right) \sqrt{-4+2 \sqrt{13}}-8 \arctanh \left(\frac{6 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right) \sqrt{13}+34 \arctanh \left(\frac{6 \sqrt{13}\, \sqrt{\frac{\tan \left(d x +c \right) \left(-3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2-3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{-3+2 \tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+4}\, \left(17 \sqrt{13}-52\right)}"," ",0,"-3/2/d*(tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)*(13^(1/2)-2-3*tan(d*x+c))*(13^(1/2)*(2*13^(1/2)+4)^(1/2)*arctan(1/56862*((17*13^(1/2)-52)*tan(d*x+c)*(-3+2*tan(d*x+c))*(52+17*13^(1/2))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)*(-4+2*13^(1/2))^(1/2)*(4*13^(1/2)+17)*(13^(1/2)+2+3*tan(d*x+c))*(17*13^(1/2)-52)*(13^(1/2)-2-3*tan(d*x+c))/tan(d*x+c)/(-3+2*tan(d*x+c)))*(-4+2*13^(1/2))^(1/2)-2*(2*13^(1/2)+4)^(1/2)*arctan(1/56862*((17*13^(1/2)-52)*tan(d*x+c)*(-3+2*tan(d*x+c))*(52+17*13^(1/2))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)*(-4+2*13^(1/2))^(1/2)*(4*13^(1/2)+17)*(13^(1/2)+2+3*tan(d*x+c))*(17*13^(1/2)-52)*(13^(1/2)-2-3*tan(d*x+c))/tan(d*x+c)/(-3+2*tan(d*x+c)))*(-4+2*13^(1/2))^(1/2)-8*arctanh(6*13^(1/2)*(tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2))*13^(1/2)+34*arctanh(6*13^(1/2)*(tan(d*x+c)*(-3+2*tan(d*x+c))/(13^(1/2)-2-3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2)))/tan(d*x+c)^(1/2)/(-3+2*tan(d*x+c))^(1/2)/(2*13^(1/2)+4)^(1/2)/(17*13^(1/2)-52)","B"
670,1,434,77,0.272000," ","int(tan(d*x+c)^(1/2)/(-3-2*tan(d*x+c))^(1/2),x)","\frac{3 \sqrt{-3-2 \tan \left(d x +c \right)}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}\, \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right) \left(\sqrt{-4+2 \sqrt{13}}\, \sqrt{13}\, \sqrt{2 \sqrt{13}+4}\, \arctanh \left(\frac{\left(\sqrt{13}+2\right) \left(\sqrt{13}+2-3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \sqrt{13}}{351 \sqrt{-4+2 \sqrt{13}}\, \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right) \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}\right)-2 \sqrt{-4+2 \sqrt{13}}\, \sqrt{2 \sqrt{13}+4}\, \arctanh \left(\frac{\left(\sqrt{13}+2\right) \left(\sqrt{13}+2-3 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right) \sqrt{13}}{351 \sqrt{-4+2 \sqrt{13}}\, \left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right) \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}\right)+8 \arctan \left(\frac{6 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right) \sqrt{13}-34 \arctan \left(\frac{6 \sqrt{13}\, \sqrt{-\frac{\tan \left(d x +c \right) \left(3+2 \tan \left(d x +c \right)\right)}{\left(\sqrt{13}-2+3 \tan \left(d x +c \right)\right)^{2}}}}{\sqrt{26 \sqrt{13}+52}}\right)\right)}{2 d \sqrt{\tan \left(d x +c \right)}\, \sqrt{2 \sqrt{13}+4}\, \left(3+2 \tan \left(d x +c \right)\right) \left(17 \sqrt{13}-52\right)}"," ",0,"3/2/d*(-3-2*tan(d*x+c))^(1/2)*(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)*(13^(1/2)-2+3*tan(d*x+c))*((-4+2*13^(1/2))^(1/2)*13^(1/2)*(2*13^(1/2)+4)^(1/2)*arctanh(1/351*(13^(1/2)+2)*(13^(1/2)+2-3*tan(d*x+c))*(17*13^(1/2)-52)/(-4+2*13^(1/2))^(1/2)/(13^(1/2)-2+3*tan(d*x+c))*13^(1/2)/(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2))-2*(-4+2*13^(1/2))^(1/2)*(2*13^(1/2)+4)^(1/2)*arctanh(1/351*(13^(1/2)+2)*(13^(1/2)+2-3*tan(d*x+c))*(17*13^(1/2)-52)/(-4+2*13^(1/2))^(1/2)/(13^(1/2)-2+3*tan(d*x+c))*13^(1/2)/(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2))+8*arctan(6*13^(1/2)*(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2))*13^(1/2)-34*arctan(6*13^(1/2)*(-tan(d*x+c)*(3+2*tan(d*x+c))/(13^(1/2)-2+3*tan(d*x+c))^2)^(1/2)/(26*13^(1/2)+52)^(1/2)))/tan(d*x+c)^(1/2)/(2*13^(1/2)+4)^(1/2)/(3+2*tan(d*x+c))/(17*13^(1/2)-52)","B"
671,1,541,384,0.299000," ","int(tan(d*x+c)^(5/3)/(a+b*tan(d*x+c)),x)","-\frac{a^{2} \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{d \left(a^{2}+b^{2}\right) b \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{a^{2} \ln \left(\tan^{\frac{2}{3}}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{2 d \left(a^{2}+b^{2}\right) b \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{a^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{d \left(a^{2}+b^{2}\right) b \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{3 \ln \left(1+\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{3}\, b}{4 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \ln \left(1+\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) a}{4 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \arctan \left(\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}\, a}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \arctan \left(\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) b}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \ln \left(1-\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{3}\, b}{4 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \ln \left(1-\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) a}{4 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \arctan \left(-\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}\, a}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \arctan \left(-\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) b}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 a \ln \left(1+\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 b \arctan \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{d \left(3 a^{2}+3 b^{2}\right)}"," ",0,"-1/d*a^2/(a^2+b^2)/b/(1/b*a)^(1/3)*ln(tan(d*x+c)^(1/3)+(1/b*a)^(1/3))+1/2/d*a^2/(a^2+b^2)/b/(1/b*a)^(1/3)*ln(tan(d*x+c)^(2/3)-(1/b*a)^(1/3)*tan(d*x+c)^(1/3)+(1/b*a)^(2/3))+1/d*a^2/(a^2+b^2)*3^(1/2)/b/(1/b*a)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)^(1/3)-1))-3/4/d/(3*a^2+3*b^2)*ln(1+3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*3^(1/2)*b+3/4/d/(3*a^2+3*b^2)*ln(1+3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*a+3/2/d/(3*a^2+3*b^2)*arctan(3^(1/2)+2*tan(d*x+c)^(1/3))*3^(1/2)*a+3/2/d/(3*a^2+3*b^2)*arctan(3^(1/2)+2*tan(d*x+c)^(1/3))*b+3/4/d/(3*a^2+3*b^2)*ln(1-3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*3^(1/2)*b+3/4/d/(3*a^2+3*b^2)*ln(1-3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*a-3/2/d/(3*a^2+3*b^2)*arctan(-3^(1/2)+2*tan(d*x+c)^(1/3))*3^(1/2)*a+3/2/d/(3*a^2+3*b^2)*arctan(-3^(1/2)+2*tan(d*x+c)^(1/3))*b-3/2/d/(3*a^2+3*b^2)*a*ln(1+tan(d*x+c)^(2/3))+3/d/(3*a^2+3*b^2)*b*arctan(tan(d*x+c)^(1/3))","A"
672,1,527,383,0.283000," ","int(tan(d*x+c)^(1/3)/(a+b*tan(d*x+c)),x)","-\frac{a \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{a \ln \left(\tan^{\frac{2}{3}}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{2 d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{3 \ln \left(1+\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{3}\, b}{4 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \ln \left(1+\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) a}{4 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \arctan \left(\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}\, a}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \arctan \left(\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) b}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \ln \left(1-\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{3}\, b}{4 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \ln \left(1-\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) a}{4 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \arctan \left(-\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) b}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \arctan \left(-\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}\, a}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 a \ln \left(1+\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 b \arctan \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{d \left(3 a^{2}+3 b^{2}\right)}"," ",0,"-1/d*a/(a^2+b^2)/(1/b*a)^(2/3)*ln(tan(d*x+c)^(1/3)+(1/b*a)^(1/3))+1/2/d*a/(a^2+b^2)/(1/b*a)^(2/3)*ln(tan(d*x+c)^(2/3)-(1/b*a)^(1/3)*tan(d*x+c)^(1/3)+(1/b*a)^(2/3))-1/d*a/(a^2+b^2)/(1/b*a)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)^(1/3)-1))+3/4/d/(3*a^2+3*b^2)*ln(1+3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*3^(1/2)*b+3/4/d/(3*a^2+3*b^2)*ln(1+3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*a-3/2/d/(3*a^2+3*b^2)*arctan(3^(1/2)+2*tan(d*x+c)^(1/3))*3^(1/2)*a+3/2/d/(3*a^2+3*b^2)*arctan(3^(1/2)+2*tan(d*x+c)^(1/3))*b-3/4/d/(3*a^2+3*b^2)*ln(1-3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*3^(1/2)*b+3/4/d/(3*a^2+3*b^2)*ln(1-3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*a+3/2/d/(3*a^2+3*b^2)*arctan(-3^(1/2)+2*tan(d*x+c)^(1/3))*b+3/2/d/(3*a^2+3*b^2)*arctan(-3^(1/2)+2*tan(d*x+c)^(1/3))*3^(1/2)*a-3/2/d/(3*a^2+3*b^2)*a*ln(1+tan(d*x+c)^(2/3))+3/d/(3*a^2+3*b^2)*b*arctan(tan(d*x+c)^(1/3))","A"
673,1,526,385,0.233000," ","int(1/tan(d*x+c)^(1/3)/(a+b*tan(d*x+c)),x)","-\frac{b \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{b \ln \left(\tan^{\frac{2}{3}}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{2 d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{3 \ln \left(1+\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{3}\, b}{4 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \ln \left(1+\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) a}{4 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \arctan \left(\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}\, a}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \arctan \left(\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) b}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \ln \left(1-\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{3}\, b}{4 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \ln \left(1-\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) a}{4 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \arctan \left(-\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}\, a}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \arctan \left(-\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) b}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 a \ln \left(1+\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 b \arctan \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{d \left(3 a^{2}+3 b^{2}\right)}"," ",0,"-1/d*b/(a^2+b^2)/(1/b*a)^(1/3)*ln(tan(d*x+c)^(1/3)+(1/b*a)^(1/3))+1/2/d*b/(a^2+b^2)/(1/b*a)^(1/3)*ln(tan(d*x+c)^(2/3)-(1/b*a)^(1/3)*tan(d*x+c)^(1/3)+(1/b*a)^(2/3))+1/d*b/(a^2+b^2)*3^(1/2)/(1/b*a)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)^(1/3)-1))+3/4/d/(3*a^2+3*b^2)*ln(1+3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*3^(1/2)*b-3/4/d/(3*a^2+3*b^2)*ln(1+3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*a-3/2/d/(3*a^2+3*b^2)*arctan(3^(1/2)+2*tan(d*x+c)^(1/3))*3^(1/2)*a-3/2/d/(3*a^2+3*b^2)*arctan(3^(1/2)+2*tan(d*x+c)^(1/3))*b-3/4/d/(3*a^2+3*b^2)*ln(1-3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*3^(1/2)*b-3/4/d/(3*a^2+3*b^2)*ln(1-3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*a+3/2/d/(3*a^2+3*b^2)*arctan(-3^(1/2)+2*tan(d*x+c)^(1/3))*3^(1/2)*a-3/2/d/(3*a^2+3*b^2)*arctan(-3^(1/2)+2*tan(d*x+c)^(1/3))*b+3/2/d/(3*a^2+3*b^2)*a*ln(1+tan(d*x+c)^(2/3))-3/d/(3*a^2+3*b^2)*b*arctan(tan(d*x+c)^(1/3))","A"
674,1,558,435,0.246000," ","int(1/tan(d*x+c)^(5/3)/(a+b*tan(d*x+c)),x)","-\frac{3}{2 a d \tan \left(d x +c \right)^{\frac{2}{3}}}-\frac{b^{2} \ln \left(\tan^{\frac{1}{3}}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{d a \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{b^{2} \ln \left(\tan^{\frac{2}{3}}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{2 d a \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{b^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{d a \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{3 \ln \left(1+\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{3}\, b}{4 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \ln \left(1+\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) a}{4 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \arctan \left(\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}\, a}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \arctan \left(\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) b}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 \ln \left(1-\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{3}\, b}{4 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \ln \left(1-\sqrt{3}\, \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)+\tan^{\frac{2}{3}}\left(d x +c \right)\right) a}{4 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \arctan \left(-\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) b}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 \arctan \left(-\sqrt{3}+2 \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)\right) \sqrt{3}\, a}{2 d \left(3 a^{2}+3 b^{2}\right)}+\frac{3 a \ln \left(1+\tan^{\frac{2}{3}}\left(d x +c \right)\right)}{2 d \left(3 a^{2}+3 b^{2}\right)}-\frac{3 b \arctan \left(\tan^{\frac{1}{3}}\left(d x +c \right)\right)}{d \left(3 a^{2}+3 b^{2}\right)}"," ",0,"-3/2/a/d/tan(d*x+c)^(2/3)-1/d/a*b^2/(a^2+b^2)/(1/b*a)^(2/3)*ln(tan(d*x+c)^(1/3)+(1/b*a)^(1/3))+1/2/d/a*b^2/(a^2+b^2)/(1/b*a)^(2/3)*ln(tan(d*x+c)^(2/3)-(1/b*a)^(1/3)*tan(d*x+c)^(1/3)+(1/b*a)^(2/3))-1/d/a*b^2/(a^2+b^2)/(1/b*a)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)^(1/3)-1))-3/4/d/(3*a^2+3*b^2)*ln(1+3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*3^(1/2)*b-3/4/d/(3*a^2+3*b^2)*ln(1+3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*a+3/2/d/(3*a^2+3*b^2)*arctan(3^(1/2)+2*tan(d*x+c)^(1/3))*3^(1/2)*a-3/2/d/(3*a^2+3*b^2)*arctan(3^(1/2)+2*tan(d*x+c)^(1/3))*b+3/4/d/(3*a^2+3*b^2)*ln(1-3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*3^(1/2)*b-3/4/d/(3*a^2+3*b^2)*ln(1-3^(1/2)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))*a-3/2/d/(3*a^2+3*b^2)*arctan(-3^(1/2)+2*tan(d*x+c)^(1/3))*b-3/2/d/(3*a^2+3*b^2)*arctan(-3^(1/2)+2*tan(d*x+c)^(1/3))*3^(1/2)*a+3/2/d/(3*a^2+3*b^2)*a*ln(1+tan(d*x+c)^(2/3))-3/d/(3*a^2+3*b^2)*b*arctan(tan(d*x+c)^(1/3))","A"
675,0,0,133,2.009000," ","int(tan(d*x+c)^(4/3)/(a+b*tan(d*x+c))^(1/2),x)","\int \frac{\tan^{\frac{4}{3}}\left(d x +c \right)}{\sqrt{a +b \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^(4/3)/(a+b*tan(d*x+c))^(1/2),x)","F"
676,0,0,133,1.903000," ","int(tan(d*x+c)^(2/3)/(a+b*tan(d*x+c))^(1/2),x)","\int \frac{\tan^{\frac{2}{3}}\left(d x +c \right)}{\sqrt{a +b \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^(2/3)/(a+b*tan(d*x+c))^(1/2),x)","F"
677,0,0,133,1.040000," ","int(tan(d*x+c)^(1/3)/(a+b*tan(d*x+c))^(1/2),x)","\int \frac{\tan^{\frac{1}{3}}\left(d x +c \right)}{\sqrt{a +b \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^(1/3)/(a+b*tan(d*x+c))^(1/2),x)","F"
678,0,0,133,1.142000," ","int(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x)","\int \frac{1}{\sqrt{a +b \tan \left(d x +c \right)}\, \tan \left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x)","F"
679,0,0,133,1.191000," ","int(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x)","\int \frac{1}{\sqrt{a +b \tan \left(d x +c \right)}\, \tan \left(d x +c \right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x)","F"
680,0,0,133,1.001000," ","int(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x)","\int \frac{1}{\sqrt{a +b \tan \left(d x +c \right)}\, \tan \left(d x +c \right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x)","F"
681,1,145,423,0.664000," ","int(tan(f*x+e)^4*(c+d*tan(f*x+e))^(1/3),x)","\frac{3 \left(c +d \tan \left(f x +e \right)\right)^{\frac{10}{3}}}{10 f \,d^{3}}-\frac{6 c \left(c +d \tan \left(f x +e \right)\right)^{\frac{7}{3}}}{7 f \,d^{3}}+\frac{3 \left(c +d \tan \left(f x +e \right)\right)^{\frac{4}{3}} c^{2}}{4 f \,d^{3}}-\frac{3 \left(c +d \tan \left(f x +e \right)\right)^{\frac{4}{3}}}{4 d f}+\frac{d \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 c \,\textit{\_Z}^{3}+c^{2}+d^{2}\right)}{\sum}\frac{\textit{\_R}^{3} \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}\right)}{2 f}"," ",0,"3/10/f/d^3*(c+d*tan(f*x+e))^(10/3)-6/7/f/d^3*c*(c+d*tan(f*x+e))^(7/3)+3/4/f/d^3*(c+d*tan(f*x+e))^(4/3)*c^2-3/4*(c+d*tan(f*x+e))^(4/3)/d/f+1/2/f*d*sum(_R^3/(_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"
682,1,131,295,0.288000," ","int(tan(f*x+e)^3*(c+d*tan(f*x+e))^(1/3),x)","\frac{3 \left(c +d \tan \left(f x +e \right)\right)^{\frac{7}{3}}}{7 f \,d^{2}}-\frac{3 c \left(c +d \tan \left(f x +e \right)\right)^{\frac{4}{3}}}{4 d^{2} f}-\frac{3 \left(c +d \tan \left(f x +e \right)\right)^{\frac{1}{3}}}{f}-\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 c \,\textit{\_Z}^{3}+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,"3/7/f/d^2*(c+d*tan(f*x+e))^(7/3)-3/4*c*(c+d*tan(f*x+e))^(4/3)/d^2/f-3*(c+d*tan(f*x+e))^(1/3)/f-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"
683,1,81,345,0.263000," ","int(tan(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x)","\frac{3 \left(c +d \tan \left(f x +e \right)\right)^{\frac{4}{3}}}{4 d f}-\frac{d \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 c \,\textit{\_Z}^{3}+c^{2}+d^{2}\right)}{\sum}\frac{\textit{\_R}^{3} \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}\right)}{2 f}"," ",0,"3/4*(c+d*tan(f*x+e))^(4/3)/d/f-1/2/f*d*sum(_R^3/(_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"
684,1,90,248,0.220000," ","int(tan(f*x+e)*(c+d*tan(f*x+e))^(1/3),x)","\frac{3 \left(c +d \tan \left(f x +e \right)\right)^{\frac{1}{3}}}{f}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 c \,\textit{\_Z}^{3}+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,"3*(c+d*tan(f*x+e))^(1/3)/f+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"
685,1,60,325,0.226000," ","int((c+d*tan(f*x+e))^(1/3),x)","\frac{d \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 c \,\textit{\_Z}^{3}+c^{2}+d^{2}\right)}{\sum}\frac{\textit{\_R}^{3} \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}\right)}{2 f}"," ",0,"1/2/f*d*sum(_R^3/(_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"
686,0,0,311,0.769000," ","int(cot(f*x+e)*(c+d*tan(f*x+e))^(1/3),x)","\int \cot \left(f x +e \right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cot(f*x+e)*(c+d*tan(f*x+e))^(1/3),x)","F"
687,0,0,431,0.632000," ","int(cot(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cot(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x)","F"
688,1,96,253,0.225000," ","int((a+b*tan(d*x+c))^(5/3),x)","\frac{3 b \left(a +b \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{2 d}+\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 a \,\textit{\_Z}^{3}+a^{2}+b^{2}\right)}{\sum}\frac{\left(2 a \,\textit{\_R}^{4}+\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}\right)}{2 d}"," ",0,"3/2*b*(a+b*tan(d*x+c))^(2/3)/d+1/2/d*b*sum((2*a*_R^4+(-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"
689,1,93,253,0.186000," ","int((a+b*tan(d*x+c))^(4/3),x)","\frac{3 b \left(a +b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{d}+\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 a \,\textit{\_Z}^{3}+a^{2}+b^{2}\right)}{\sum}\frac{\left(2 \textit{\_R}^{3} a -a^{2}-b^{2}\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}\right)}{2 d}"," ",0,"3*b*(a+b*tan(d*x+c))^(1/3)/d+1/2/d*b*sum((2*_R^3*a-a^2-b^2)/(_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"
690,1,60,325,0.192000," ","int((a+b*tan(d*x+c))^(2/3),x)","\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 a \,\textit{\_Z}^{3}+a^{2}+b^{2}\right)}{\sum}\frac{\textit{\_R}^{4} \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}\right)}{2 d}"," ",0,"1/2/d*b*sum(_R^4/(_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"
691,1,60,325,0.186000," ","int((a+b*tan(d*x+c))^(1/3),x)","\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 a \,\textit{\_Z}^{3}+a^{2}+b^{2}\right)}{\sum}\frac{\textit{\_R}^{3} \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}\right)}{2 d}"," ",0,"1/2/d*b*sum(_R^3/(_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"
692,1,58,325,0.189000," ","int(1/(a+b*tan(d*x+c))^(1/3),x)","\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 a \,\textit{\_Z}^{3}+a^{2}+b^{2}\right)}{\sum}\frac{\textit{\_R} \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}\right)}{2 d}"," ",0,"1/2/d*b*sum(_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"
693,1,57,325,0.191000," ","int(1/(a+b*tan(d*x+c))^(2/3),x)","\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 a \,\textit{\_Z}^{3}+a^{2}+b^{2}\right)}{\sum}\frac{\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}\right)}{2 d}"," ",0,"1/2/d*b*sum(1/(_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"
694,1,102,262,0.186000," ","int(1/(a+b*tan(d*x+c))^(4/3),x)","-\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 a \,\textit{\_Z}^{3}+a^{2}+b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{4}-2 \textit{\_R} a \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}\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{3 b}{\left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}"," ",0,"-1/2/d*b/(a^2+b^2)*sum((_R^4-2*_R*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))-3*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(1/3)","C"
695,1,103,262,0.214000," ","int(1/(a+b*tan(d*x+c))^(5/3),x)","-\frac{3 b}{2 \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{\frac{2}{3}}}+\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-2 a \,\textit{\_Z}^{3}+a^{2}+b^{2}\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+2 a \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}\right)}{2 d \left(a^{2}+b^{2}\right)}"," ",0,"-3/2*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(2/3)+1/2/d*b/(a^2+b^2)*sum((-_R^3+2*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"
696,0,0,257,1.156000," ","int((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^4,x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{4}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^4,x)","F"
697,0,0,194,1.068000," ","int((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^3,x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^3,x)","F"
698,0,0,136,1.048000," ","int((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^2,x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^2,x)","F"
699,0,0,99,1.753000," ","int((d*tan(f*x+e))^n*(a+b*tan(f*x+e)),x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +b \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+b*tan(f*x+e)),x)","F"
700,0,0,179,1.295000," ","int((d*tan(f*x+e))^n/(a+b*tan(f*x+e)),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{a +b \tan \left(f x +e \right)}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a+b*tan(f*x+e)),x)","F"
701,0,0,250,1.533000," ","int((d*tan(f*x+e))^n/(a+b*tan(f*x+e))^2,x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{\left(a +b \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a+b*tan(f*x+e))^2,x)","F"
702,0,0,157,0.996000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2),x)","\int \left(\tan^{m}\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))^(3/2),x)","F"
703,0,0,155,0.923000," ","int(tan(d*x+c)^m*(a+b*tan(d*x+c))^(1/2),x)","\int \left(\tan^{m}\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))^(1/2),x)","F"
704,0,0,155,0.911000," ","int(tan(d*x+c)^m/(a+b*tan(d*x+c))^(1/2),x)","\int \frac{\tan^{m}\left(d x +c \right)}{\sqrt{a +b \tan \left(d x +c \right)}}\, dx"," ",0,"int(tan(d*x+c)^m/(a+b*tan(d*x+c))^(1/2),x)","F"
705,0,0,161,0.886000," ","int(tan(d*x+c)^m/(a+b*tan(d*x+c))^(3/2),x)","\int \frac{\tan^{m}\left(d x +c \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))^(3/2),x)","F"
706,0,0,173,0.871000," ","int((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^m,x)","\int \left(d \tan \left(f x +e \right)\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^m,x)","F"
707,0,0,285,0.789000," ","int(tan(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","\int \left(\tan^{4}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(tan(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","F"
708,0,0,188,0.833000," ","int(tan(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","\int \left(\tan^{3}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(tan(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","F"
709,0,0,181,0.713000," ","int(tan(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","\int \left(\tan^{2}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(tan(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","F"
710,0,0,123,1.014000," ","int(tan(d*x+c)*(a+b*tan(d*x+c))^n,x)","\int \tan \left(d x +c \right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(tan(d*x+c)*(a+b*tan(d*x+c))^n,x)","F"
711,0,0,155,0.650000," ","int((a+b*tan(d*x+c))^n,x)","\int \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a+b*tan(d*x+c))^n,x)","F"
712,0,0,173,1.167000," ","int(cot(d*x+c)*(a+b*tan(d*x+c))^n,x)","\int \cot \left(d x +c \right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)*(a+b*tan(d*x+c))^n,x)","F"
713,0,0,235,0.815000," ","int(cot(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","F"
714,0,0,253,0.801000," ","int(cot(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","F"
715,0,0,141,1.054000," ","int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x)","\int \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x)","F"
716,0,0,141,0.950000," ","int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n,x)","\int \left(\sqrt{\tan}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n,x)","F"
717,0,0,139,0.979000," ","int((a+b*tan(d*x+c))^n/tan(d*x+c)^(1/2),x)","\int \frac{\left(a +b \tan \left(d x +c \right)\right)^{n}}{\sqrt{\tan \left(d x +c \right)}}\, dx"," ",0,"int((a+b*tan(d*x+c))^n/tan(d*x+c)^(1/2),x)","F"
718,0,0,141,1.001000," ","int((a+b*tan(d*x+c))^n/tan(d*x+c)^(3/2),x)","\int \frac{\left(a +b \tan \left(d x +c \right)\right)^{n}}{\tan \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(d*x+c))^n/tan(d*x+c)^(3/2),x)","F"
719,1,776,52,1.183000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c)),x)","-\frac{a \left(-3 i \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \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 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+3 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\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*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)+cos(d*x+c)^2*2^(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"
720,1,722,37,1.108000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c)),x)","-\frac{a \left(i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \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{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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \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{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/d*(I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+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"
721,1,242,22,1.093000," ","int(cot(d*x+c)^(1/2)*(a+I*a*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) \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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}}{d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"a/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(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"
722,1,414,38,1.144000," ","int((a+I*a*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(i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \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 \cos \left(d x +c \right) \sqrt{2}-i \sqrt{2}\right) \sqrt{2}}{d \sin \left(d x +c \right)^{4} \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+I*cos(d*x+c)*2^(1/2)-I*2^(1/2))/sin(d*x+c)^4/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
723,1,469,52,1.152000," ","int((a+I*a*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 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-i \sin \left(d x +c \right) \sqrt{2}+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-3 \cos \left(d x +c \right) \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{3 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,"1/3*a/d*(-1+cos(d*x+c))*(-3*I*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+I*sin(d*x+c)*cos(d*x+c)*2^(1/2)-I*sin(d*x+c)*2^(1/2)+3*cos(d*x+c)^2*2^(1/2)-3*cos(d*x+c)*2^(1/2))*(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"
724,1,1458,74,1.391000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^2,x)","-\frac{a^{2} \left(-30 i \left(\cos^{3}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+30 i \left(\cos^{3}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-30 i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+30 i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-30 \left(\cos^{3}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+30 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-30 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-30 \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+10 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+30 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-30 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+30 \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+33 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+30 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-30 \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{7}{2}} \sin \left(d x +c \right) \sqrt{2}}{15 d \cos \left(d x +c \right)^{4}}"," ",0,"-1/15*a^2/d*(-30*I*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+30*I*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-30*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+30*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-30*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+30*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-30*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-30*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+10*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+30*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-30*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+30*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+33*2^(1/2)*cos(d*x+c)^3+30*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-30*cos(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"
725,1,778,58,1.283000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2,x)","-\frac{a^{2} \left(-6 i \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+6 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-6 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \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 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+6 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\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*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+6*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-6*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-6*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+6*I*sin(d*x+c)*cos(d*x+c)*2^(1/2)+cos(d*x+c)^2*2^(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"
726,1,724,41,1.260000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2,x)","-\frac{a^{2} \left(2 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-2 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-2 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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{\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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \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{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*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+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"
727,1,420,41,1.326000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2,x)","\frac{a^{2} \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 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \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 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(d x +c \right) \sqrt{2}+\sqrt{2}\right) \sqrt{2}}{d \cos \left(d x +c \right) \sin \left(d x +c \right)^{3}}"," ",0,"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*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+2*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-cos(d*x+c)*2^(1/2)+2^(1/2))/cos(d*x+c)/sin(d*x+c)^3*2^(1/2)","C"
728,1,479,58,1.314000," ","int((a+I*a*tan(d*x+c))^2/cot(d*x+c)^(1/2),x)","-\frac{a^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(6 i \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 i \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+6 i \cos \left(d x +c \right) \sqrt{2}+\sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-\sqrt{2}\, \sin \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^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(6*I*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-6*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*I*2^(1/2)*cos(d*x+c)^2+6*I*cos(d*x+c)*2^(1/2)+2^(1/2)*cos(d*x+c)*sin(d*x+c)-2^(1/2)*sin(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"
729,1,511,74,1.282000," ","int((a+I*a*tan(d*x+c))^2/cot(d*x+c)^(3/2),x)","\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(-30 i \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+30 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-30 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+10 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-10 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+33 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-33 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-3 \cos \left(d x +c \right) \sqrt{2}+3 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{15 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} \cos \left(d x +c \right)}"," ",0,"1/15*a^2/d*(-1+cos(d*x+c))*(-30*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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+30*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-30*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+10*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-10*I*cos(d*x+c)*sin(d*x+c)*2^(1/2)+33*2^(1/2)*cos(d*x+c)^3-33*cos(d*x+c)^2*2^(1/2)-3*cos(d*x+c)*2^(1/2)+3*2^(1/2))*(1+cos(d*x+c))^2/(cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^5/cos(d*x+c)*2^(1/2)","C"
730,1,1458,88,1.495000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^3,x)","-\frac{a^{3} \left(-20 i \left(\cos^{3}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+20 i \left(\cos^{3}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-20 i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+20 i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-20 \left(\cos^{3}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+20 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-20 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-20 \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+20 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-20 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+20 \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+20 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-20 \cos \left(d x +c \right) \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{7}{2}} \sqrt{2}}{5 d \cos \left(d x +c \right)^{4}}"," ",0,"-1/5*a^3/d*(-20*I*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+20*I*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-20*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+20*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-20*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+20*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-20*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-20*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*I*sin(d*x+c)*cos(d*x+c)^2*2^(1/2)+20*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-20*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+20*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+21*2^(1/2)*cos(d*x+c)^3+20*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-20*cos(d*x+c)*2^(1/2))*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(7/2)/cos(d*x+c)^4*2^(1/2)","C"
731,1,779,72,1.478000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^3,x)","\frac{a^{3} \left(12 i \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-12 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+12 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+12 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-12 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-9 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-12*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+12*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-9*I*cos(d*x+c)*sin(d*x+c)*2^(1/2)-cos(d*x+c)^2*2^(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"
732,1,736,55,1.507000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3,x)","-\frac{a^{3} \left(4 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-4 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+4 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-4 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \sin \left(d x +c \right) \sqrt{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}}{d \cos \left(d x +c \right)^{2}}"," ",0,"-a^3/d*(4*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-4*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+4*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-4*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*2^(1/2)*sin(d*x+c)+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"
733,1,479,71,1.480000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3,x)","\frac{a^{3} \left(-1+\cos \left(d x +c \right)\right) \left(12 i \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-12 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+12 \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+i \sin \left(d x +c \right) \sqrt{2}-9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+9 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{3 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{3}}"," ",0,"1/3*a^3/d*(-1+cos(d*x+c))*(12*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-I*2^(1/2)*cos(d*x+c)*sin(d*x+c)+I*2^(1/2)*sin(d*x+c)-9*cos(d*x+c)^2*2^(1/2)+9*cos(d*x+c)*2^(1/2))*(cos(d*x+c)/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2/cos(d*x+c)^2/sin(d*x+c)^3*2^(1/2)","C"
734,1,514,88,1.380000," ","int((a+I*a*tan(d*x+c))^3/cot(d*x+c)^(1/2),x)","\frac{a^{3} \left(-1+\cos \left(d x +c \right)\right) \left(-20 i \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+20 i \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+20 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+21 i \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-21 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-5 \sin \left(d x +c \right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-i \cos \left(d x +c \right) \sqrt{2}+5 \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+i \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{5 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,"1/5*a^3/d*(-1+cos(d*x+c))*(-20*I*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+20*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+20*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+21*I*2^(1/2)*cos(d*x+c)^3-21*I*2^(1/2)*cos(d*x+c)^2-5*sin(d*x+c)*2^(1/2)*cos(d*x+c)^2-I*cos(d*x+c)*2^(1/2)+5*2^(1/2)*cos(d*x+c)*sin(d*x+c)+I*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"
735,1,1205,170,1.115000," ","int(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x)","\frac{\left(i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)+3 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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{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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+4 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)+3 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-i \sqrt{2}\, \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+4 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-5 \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}}{4 a d \cos \left(d x +c \right)^{2}}"," ",0,"1/4/a/d*(I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)-4*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+3*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+4*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+4*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2^(1/2)*cos(d*x+c)^3-5*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"
736,1,701,154,1.120000," ","int(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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 \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \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 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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 \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+\sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-\left(\cos^{2}\left(d x +c \right)\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}}{4 a d \cos \left(d x +c \right) \sin \left(d x +c \right)^{3}}"," ",0,"1/4/a/d*(-1+cos(d*x+c))*(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)-I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)+I*sin(d*x+c)*cos(d*x+c)*2^(1/2)+2^(1/2)*cos(d*x+c)^3-cos(d*x+c)^2*2^(1/2))*(1+cos(d*x+c))^2*(cos(d*x+c)/sin(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)^3*2^(1/2)","C"
737,1,1134,54,1.341000," ","int(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \cos \left(d x +c \right) \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{4 a d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)^{4}}"," ",0,"-1/4/a/d*(-1+cos(d*x+c))*(I*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*cos(d*x+c)*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*cos(d*x+c)^2*2^(1/2)+((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*cos(d*x+c)*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"
738,1,1836,154,1.273000," ","int(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-2 i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 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{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) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+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)}{\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{1-\cos \left(d x +c \right)+\sin \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) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \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{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) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-\cos \left(d x +c \right) \sqrt{2}\right) \cos \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{4 a d \left(i \sin \left(d x +c \right)+\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)^{5}}"," ",0,"-1/4/a/d*(-1+cos(d*x+c))*(-2*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+I*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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)-cos(d*x+c)*2^(1/2))*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))^(3/2)/sin(d*x+c)^5*2^(1/2)","C"
739,1,1867,171,1.489000," ","int(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(4 i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-5 i \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 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{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) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-5 \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \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{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) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\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{-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{1-\cos \left(d x +c \right)+\sin \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) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \sin \left(d x +c \right) \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-5 i \cos \left(d x +c \right) \sqrt{2}+4 \sqrt{2}\, \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{4 a d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{6} \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/4/a/d*(-1+cos(d*x+c))*(5*I*2^(1/2)*cos(d*x+c)^2+4*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*I*cos(d*x+c)*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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)-5*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*2^(1/2)*cos(d*x+c)*sin(d*x+c)-5*I*cos(d*x+c)*2^(1/2)+4*2^(1/2)*sin(d*x+c))*cos(d*x+c)^2*(1+cos(d*x+c))^2/(I*sin(d*x+c)+cos(d*x+c))/sin(d*x+c)^6/(cos(d*x+c)/sin(d*x+c))^(5/2)*2^(1/2)","C"
740,1,1241,197,1.392000," ","int(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{\left(4 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+23 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)-2 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-21 i \cos \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-4 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-23 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)+23 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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{\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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-21 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+7 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-23 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+25 \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}}{16 a^{2} d \cos \left(d x +c \right)^{2}}"," ",0,"-1/16/a^2/d*(4*I*cos(d*x+c)^4*sin(d*x+c)*2^(1/2)+23*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)-21*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)-4*cos(d*x+c)^5*2^(1/2)-23*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-21*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+7*I*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)-23*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*2^(1/2)*cos(d*x+c)^3+25*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"
741,1,768,181,1.330000," ","int(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(4 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-4 i \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+7 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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}+5 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+7 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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)-9 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+2 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)-5 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-3 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+3 \left(\cos^{2}\left(d x +c \right)\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}}{16 a^{2} d \cos \left(d x +c \right) \sin \left(d x +c \right)^{3}}"," ",0,"-1/16/a^2/d*(-1+cos(d*x+c))*(4*I*cos(d*x+c)^4*sin(d*x+c)*2^(1/2)-4*I*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+7*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*cos(d*x+c)^5*2^(1/2)+5*I*sin(d*x+c)*cos(d*x+c)^2*2^(1/2)+4*2^(1/2)*cos(d*x+c)^4+7*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)-9*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-5*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)-3*2^(1/2)*cos(d*x+c)^3+3*cos(d*x+c)^2*2^(1/2))*(1+cos(d*x+c))^2*(cos(d*x+c)/sin(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)^3*2^(1/2)","C"
742,1,2495,182,1.623000," ","int(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x)","\text{Expression too large to display}"," ",0,"1/16/a^2/d*(-1+cos(d*x+c))*(2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*2^(1/2)*cos(d*x+c)^2+2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-4*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+4*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+4*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*2^(1/2)*cos(d*x+c)^3-2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+4*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)-4*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)-2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-sin(d*x+c)*2^(1/2)*cos(d*x+c)^2+2^(1/2)*cos(d*x+c)*sin(d*x+c))*(1+cos(d*x+c))^2/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/(cos(d*x+c)/sin(d*x+c))^(1/2)/sin(d*x+c)^4*2^(1/2)","C"
743,1,2502,182,1.462000," ","int(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x)","\text{Expression too large to display}"," ",0,"-1/16/a^2/d*(-1+cos(d*x+c))*(-2*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+4*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+2*I*cos(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+4*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+2*I*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*I*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+4*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)-4*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)-sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-3*I*sin(d*x+c)*2^(1/2)*cos(d*x+c)^2-2^(1/2)*cos(d*x+c)^3+cos(d*x+c)^2*2^(1/2))*cos(d*x+c)*(1+cos(d*x+c))^2/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/(cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^5*2^(1/2)","C"
744,1,2505,182,1.472000," ","int(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^2,x)","\text{Expression too large to display}"," ",0,"1/16/a^2/d*(-1+cos(d*x+c))*(14*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*I*2^(1/2)*cos(d*x+c)^2+14*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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+4*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-4*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-10*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-4*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+14*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-14*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*I*2^(1/2)*cos(d*x+c)^3-14*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-7*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))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*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))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-4*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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+10*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+4*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-14*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+7*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)-10*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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-7*sin(d*x+c)*2^(1/2)*cos(d*x+c)^2+7*2^(1/2)*cos(d*x+c)*sin(d*x+c))*cos(d*x+c)^2*(1+cos(d*x+c))^2/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/(cos(d*x+c)/sin(d*x+c))^(5/2)/sin(d*x+c)^6*2^(1/2)","C"
745,1,2521,198,1.570000," ","int(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^2,x)","\text{Expression too large to display}"," ",0,"1/16/a^2/d*(-1+cos(d*x+c))*(-25*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-16*2^(1/2)+23*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)-4*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+50*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-41*2^(1/2)*cos(d*x+c)^3+23*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+46*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+4*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+43*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)-43*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-4*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-46*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+16*cos(d*x+c)*2^(1/2)+2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)+46*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)-46*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+4*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-50*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-46*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+50*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-46*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+4*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+41*cos(d*x+c)^2*2^(1/2))*cos(d*x+c)^3*(1+cos(d*x+c))^2/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/sin(d*x+c)^7/(cos(d*x+c)/sin(d*x+c))^(7/2)*2^(1/2)","C"
746,1,834,217,1.602000," ","int(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(16 i \sqrt{2}\, \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)+18 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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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)-16 \sqrt{2}\, \left(\cos^{7}\left(d x +c \right)\right)-3 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+16 \sqrt{2}\, \left(\cos^{6}\left(d x +c \right)\right)-16 i \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)-12 i \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+12 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-4 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-15 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+4 \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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)-21 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+18 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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)+15 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-7 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+7 \left(\cos^{2}\left(d x +c \right)\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}}{48 a^{3} d \cos \left(d x +c \right) \sin \left(d x +c \right)^{3}}"," ",0,"-1/48/a^3/d*(-1+cos(d*x+c))*(16*I*2^(1/2)*cos(d*x+c)^6*sin(d*x+c)+18*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-16*2^(1/2)*cos(d*x+c)^7-3*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+16*2^(1/2)*cos(d*x+c)^6-16*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)^5-12*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)^3+12*I*2^(1/2)*cos(d*x+c)^4*sin(d*x+c)-4*cos(d*x+c)^5*2^(1/2)-15*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)+4*2^(1/2)*cos(d*x+c)^4+3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-21*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+18*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)+15*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-7*2^(1/2)*cos(d*x+c)^3+7*cos(d*x+c)^2*2^(1/2))*(1+cos(d*x+c))^2*(cos(d*x+c)/sin(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)^3*2^(1/2)","C"
747,1,3101,214,1.925000," ","int(1/cot(d*x+c)^(1/2)/(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*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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))/sin(d*x+c))^(1/2)+3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+30*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-9*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-12*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-15*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+15*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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))/sin(d*x+c))^(1/2)+2*sin(d*x+c)*2^(1/2)*cos(d*x+c)^2+3*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-24*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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))/sin(d*x+c))^(1/2)-24*I*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*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))/sin(d*x+c))^(1/2)-6*I*cos(d*x+c)^3*2^(1/2)-2*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)+6*I*cos(d*x+c)^4*2^(1/2)-9*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)-9*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)+18*I*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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))/sin(d*x+c))^(1/2)+9*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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/(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))^(1/2)/sin(d*x+c)^4*2^(1/2)","C"
748,1,1953,117,1.753000," ","int(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"1/48/a^3/d*(-1+cos(d*x+c))*(9*I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-12*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-15*I*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-12*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-12*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+12*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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))/sin(d*x+c))^(1/2)-3*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+10*I*sin(d*x+c)*2^(1/2)*cos(d*x+c)^3-12*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+15*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+15*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+9*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-9*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+12*I*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4-10*I*sin(d*x+c)*2^(1/2)*cos(d*x+c)^2+6*2^(1/2)*cos(d*x+c)^4-6*2^(1/2)*cos(d*x+c)^3-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*cos(d*x+c)^2*2^(1/2)+3*cos(d*x+c)*2^(1/2))*cos(d*x+c)*(1+cos(d*x+c))^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))^(3/2)/sin(d*x+c)^5*2^(1/2)","C"
749,1,2063,178,1.826000," ","int(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-1/48/a^3/d*(-1+cos(d*x+c))*(-12*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+12*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+12*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-9*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+12*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+9*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-3*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-3*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-9*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)-9*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*sin(d*x+c)*cos(d*x+c)*2^(1/2)-6*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-2*2^(1/2)*cos(d*x+c)^3+2*cos(d*x+c)^2*2^(1/2))*cos(d*x+c)^2*(1+cos(d*x+c))^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)/sin(d*x+c)^5*2^(1/2)","C"
750,1,3134,218,1.802000," ","int(1/cot(d*x+c)^(7/2)/(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))*(60*I*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+72*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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))/sin(d*x+c))^(1/2)+18*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+38*I*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-38*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-60*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-90*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-42*2^(1/2)*cos(d*x+c)^3+9*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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))/sin(d*x+c))^(1/2)+72*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*sin(d*x+c)-54*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)+42*2^(1/2)*cos(d*x+c)^4+45*sin(d*x+c)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+72*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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))/sin(d*x+c))^(1/2)+27*cos(d*x+c)*2^(1/2)+12*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4-75*I*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+90*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-72*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4-27*cos(d*x+c)^2*2^(1/2)+15*I*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-18*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+3*I*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-9*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)-54*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2)))*cos(d*x+c)^3*(1+cos(d*x+c))^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))^(7/2)/sin(d*x+c)^7*2^(1/2)","C"
751,1,1146,139,1.786000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(30 i \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) \sin \left(d x +c \right)+30 i \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) \sin \left(d x +c \right)-15 i \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) \sin \left(d x +c \right)-30 i \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) \sin \left(d x +c \right)-30 \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) \sin \left(d x +c \right)-15 \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) \sin \left(d x +c \right)-30 \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) \sin \left(d x +c \right)+15 i \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) \sin \left(d x +c \right)-26 i \sin \left(d x +c \right) \sqrt{2}-30 i \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) \sin \left(d x +c \right)-2 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+34 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+34 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+30 \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) \sin \left(d x +c \right)+15 \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) \sin \left(d x +c \right)+30 \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) \sin \left(d x +c \right)-32 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-28 \cos \left(d x +c \right) \sqrt{2}+26 \sqrt{2}\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{7}{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}}{30 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{3}}"," ",0,"-1/30/d*(30*I*((-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*((-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)-15*I*((-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))*sin(d*x+c)-30*I*((-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*((-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)-15*((-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)-30*((-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)+15*I*((-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)-26*I*2^(1/2)*sin(d*x+c)-30*I*((-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)-2*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)+34*2^(1/2)*cos(d*x+c)^3+34*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+30*((-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*((-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))*sin(d*x+c)+30*((-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)-32*cos(d*x+c)^2*2^(1/2)-28*cos(d*x+c)*2^(1/2)+26*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)","B"
752,1,1041,112,1.676000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(-3 i \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 \left(\cos^{2}\left(d x +c \right)\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)+6 i \left(\cos^{2}\left(d x +c \right)\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 \sin \left(d x +c \right) \sqrt{2}+6 \left(\cos^{2}\left(d x +c \right)\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)+6 \left(\cos^{2}\left(d x +c \right)\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)+3 \left(\cos^{2}\left(d x +c \right)\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)-6 i \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 \left(\cos^{2}\left(d x +c \right)\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)-6 i \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 \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-2 \cos \left(d x +c \right) \sqrt{2}-6 \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 \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 \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 \sqrt{2}\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*(-3*I*((-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*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)+6*I*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)-2*I*sin(d*x+c)*2^(1/2)+6*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)+6*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)+3*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))-6*I*((-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*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))-6*I*((-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*I*cos(d*x+c)*sin(d*x+c)*2^(1/2)+4*cos(d*x+c)^2*2^(1/2)-2*cos(d*x+c)*2^(1/2)-6*((-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*((-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*((-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*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"
753,1,575,84,1.673000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(2 i \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) \sin \left(d x +c \right)+2 i \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) \sin \left(d x +c \right)+i \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) \sin \left(d x +c \right)+2 i \sin \left(d x +c \right) \sqrt{2}-2 \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) \sin \left(d x +c \right)-2 \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) \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) \sin \left(d x +c \right)+2 \cos \left(d x +c \right) \sqrt{2}-2 \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*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*I*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*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*sin(d*x+c)*2^(1/2)-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)*sin(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)*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))*sin(d*x+c)+2*cos(d*x+c)*2^(1/2)-2*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"
754,1,408,56,1.614000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\sqrt{2}\, \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{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(i \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 \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 i \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+2 \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\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)\right)}{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*2^(1/2)*(cos(d*x+c)/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(I*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*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*I*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+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*sin(d*x+c)+cos(d*x+c)-1)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)","B"
755,1,582,114,1.722000," ","int((a+I*a*tan(d*x+c))^(1/2)/cot(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)}}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right) \left(i \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-i \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 i \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right)+\sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-\sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-2 \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right)-2 i \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-2 i \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-i \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 \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+2 \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\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)\right) \sqrt{2}}{2 d \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \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*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))*(I*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-I*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*I*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))+2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-2*I*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*I*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-I*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*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+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)))/sin(d*x+c)/(cos(d*x+c)/sin(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)*2^(1/2)","B"
756,1,2093,140,1.812000," ","int((a+I*a*tan(d*x+c))^(1/2)/cot(d*x+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/4/d*(2*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-2*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*2^(1/2)*cos(d*x+c)^2*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-I*2^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2*I*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*I*2^(1/2)*cos(d*x+c)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-2*I*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*I*cos(d*x+c)*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2*I*cos(d*x+c)*sin(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*I*cos(d*x+c)*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+I*2^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+I*2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2^(1/2)*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*2^(1/2)*cos(d*x+c)*sin(d*x+c)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-2^(1/2)*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-4*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-4*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*cos(d*x+c)^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*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+I*2^(1/2)*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-I*2^(1/2)*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-2*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+4*cos(d*x+c)*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+4*cos(d*x+c)*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*cos(d*x+c)*sin(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^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*2^(1/2)*cos(d*x+c)^2*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))+2^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*2^(1/2)*cos(d*x+c)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-2*I*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*I*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2*I*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*I*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*I*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-2*I*cos(d*x+c)^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*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+4*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+2*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)))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)/(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))^(3/2)/sin(d*x+c)^2*2^(1/2)","B"
757,1,1147,175,1.690000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(10 i \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) \sin \left(d x +c \right)+10 i \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) \sin \left(d x +c \right)-5 i \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) \sin \left(d x +c \right)+5 i \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) \sin \left(d x +c \right)-5 \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) \sin \left(d x +c \right)-10 \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) \sin \left(d x +c \right)-10 \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) \sin \left(d x +c \right)+9 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-10 i \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) \sin \left(d x +c \right)-6 i \sin \left(d x +c \right) \sqrt{2}-10 i \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) \sin \left(d x +c \right)-2 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+9 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 \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) \sin \left(d x +c \right)+10 \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) \sin \left(d x +c \right)+10 \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) \sin \left(d x +c \right)-8 \cos \left(d x +c \right) \sqrt{2}+6 \sqrt{2}\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{7}{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}{5 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{3}}"," ",0,"-1/5/d*(10*I*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)+10*I*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)-5*I*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*I*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))-5*((-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)-10*((-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)-10*((-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)+9*2^(1/2)*cos(d*x+c)^3-10*I*((-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)-6*I*2^(1/2)*sin(d*x+c)-10*I*((-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)-2*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)-7*cos(d*x+c)^2*2^(1/2)+9*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+5*((-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))*sin(d*x+c)+10*((-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)+10*((-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)-8*cos(d*x+c)*2^(1/2)+6*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","B"
758,1,1042,113,1.615000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(3 i \left(\cos^{2}\left(d x +c \right)\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)+6 i \left(\cos^{2}\left(d x +c \right)\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)+6 i \left(\cos^{2}\left(d x +c \right)\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)-3 i \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 \left(\cos^{2}\left(d x +c \right)\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)+6 \left(\cos^{2}\left(d x +c \right)\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)+3 \left(\cos^{2}\left(d x +c \right)\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)+5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 i \sin \left(d x +c \right) \sqrt{2}-6 i \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 i \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 \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-\cos \left(d x +c \right) \sqrt{2}-6 \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 \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 \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 \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{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)}}\, \sqrt{2}\, a}{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*(3*I*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))+6*I*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)+6*I*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)-3*I*((-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*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)+6*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)+3*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))+5*cos(d*x+c)^2*2^(1/2)-4*I*2^(1/2)*sin(d*x+c)-6*I*((-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*I*((-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)+5*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)-cos(d*x+c)*2^(1/2)-6*((-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*((-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*((-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*2^(1/2))*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)-1)/cos(d*x+c)^2*2^(1/2)*a","B"
759,1,575,85,1.629000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(2 i \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) \sin \left(d x +c \right)+2 i \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) \sin \left(d x +c \right)+i \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) \sin \left(d x +c \right)+i \sin \left(d x +c \right) \sqrt{2}-2 \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) \sin \left(d x +c \right)-2 \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) \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) \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{2}-\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}\, a}{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/d*(2*I*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*I*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*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))+I*2^(1/2)*sin(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)*sin(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)*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))*sin(d*x+c)+cos(d*x+c)*2^(1/2)-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)*a","B"
760,1,571,114,1.633000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2),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 \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-i \sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-2 i \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right)+2 i \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 \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+4 i \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-\sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+\sqrt{2}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-2 \sqrt{2}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right)+4 \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+4 \arctan \left(\sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+2 \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)\right) \sqrt{2}\, a}{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*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-I*2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*I*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)+2*I*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*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+4*I*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2^(1/2)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*2^(1/2)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))+4*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+4*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-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)))/(I*sin(d*x+c)+cos(d*x+c)-1)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)*a","B"
761,1,2091,175,2.063000," ","int((a+I*a*tan(d*x+c))^(3/2)/cot(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/4/d*(-2*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-2*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*I*2^(1/2)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*2^(1/2)*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-6*2^(1/2)*cos(d*x+c)*sin(d*x+c)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))+3*2^(1/2)*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-8*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-8*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+8*cos(d*x+c)*arctan(2^(1/2)*((-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)-3*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2*2^(1/2)+3*I*2^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-6*I*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)^2*2^(1/2)-8*I*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)-8*I*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*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)+3*I*2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-3*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*2^(1/2)+6*I*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)*2^(1/2)+3*2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+8*I*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+8*I*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+4*I*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)^2-8*I*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)-8*I*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)-4*I*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*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)+8*cos(d*x+c)*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+8*cos(d*x+c)*sin(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+3*2^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+6*2^(1/2)*cos(d*x+c)^2*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-3*2^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-3*2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-6*2^(1/2)*cos(d*x+c)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))-2*I*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*2^(1/2)+3*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-3*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)*2^(1/2)+6*I*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-4*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*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)+8*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1))*(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)/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"
762,1,1581,179,1.749000," ","int(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(52 \sqrt{2}-68 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+80 i \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-61 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-84 \left(\cos^{2}\left(d x +c \right)\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)-168 \left(\cos^{2}\left(d x +c \right)\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)-168 \left(\cos^{2}\left(d x +c \right)\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)+84 i \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)+42 i \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)+84 i \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)+42 i \left(\cos^{4}\left(d x +c \right)\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)+84 i \left(\cos^{4}\left(d x +c \right)\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)+84 i \left(\cos^{4}\left(d x +c \right)\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)-168 i \left(\cos^{2}\left(d x +c \right)\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)-168 i \left(\cos^{2}\left(d x +c \right)\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)-84 i \left(\cos^{2}\left(d x +c \right)\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)+52 i \sin \left(d x +c \right) \sqrt{2}+42 \left(\cos^{4}\left(d x +c \right)\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)+84 \left(\cos^{4}\left(d x +c \right)\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)+84 \left(\cos^{4}\left(d x +c \right)\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)-129 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+16 \cos \left(d x +c \right) \sqrt{2}+84 \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)+84 \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)+42 \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)-19 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+80 \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)\right) \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{9}{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)}}\, \sqrt{2}\, a^{2}}{21 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{4}}"," ",0,"-1/21/d*(52*2^(1/2)-19*2^(1/2)*cos(d*x+c)^3-61*I*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)-84*I*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))-168*I*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)-168*I*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)-68*I*cos(d*x+c)*sin(d*x+c)*2^(1/2)-168*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)-168*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)-84*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))+80*2^(1/2)*cos(d*x+c)^4+42*I*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))+84*I*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)+84*I*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)+80*I*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)+84*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)+84*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)+42*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))+52*I*2^(1/2)*sin(d*x+c)+42*I*((-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))+84*I*((-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)+84*I*((-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)+16*cos(d*x+c)*2^(1/2)+84*((-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)+84*((-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)+42*((-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))-129*cos(d*x+c)^2*2^(1/2))*sin(d*x+c)*(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)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^4*2^(1/2)*a^2","B"
763,1,1149,143,1.869000," ","int(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(60 i \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) \sin \left(d x +c \right)+30 i \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) \sin \left(d x +c \right)+60 i \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) \sin \left(d x +c \right)-60 i \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) \sin \left(d x +c \right)-60 \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) \sin \left(d x +c \right)-60 \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) \sin \left(d x +c \right)-30 \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) \sin \left(d x +c \right)-38 i \sin \left(d x +c \right) \sqrt{2}-60 i \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) \sin \left(d x +c \right)-11 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+52 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+52 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-30 i \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) \sin \left(d x +c \right)+60 \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) \sin \left(d x +c \right)+60 \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) \sin \left(d x +c \right)+30 \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) \sin \left(d x +c \right)-41 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-49 \cos \left(d x +c \right) \sqrt{2}+38 \sqrt{2}\right) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{7}{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}}{15 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{3}}"," ",0,"-1/15/d*(60*I*((-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*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)+60*I*((-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*((-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*((-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*((-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*((-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)-38*I*2^(1/2)*sin(d*x+c)-60*I*((-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)-11*I*cos(d*x+c)*sin(d*x+c)*2^(1/2)+52*I*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)+52*2^(1/2)*cos(d*x+c)^3-30*I*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*((-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*((-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*((-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))*sin(d*x+c)-41*cos(d*x+c)^2*2^(1/2)-49*cos(d*x+c)*2^(1/2)+38*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"
764,1,1044,116,1.743000," ","int(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(-6 i \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)+12 i \left(\cos^{2}\left(d x +c \right)\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)+12 i \left(\cos^{2}\left(d x +c \right)\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)-7 i \sin \left(d x +c \right) \sqrt{2}+12 \left(\cos^{2}\left(d x +c \right)\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)+12 \left(\cos^{2}\left(d x +c \right)\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)+6 \left(\cos^{2}\left(d x +c \right)\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)-12 i \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 i \left(\cos^{2}\left(d x +c \right)\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)-12 i \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)+8 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+8 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-\cos \left(d x +c \right) \sqrt{2}-12 \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)-12 \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 \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)-7 \sqrt{2}\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}\, a^{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*(-6*I*((-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))+12*I*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)+12*I*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)-7*I*2^(1/2)*sin(d*x+c)+12*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)+12*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)+6*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))-12*I*((-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*I*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))-12*I*((-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)+8*I*cos(d*x+c)*sin(d*x+c)*2^(1/2)+8*cos(d*x+c)^2*2^(1/2)-cos(d*x+c)*2^(1/2)-12*((-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*((-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*((-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))-7*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"
765,1,888,144,1.675000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(-i \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sqrt{2}+i \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{2}-2 i \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{2}+8 i \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) \sin \left(d x +c \right)+8 i \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) \sin \left(d x +c \right)+4 i \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) \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)}}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \sqrt{2}+\sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \sqrt{2}+2 \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right) \sqrt{2}-8 \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) \sin \left(d x +c \right)-8 \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) \sin \left(d x +c \right)-4 \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) \sin \left(d x +c \right)+2 i \sin \left(d x +c \right) \sqrt{2}+2 \cos \left(d x +c \right) \sqrt{2}-2 \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)}}\, \sqrt{2}\, a^{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*(-I*sin(d*x+c)*((-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)+I*sin(d*x+c)*((-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)-2*I*sin(d*x+c)*((-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)+8*I*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)+8*I*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*I*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))-sin(d*x+c)*((-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)+sin(d*x+c)*((-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)+2*sin(d*x+c)*((-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)-8*((-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)-8*((-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)-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))*sin(d*x+c)+2*I*sin(d*x+c)*2^(1/2)+2*cos(d*x+c)*2^(1/2)-2*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)*2^(1/2)*a^2","B"
766,1,740,144,1.811000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(5 i \sqrt{2}\, \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-5 i \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) \sqrt{2}-2 i \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}-10 i \sqrt{2}\, \cos \left(d x +c \right) \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right)+16 i \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 \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)+16 i \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)-2 i \sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-5 \sqrt{2}\, \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+5 \sqrt{2}\, \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-10 \sqrt{2}\, \cos \left(d x +c \right) \arctan \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\right)+2 \sqrt{2}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+16 \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)+16 \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 \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)\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^{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) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"-1/4/d*(-1+cos(d*x+c))*(5*I*2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-5*I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)-2*I*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)-10*I*cos(d*x+c)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)+16*I*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+8*I*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))+16*I*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-2*I*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-5*2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+5*2^(1/2)*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-10*2^(1/2)*cos(d*x+c)*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))+2*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+16*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+16*cos(d*x+c)*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+8*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)))*(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^2","B"
767,1,2352,175,2.455000," ","int((a+I*a*tan(d*x+c))^(5/2)/cot(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/16/d*(4*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-23*I*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*sin(d*x+c)+46*I*cos(d*x+c)^2*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*sin(d*x+c)+22*I*cos(d*x+c)^2*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-18*I*cos(d*x+c)*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-18*2^(1/2)*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+64*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+64*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+4*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+23*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*sin(d*x+c)-23*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)*sin(d*x+c)-46*cos(d*x+c)^2*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)*sin(d*x+c)-64*I*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)-64*I*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)+23*I*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)*sin(d*x+c)-23*2^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-46*2^(1/2)*cos(d*x+c)^2*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))+23*2^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-4*2^(1/2)*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-22*cos(d*x+c)*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+64*I*cos(d*x+c)^3*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+64*I*cos(d*x+c)^3*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+32*I*cos(d*x+c)^3*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))-32*I*cos(d*x+c)^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))*sin(d*x+c)+23*I*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)-23*I*2^(1/2)*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+46*I*cos(d*x+c)^2*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)-4*I*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-22*cos(d*x+c)^2*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-23*I*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)+23*I*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)-46*I*cos(d*x+c)^3*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)+22*I*cos(d*x+c)^3*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*I*cos(d*x+c)^2*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-22*I*cos(d*x+c)*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-64*I*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-64*I*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-32*I*cos(d*x+c)^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*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-23*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*2^(1/2)+23*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*2^(1/2)+46*cos(d*x+c)^3*arctan(((-1+cos(d*x+c))/sin(d*x+c))^(1/2))*2^(1/2)+64*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)+64*cos(d*x+c)^2*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)+32*cos(d*x+c)^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))*sin(d*x+c)+22*cos(d*x+c)^3*2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-64*cos(d*x+c)^3*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-64*cos(d*x+c)^3*arctan(2^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-32*cos(d*x+c)^3*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))+32*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)*(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^2","B"
768,1,374,144,1.927000," ","int(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(-\frac{1}{6}-\frac{i}{6}\right) \left(3 i \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) \sqrt{2}+3 i \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) \sqrt{2}+3 \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) \sqrt{2}+5 i \left(\cos^{2}\left(d x +c \right)\right)-2 i \cos \left(d x +c \right) \sin \left(d x +c \right)-3 \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)}}\, \sqrt{2}-5 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right)+7-7 i\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)}{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*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)*2^(1/2)+3*I*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)*2^(1/2)+3*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*2^(1/2)+5*I*cos(d*x+c)^2-2*I*cos(d*x+c)*sin(d*x+c)-3*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^(1/2)-5*cos(d*x+c)^2-2*cos(d*x+c)*sin(d*x+c)+7-7*I)*(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))/cos(d*x+c)^2/a","B"
769,1,287,113,1.868000," ","int(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(-\frac{1}{2}-\frac{i}{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)}}\, \left(-i \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) \sqrt{2}+\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) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \left(\cos^{2}\left(d x +c \right)\right)+i \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) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{2}-\left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right) \sin \left(d x +c \right)+3-3 i\right)}{d \cos \left(d x +c \right) a}"," ",0,"(-1/2-1/2*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)*(-I*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))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+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))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*cos(d*x+c)^2+I*sin(d*x+c)*cos(d*x+c)+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^(1/2)-cos(d*x+c)^2+cos(d*x+c)*sin(d*x+c)+3-3*I)/cos(d*x+c)/a","B"
770,1,257,83,1.874000," ","int(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 \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}\, \sin \left(d x +c \right)+i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \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) \sqrt{2}\, \cos \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)-\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) \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*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)+I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*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)*cos(d*x+c)-((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*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))*(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"
771,1,270,85,1.947000," ","int(1/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 \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}\, \sin \left(d x +c \right)-i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \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) \sqrt{2}\, \cos \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}+\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \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{\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}"," ",0,"(-1/2+1/2*I)/d*(I*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)-I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*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)*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)+((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c))*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))/(cos(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","B"
772,1,621,141,1.928000," ","int(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)+i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+i \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}\, \sin \left(d x +c \right)+i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\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}\, \cos \left(d x +c \right)-i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)-i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\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}+\sin \left(d x +c \right) \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) \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) \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) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)-\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \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)}}\, \left(\cos^{2}\left(d x +c \right)\right)}{d \left(i \sin \left(d x +c \right)+\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)^{2} \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a}"," ",0,"(1/2+1/2*I)/d*(-I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)+I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+I*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)+I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+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)-I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)+I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2/(I*sin(d*x+c)+cos(d*x+c))/(cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^2/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/a","B"
773,1,801,172,1.935000," ","int(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(-\frac{1}{4}-\frac{i}{4}\right) \left(2 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+2 i \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}\, \left(\cos^{2}\left(d x +c \right)\right)+i \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)-i \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-2 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-2 i \cos \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}-2 \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) \sqrt{2}+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)}}-\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)-\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)+\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)+\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)+4 \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 \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)}}+\cos \left(d x +c \right) \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) \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) \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) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)-2 \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)}}\, \left(\cos^{2}\left(d x +c \right)\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)}}\, \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{3} a}"," ",0,"(-1/4-1/4*I)/d*(2*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+2*I*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+I*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-I*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-2*I*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-2*I*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)-2*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)+2*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)^2-ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2+ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)^2+4*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)+cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-2*((-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)^2/(I*sin(d*x+c)+cos(d*x+c))/((-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)^3/a","B"
774,1,445,175,2.082000," ","int(cot(d*x+c)^(5/2)/(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{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) \left(-15 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+39 i \sin \left(d x +c \right)-4 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \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) \sqrt{2}-3 i \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) \sqrt{2}+4 \left(\cos^{5}\left(d x +c \right)\right)-4 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)-3 i \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) \sqrt{2}+21 i \cos \left(d x +c \right)-3 \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)}}\, \sqrt{2}+13 \left(\cos^{3}\left(d x +c \right)\right)-15 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-13 i \left(\cos^{3}\left(d x +c \right)\right)-4 i \left(\cos^{5}\left(d x +c \right)\right)-21 \cos \left(d x +c \right)+39 \sin \left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2} a^{2}}"," ",0,"(1/12+1/12*I)/d*(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)*(-15*I*cos(d*x+c)^2*sin(d*x+c)+39*I*sin(d*x+c)-4*I*cos(d*x+c)^4*sin(d*x+c)+3*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*2^(1/2)-3*I*((-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)*sin(d*x+c)*2^(1/2)+4*cos(d*x+c)^5-4*cos(d*x+c)^4*sin(d*x+c)-3*I*((-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))*sin(d*x+c)*2^(1/2)+21*I*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))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)+13*cos(d*x+c)^3-15*cos(d*x+c)^2*sin(d*x+c)-13*I*cos(d*x+c)^3-4*I*cos(d*x+c)^5-21*cos(d*x+c)+39*sin(d*x+c))/cos(d*x+c)^2/a^2","B"
775,1,344,144,1.783000," ","int(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(\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) \left(4 i \left(\cos^{4}\left(d x +c \right)\right)+4 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-3 i \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) \sqrt{2}-4 \left(\cos^{4}\left(d x +c \right)\right)+4 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \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) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+9 i \left(\cos^{2}\left(d x +c \right)\right)+11 i \cos \left(d x +c \right) \sin \left(d x +c \right)+3 \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)}}\, \sqrt{2}-9 \left(\cos^{2}\left(d x +c \right)\right)+11 \cos \left(d x +c \right) \sin \left(d x +c \right)+25-25 i\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)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)*(4*I*cos(d*x+c)^4+4*I*cos(d*x+c)^3*sin(d*x+c)-3*I*((-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))*sin(d*x+c)*2^(1/2)-4*cos(d*x+c)^4+4*cos(d*x+c)^3*sin(d*x+c)+3*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))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+9*I*cos(d*x+c)^2+11*I*sin(d*x+c)*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))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2)-9*cos(d*x+c)^2+11*cos(d*x+c)*sin(d*x+c)+25-25*I)/cos(d*x+c)/a^2","B"
776,1,468,114,2.012000," ","int(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(6 i \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) \sqrt{2}+7 i \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 \left(\cos^{2}\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}+9 i \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 \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}\, \sin \left(d x +c \right)+7 \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 \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 \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}\, \cos \left(d x +c \right)-7 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 \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 \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*(6*I*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)+7*I*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+6*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)+9*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)+7*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-9*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*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)-7*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-7*((-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"
777,1,482,115,3.869000," ","int(1/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(6 i \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}\, \left(\cos^{2}\left(d x +c \right)\right)+3 i \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 \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) \sqrt{2}-i \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 \cos \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}+3 \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 \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 \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)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \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)}}\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) \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^{2}}"," ",0,"(1/12+1/12*I)/d*(6*I*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+3*I*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)-6*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)-I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-3*I*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)+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*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*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*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*((-1+cos(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*(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)/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^2","B"
778,1,484,115,2.163000," ","int(1/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(-6 i \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) \sqrt{2}+5 i \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 \left(\cos^{2}\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}+3 i \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 \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}\, \sin \left(d x +c \right)+5 \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 \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 \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}\, \cos \left(d x +c \right)-5 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+3 \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}-5 \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{\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*2^(1/2)*cos(d*x+c)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*sin(d*x+c)+5*I*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*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)+3*I*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+3*I*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)+5*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*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)-5*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)-5*((-1+cos(d*x+c))/sin(d*x+c))^(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"
779,1,1111,172,2.255000," ","int(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(-\frac{1}{12}-\frac{i}{12}\right) \left(-12 i \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-12 i \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+12 i \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)+12 i \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-3 i \cos \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}-6 \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) \sqrt{2}-9 i \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 i \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}\, \left(\cos^{2}\left(d x +c \right)\right)+3 \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 \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)-9 \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 \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+6 \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+11 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+11 i \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 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-11 \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 \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-6 \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-6 \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)+6 \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)-6 i \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 \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 \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 \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 \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+12 \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 \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 \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 \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)\right) \left(\cos^{3}\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{5}{2}} \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"(-1/12-1/12*I)/d*(3*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*2^(1/2)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))-11*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*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)+12*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)*sin(d*x+c)-12*I*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+12*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)*sin(d*x+c)-12*I*cos(d*x+c)*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-9*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+6*I*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)^2-3*I*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)+6*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-6*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-11*cos(d*x+c)^2*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+12*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)^2+12*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2-12*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2-12*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)^2-6*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-6*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+6*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+6*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)+11*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-9*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+6*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-6*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+11*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-6*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*sin(d*x+c)+6*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*sin(d*x+c)-6*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*sin(d*x+c)+6*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*sin(d*x+c))*cos(d*x+c)^3*(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))^(5/2)/sin(d*x+c)^3/a^2","B"
780,1,1265,202,2.520000," ","int(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(-\frac{1}{12}-\frac{i}{12}\right) \left(6 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \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}\, \cos \left(d x +c \right)-27 i \sqrt{\frac{-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)-3 \left(\cos^{2}\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}-9 i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+9 i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+9 i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-3 i \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) \sqrt{2}+6 i \sqrt{2}\, \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)-9 i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-9 i \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)-18 i \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-18 i \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+9 i \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)-29 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+18 i \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+18 i \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-9 i \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)+9 i \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+6 \sqrt{2}\, \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)+18 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)-18 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-18 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+18 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+27 \sqrt{\frac{-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)+29 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)-9 \sin \left(d x +c \right) \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)+9 \sin \left(d x +c \right) \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)+9 \sin \left(d x +c \right) \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)-9 \sin \left(d x +c \right) \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)-29 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-6 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+29 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)\right) \left(\cos^{3}\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{7}{2}} \sin \left(d x +c \right)^{4} a^{2}}"," ",0,"(-1/12-1/12*I)/d*(-3*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)-27*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+6*I*2^(1/2)*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))-3*I*2^(1/2)*sin(d*x+c)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*cos(d*x+c)+6*2^(1/2)*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))-18*cos(d*x+c)^2*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+18*cos(d*x+c)^2*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-18*cos(d*x+c)^2*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)+18*cos(d*x+c)^2*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+27*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+9*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)-9*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)+9*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)-9*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)-9*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)+9*I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-9*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)+9*I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+29*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+6*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+18*I*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-18*I*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)+18*I*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-18*I*cos(d*x+c)^3*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-29*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-9*I*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+9*I*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-9*I*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)+9*I*cos(d*x+c)^2*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-3*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)-6*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-29*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+29*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c))*cos(d*x+c)^3*(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))^(7/2)/sin(d*x+c)^4/a^2","B"
781,1,499,205,2.639000," ","int(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-\frac{1}{120}-\frac{i}{120}\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) \left(48 i \left(\cos^{7}\left(d x +c \right)\right)+267 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-48 \left(\cos^{7}\left(d x +c \right)\right)+48 \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)-707 i \sin \left(d x +c \right)+48 i \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)+48 i \left(\cos^{5}\left(d x +c \right)\right)+15 i \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) \sqrt{2}-48 \left(\cos^{5}\left(d x +c \right)\right)+72 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)-15 \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) \sqrt{2}+72 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)-361 i \cos \left(d x +c \right)-225 \left(\cos^{3}\left(d x +c \right)\right)+267 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 \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)}}\, \sqrt{2}+225 i \left(\cos^{3}\left(d x +c \right)\right)+15 i \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) \sqrt{2}+361 \cos \left(d x +c \right)-707 \sin \left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2} a^{3}}"," ",0,"(-1/120-1/120*I)/d*(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)*(48*I*cos(d*x+c)^7+267*I*cos(d*x+c)^2*sin(d*x+c)-48*cos(d*x+c)^7+48*cos(d*x+c)^6*sin(d*x+c)-707*I*sin(d*x+c)+48*I*cos(d*x+c)^6*sin(d*x+c)+48*I*cos(d*x+c)^5+15*I*cos(d*x+c)*sin(d*x+c)*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))-48*cos(d*x+c)^5+72*cos(d*x+c)^4*sin(d*x+c)-15*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*2^(1/2)+72*I*cos(d*x+c)^4*sin(d*x+c)-361*I*cos(d*x+c)-225*cos(d*x+c)^3+267*cos(d*x+c)^2*sin(d*x+c)+15*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^(1/2)+225*I*cos(d*x+c)^3+15*I*sin(d*x+c)*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))+361*cos(d*x+c)-707*sin(d*x+c))/cos(d*x+c)^2/a^3","B"
782,1,398,174,2.339000," ","int(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) \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(151 i \cos \left(d x +c \right) \sin \left(d x +c \right)+32 i \left(\cos^{4}\left(d x +c \right)\right)-48 \left(\cos^{6}\left(d x +c \right)\right)+48 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+48 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+48 i \left(\cos^{6}\left(d x +c \right)\right)-15 i \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) \sqrt{2}+15 \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) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-32 \left(\cos^{4}\left(d x +c \right)\right)+56 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 \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)}}\, \sqrt{2}+117 i \left(\cos^{2}\left(d x +c \right)\right)+56 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-117 \left(\cos^{2}\left(d x +c \right)\right)+151 \cos \left(d x +c \right) \sin \left(d x +c \right)+317-317 i\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)*(151*I*sin(d*x+c)*cos(d*x+c)+32*I*cos(d*x+c)^4-48*cos(d*x+c)^6+48*cos(d*x+c)^5*sin(d*x+c)+48*I*cos(d*x+c)^5*sin(d*x+c)+48*I*cos(d*x+c)^6-15*I*2^(1/2)*sin(d*x+c)*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+15*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))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-32*cos(d*x+c)^4+56*cos(d*x+c)^3*sin(d*x+c)+15*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^(1/2)+117*I*cos(d*x+c)^2+56*I*cos(d*x+c)^3*sin(d*x+c)-117*cos(d*x+c)^2+151*cos(d*x+c)*sin(d*x+c)+317-317*I)/cos(d*x+c)/a^3","B"
783,1,644,144,3.610000," ","int(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(60 i \sqrt{2}\, \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)+160 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+172 i \sqrt{\frac{-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)-30 i \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) \sqrt{2}+60 \sqrt{2}\, \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)-15 i \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}\, \sin \left(d x +c \right)+160 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-172 \sqrt{\frac{-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)-30 \left(\cos^{2}\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}-160 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)-67 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-45 \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}\, \cos \left(d x +c \right)-160 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)+67 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+15 \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) \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*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)+160*I*cos(d*x+c)^3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+172*I*cos(d*x+c)^2*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-30*I*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)+60*2^(1/2)*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))-15*I*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)+160*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-172*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-30*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)-160*I*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-67*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-45*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)-160*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+67*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+15*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)/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"
784,1,544,147,3.622000," ","int(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(\frac{1}{40}-\frac{i}{40}\right) \left(-20 i \sqrt{2}\, \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)+4 i \sqrt{\frac{-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)+10 i \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) \sqrt{2}-20 \sqrt{2}\, \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)-4 \sqrt{\frac{-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)+5 i \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}\, \sin \left(d x +c \right)+10 \left(\cos^{2}\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}+i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+15 \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}\, \cos \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)-5 \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) \sqrt{\frac{\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) a^{3}}"," ",0,"(1/40-1/40*I)/d*(-20*I*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*sin(d*x+c)+4*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+10*I*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)*sin(d*x+c)-20*2^(1/2)*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))-4*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+5*I*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)+10*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)+I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+15*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)-((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-5*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)*(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))^(1/2)/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/sin(d*x+c)/a^3","B"
785,1,660,145,3.319000," ","int(1/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(60 i \sqrt{2}\, \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)-28 i \sqrt{\frac{-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)-30 i \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) \sqrt{2}+60 \sqrt{2}\, \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)-40 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+28 \sqrt{\frac{-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)-15 i \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}\, \sin \left(d x +c \right)-40 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-30 \left(\cos^{2}\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}+13 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-45 \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}\, \cos \left(d x +c \right)+40 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)-13 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+40 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)+15 \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) \sin \left(d x +c \right)^{2} \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}} a^{3}}"," ",0,"(1/120+1/120*I)/d*(60*I*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)-28*I*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-30*I*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)+60*2^(1/2)*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))-40*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+28*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-15*I*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)-40*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-30*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)+13*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-45*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)+40*I*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-13*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+40*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)+15*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*(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)^2/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/(cos(d*x+c)/sin(d*x+c))^(3/2)/a^3","B"
786,1,661,146,3.295000," ","int(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-\frac{1}{120}-\frac{i}{120}\right) \left(60 i \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}\, \left(\cos^{3}\left(d x +c \right)\right)+52 i \sqrt{\frac{-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)-40 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-30 i \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}\, \left(\cos^{2}\left(d x +c \right)\right)-60 \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}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+52 \sqrt{\frac{-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)+40 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-45 i \cos \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 \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) \sqrt{2}-37 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+40 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)+15 i \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 \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)-37 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-40 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)\right) \left(\cos^{3}\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)}}\, \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{3} a^{3}}"," ",0,"(-1/120-1/120*I)/d*(60*I*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+52*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-40*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-30*I*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)^2-60*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*sin(d*x+c)+52*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+40*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-45*I*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)+30*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)-37*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+40*I*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+15*I*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+15*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*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-40*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c))*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))/((-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)^3/a^3","B"
787,1,1578,202,3.216000," ","int(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-\frac{1}{40}-\frac{i}{40}\right) \left(-5 i \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}\, \sin \left(d x +c \right)-49 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-15 \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}\, \cos \left(d x +c \right)+84 i \sqrt{\frac{-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)-10 \left(\cos^{2}\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}+60 i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+60 i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-60 i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)-60 i \cos \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-10 i \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) \sqrt{2}-20 \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)+20 \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+20 i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+40 i \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)-80 i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right) \left(\cos^{3}\left(d x +c \right)\right)+80 i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right) \left(\cos^{3}\left(d x +c \right)\right)+80 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+20 i \sqrt{2}\, \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)+80 i \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)-40 i \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+80 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-80 i \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)+40 i \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-40 i \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+20 \sqrt{2}\, \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)-80 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-i\right)+80 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)-80 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-84 \sqrt{\frac{-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)-80 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)+40 \sin \left(d x +c \right) \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)-40 \sin \left(d x +c \right) \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)-40 \sin \left(d x +c \right) \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)+40 \sin \left(d x +c \right) \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)-20 i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+i\right)+20 i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)-20 \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+20 \sin \left(d x +c \right) \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}-1\right)+80 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+5 \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}-20 i \ln \left(\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}+1\right)+49 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-80 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \cos \left(d x +c \right)\right) \left(\cos^{4}\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) \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{4} \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a^{3}}"," ",0,"(-1/40-1/40*I)/d*(80*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-5*I*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)+84*I*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*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)-80*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^3-80*I*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-49*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+80*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)^3-80*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)^3+80*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^3+40*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)^2-40*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)^2+40*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)^2-40*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)^2+60*I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-60*I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)+60*I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-60*I*cos(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+20*2^(1/2)*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))+80*cos(d*x+c)^2*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)-80*cos(d*x+c)^2*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)+80*cos(d*x+c)^2*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)-80*cos(d*x+c)^2*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-84*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-40*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)*cos(d*x+c)+40*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)*cos(d*x+c)-40*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)*cos(d*x+c)+40*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)*cos(d*x+c)+20*I*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)*cos(d*x+c)^2-10*I*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)-10*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)-20*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+20*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)-20*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)+20*sin(d*x+c)*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-20*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+1)+20*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-I)-20*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I)+20*I*ln(((-1+cos(d*x+c))/sin(d*x+c))^(1/2)-1)+49*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+5*arctan((1/2+1/2*I)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*2^(1/2))*2^(1/2)+80*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-80*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c))*cos(d*x+c)^4*(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))^(7/2)/sin(d*x+c)^4/((-1+cos(d*x+c))/sin(d*x+c))^(1/2)/a^3","B"
788,0,0,133,1.523000," ","int((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x)","F"
789,0,0,73,1.841000," ","int((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x)","F"
790,0,0,37,1.550000," ","int((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e)),x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e)),x)","F"
791,0,0,145,2.236000," ","int((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","\int \frac{\left(d \cot \left(f x +e \right)\right)^{n}}{a +i a \tan \left(f x +e \right)}\, dx"," ",0,"int((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","F"
792,0,0,186,2.212000," ","int((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","\int \frac{\left(d \cot \left(f x +e \right)\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","F"
793,0,0,91,2.307000," ","int((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x)","F"
794,0,0,69,1.255000," ","int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n,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}\, dx"," ",0,"int(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n,x)","F"
795,0,0,69,1.254000," ","int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n,x)","\int \left(\sqrt{\cot}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n,x)","F"
796,0,0,69,1.322000," ","int((a+I*a*tan(d*x+c))^n/cot(d*x+c)^(1/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n}}{\sqrt{\cot \left(d x +c \right)}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n/cot(d*x+c)^(1/2),x)","F"
797,0,0,69,1.235000," ","int((a+I*a*tan(d*x+c))^n/cot(d*x+c)^(3/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n}}{\cot \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n/cot(d*x+c)^(3/2),x)","F"
798,1,4249,164,1.166000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/30/d*(30*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b-15*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+10*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)*b-15*I*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+15*I*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+15*I*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-15*I*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-15*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+15*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+15*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-15*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-15*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-15*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-30*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b+15*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+15*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+15*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+15*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+15*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-15*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-15*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+15*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-15*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-15*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-15*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-15*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+30*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b-15*cos(d*x+c)^3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-30*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b+15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+36*2^(1/2)*cos(d*x+c)^3*a-30*2^(1/2)*cos(d*x+c)*a+15*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-15*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-15*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+15*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b)*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(7/2)/cos(d*x+c)^4*2^(1/2)","C"
799,1,2217,150,1.167000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/6/d*(-3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+3*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+3*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+3*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-6*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a-3*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+3*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-6*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a+2*cos(d*x+c)^2*2^(1/2)*a+6*cos(d*x+c)*sin(d*x+c)*2^(1/2)*b)*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(5/2)/cos(d*x+c)^3*2^(1/2)","C"
800,1,2089,136,1.064000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/2/d*(I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+2*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b+2*2^(1/2)*cos(d*x+c)*a)*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(3/2)/cos(d*x+c)^2*2^(1/2)","C"
801,1,482,122,1.166000," ","int(cot(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)}}\, \left(-1+\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{-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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -2 a \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b +\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b \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/d*(cos(d*x+c)/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-2*a*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b)/sin(d*x+c)^2/cos(d*x+c)*(1+cos(d*x+c))^2*2^(1/2)","C"
802,1,1112,136,1.127000," ","int((a+b*tan(d*x+c))/cot(d*x+c)^(1/2),x)","\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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{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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +\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)}{\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{1-\cos \left(d x +c \right)+\sin \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{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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +\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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -2 \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, b +2 \cos \left(d x +c \right) \sqrt{2}\, b -2 b \sqrt{2}\right) \sqrt{2}}{2 d \sin \left(d x +c \right)^{4} \sqrt{\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"1/2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*a-I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*b-I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*a+I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*b+sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-2*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*b+2*cos(d*x+c)*2^(1/2)*b-2*b*2^(1/2))/sin(d*x+c)^4/(cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
803,1,1208,150,1.049000," ","int((a+b*tan(d*x+c))/cot(d*x+c)^(3/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(3 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +3 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -3 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -3 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b +3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -6 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) a +3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b +6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, a +2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, b -6 \sqrt{2}\, \cos \left(d x +c \right) a -2 \sin \left(d x +c \right) \sqrt{2}\, b \right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{6 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,"1/6/d*(-1+cos(d*x+c))*(3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+3*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-3*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-6*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a+3*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-3*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+6*cos(d*x+c)^2*2^(1/2)*a+2*cos(d*x+c)*sin(d*x+c)*2^(1/2)*b-6*2^(1/2)*cos(d*x+c)*a-2*sin(d*x+c)*2^(1/2)*b)*(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"
804,1,1254,164,1.250000," ","int((a+b*tan(d*x+c))/cot(d*x+c)^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(15 i \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -15 i \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -15 i \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +15 i \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -30 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) b +15 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +15 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b +15 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +15 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b +36 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) b -10 \sin \left(d x +c \right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) a -36 \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) b +10 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, a -6 \cos \left(d x +c \right) \sqrt{2}\, b +6 b \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{30 d \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{6}}"," ",0,"-1/30/d*(-1+cos(d*x+c))*(15*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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-15*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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-15*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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+15*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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-30*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b+15*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+15*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+15*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+15*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+36*2^(1/2)*cos(d*x+c)^3*b-10*sin(d*x+c)*2^(1/2)*cos(d*x+c)^2*a-36*2^(1/2)*cos(d*x+c)^2*b+10*cos(d*x+c)*sin(d*x+c)*2^(1/2)*a-6*cos(d*x+c)*2^(1/2)*b+6*b*2^(1/2))*(1+cos(d*x+c))^2/(cos(d*x+c)/sin(d*x+c))^(5/2)/sin(d*x+c)^6*2^(1/2)","C"
805,1,7045,226,1.568000," ","int(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
806,1,6224,211,1.426000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
807,1,3456,189,1.369000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"-1/6/d*(-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*b^2-3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*a*b-6*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*a*b-6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*a*b-6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*a*b+3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a^2+6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b^2+3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*a^2+2*2^(1/2)*cos(d*x+c)^2*a^2+3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*a^2-3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*b^2-3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*a^2+3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*b^2-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*b^2-6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a^2+6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b^2+3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*a^2+6*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*2^(1/2)*cos(d*x+c)*sin(d*x+c)*a*b)*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(5/2)/cos(d*x+c)^3*2^(1/2)","C"
808,1,3037,174,1.329000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"-1/2/d*(-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+2*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b-2*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+2*2^(1/2)*cos(d*x+c)*a^2+4*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a*b-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2+2*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2-2*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2+cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2+cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2-2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b-2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b-2*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b-2*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b+4*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a*b)*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(3/2)/cos(d*x+c)^2*2^(1/2)","C"
809,1,1729,174,1.379000," ","int(cot(d*x+c)^(1/2)*(a+b*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(-2 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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) \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a b +i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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^{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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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^{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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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) \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, a b -i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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^{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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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^{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{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)}{\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{1-\cos \left(d x +c \right)+\sin \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^{2}-2 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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 b -\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)}{\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{1-\cos \left(d x +c \right)+\sin \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^{2}+\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)}{\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{1-\cos \left(d x +c \right)+\sin \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^{2}-2 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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 b -\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)}{\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{1-\cos \left(d x +c \right)+\sin \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^{2}-2 \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)}{\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) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) a^{2}+2 \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)}{\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) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) b^{2}-2 \sqrt{2}\, \cos \left(d x +c \right) b^{2}+2 \sqrt{2}\, b^{2}\right) \sqrt{2}}{2 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{3}}"," ",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))*(-2*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*a*b+2*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*a*b-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*a^2-2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*a*b-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*b^2+((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*a^2-2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*a*b-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*b^2-2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a^2+2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b^2-2*2^(1/2)*cos(d*x+c)*b^2+2*2^(1/2)*b^2)/cos(d*x+c)/sin(d*x+c)^3*2^(1/2)","C"
810,1,1733,189,1.352000," ","int((a+b*tan(d*x+c))^2/cot(d*x+c)^(1/2),x)","\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(6 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) a b +3 i a^{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{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) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \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^{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{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) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i b^{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{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) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i b^{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{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) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) a b +3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) a^{2}+6 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) a b -3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) b^{2}+3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) a^{2}+6 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) a b -3 \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)}{\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{1-\cos \left(d x +c \right)+\sin \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) b^{2}-12 \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{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) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) a b +12 \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) a b +2 \sqrt{2}\, b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)-12 \sqrt{2}\, \cos \left(d x +c \right) a b -2 \sqrt{2}\, b^{2} \sin \left(d x +c \right)\right) \sqrt{2}}{6 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,"1/6/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(-3*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-6*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+6*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2-12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a*b+12*2^(1/2)*cos(d*x+c)^2*a*b+2*2^(1/2)*b^2*cos(d*x+c)*sin(d*x+c)-12*2^(1/2)*cos(d*x+c)*a*b-2*2^(1/2)*b^2*sin(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"
811,1,1947,211,1.286000," ","int((a+b*tan(d*x+c))^2/cot(d*x+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/30/d*(-1+cos(d*x+c))*(30*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b+15*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-30*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b+15*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2-30*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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-15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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+15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2-30*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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-15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2-30*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a^2+30*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b^2+30*2^(1/2)*cos(d*x+c)^3*a^2-36*2^(1/2)*cos(d*x+c)^3*b^2+20*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b-30*2^(1/2)*cos(d*x+c)^2*a^2+36*2^(1/2)*cos(d*x+c)^2*b^2-20*2^(1/2)*cos(d*x+c)*sin(d*x+c)*a*b+6*2^(1/2)*cos(d*x+c)*b^2-6*2^(1/2)*b^2)*(1+cos(d*x+c))^2/(cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^5/cos(d*x+c)*2^(1/2)","C"
812,1,1877,226,1.421000," ","int((a+b*tan(d*x+c))^2/cot(d*x+c)^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-105 i \sin \left(d x +c \right) a^{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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-105 i \sin \left(d x +c \right) b^{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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+105 i \sin \left(d x +c \right) a^{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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+210 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a b -210 i \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a b +105 i \sin \left(d x +c \right) b^{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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-420 \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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) a b +105 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2}+210 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a b -105 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{2}+105 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2}+210 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a b -105 \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)}{\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{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{2}+504 \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right) a b -70 \sin \left(d x +c \right) \sqrt{2}\, a^{2} \left(\cos^{3}\left(d x +c \right)\right)+100 \sin \left(d x +c \right) \sqrt{2}\, b^{2} \left(\cos^{3}\left(d x +c \right)\right)-504 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) a b +70 \sin \left(d x +c \right) \sqrt{2}\, a^{2} \left(\cos^{2}\left(d x +c \right)\right)-100 \sin \left(d x +c \right) \sqrt{2}\, b^{2} \left(\cos^{2}\left(d x +c \right)\right)-84 \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) a b -30 \sqrt{2}\, b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)+84 \sqrt{2}\, \cos \left(d x +c \right) a b +30 \sqrt{2}\, b^{2} \sin \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{210 d \left(\frac{\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{6} \cos \left(d x +c \right)}"," ",0,"-1/210/d*(-1+cos(d*x+c))*(105*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-210*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a*b+105*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+210*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a*b-105*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-105*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-420*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a*b+105*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a^2+210*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a*b-105*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*b^2+105*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a^2+210*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a*b-105*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*b^2+504*2^(1/2)*cos(d*x+c)^4*a*b-70*sin(d*x+c)*2^(1/2)*a^2*cos(d*x+c)^3+100*sin(d*x+c)*2^(1/2)*b^2*cos(d*x+c)^3-504*2^(1/2)*cos(d*x+c)^3*a*b+70*sin(d*x+c)*2^(1/2)*a^2*cos(d*x+c)^2-100*sin(d*x+c)*2^(1/2)*b^2*cos(d*x+c)^2-84*2^(1/2)*cos(d*x+c)^2*a*b-30*2^(1/2)*b^2*cos(d*x+c)*sin(d*x+c)+84*2^(1/2)*cos(d*x+c)*a*b+30*2^(1/2)*b^2*sin(d*x+c))*(1+cos(d*x+c))^2/(cos(d*x+c)/sin(d*x+c))^(5/2)/sin(d*x+c)^6/cos(d*x+c)*2^(1/2)","C"
813,1,9129,257,1.655000," ","int(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
814,1,8630,232,1.530000," ","int(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"
815,1,4456,209,1.487000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"1/6/d*(-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*b^3-3*I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3-3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3+3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3+9*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*b-9*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*b^2-9*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b+9*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2-18*2^(1/2)*cos(d*x+c)*sin(d*x+c)*a^2*b+3*I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3+6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)*a^3+3*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3-3*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3-3*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3+3*I*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3-2*2^(1/2)*cos(d*x+c)^2*a^3-3*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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)*a^3-3*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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)*b^3-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^3-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^3+6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^3+9*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*a^2*b+9*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*a*b^2+9*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*a^2*b+9*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*a*b^2-18*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)*a*b^2-3*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*a^3-3*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*b^3-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*a^3+9*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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)*a*b^2+9*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*b+9*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2-18*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^2+9*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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)*a^2*b+9*I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*b-9*I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*b^2-9*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b+9*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2)*sin(d*x+c)*(cos(d*x+c)/sin(d*x+c))^(5/2)/cos(d*x+c)^3*2^(1/2)","C"
816,1,4227,213,1.442000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"-1/2/d*(3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3-2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b^3-3*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*b-3*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*b^2+3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b+3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*a^3-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*b^3+I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3+I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3+3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*a*b^2-3*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*b^2-3*I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^2*b+3*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*a^2*b-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b+3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2+6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a^2*b-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*a^3+((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*b^3-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*a^3+((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*b^3-2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*b^3-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^(1/2)*b^3-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*a^2*b+3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*a*b^2+6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*a^2*b+2*cos(d*x+c)*2^(1/2)*a^3-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3+I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3+I*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*a^2*b+3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*a*b^2)*(cos(d*x+c)/sin(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)^2*2^(1/2)","C"
817,1,2370,209,1.524000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"1/6/d*(-1+cos(d*x+c))*(3*I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3+9*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2-3*I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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^3+9*I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*b-3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3-9*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b+3*I*cos(d*x+c)*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3-9*I*cos(d*x+c)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*b^2-3*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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)*a^3+9*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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)*a^2*b+9*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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)*a*b^2-3*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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)*b^3+6*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a^3-18*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^2-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^3+9*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*b+9*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2-3*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^3+18*2^(1/2)*cos(d*x+c)^2*a*b^2+2*2^(1/2)*cos(d*x+c)*sin(d*x+c)*b^3-18*cos(d*x+c)*2^(1/2)*a*b^2-2*sin(d*x+c)*2^(1/2)*b^3)*(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"
818,1,2472,234,1.516000," ","int((a+b*tan(d*x+c))^3/cot(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/10/d*(-1+cos(d*x+c))*(10*sin(d*x+c)*b^2*cos(d*x+c)^2*2^(1/2)*a-10*cos(d*x+c)*sin(d*x+c)*b^2*2^(1/2)*a+30*cos(d*x+c)^3*2^(1/2)*a^2*b-30*cos(d*x+c)^2*2^(1/2)*a^2*b-30*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*b+5*I*sin(d*x+c)*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*I*sin(d*x+c)*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*I*sin(d*x+c)*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*I*sin(d*x+c)*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*b^3*2^(1/2)-12*b^3*cos(d*x+c)^3*2^(1/2)+12*b^3*cos(d*x+c)^2*2^(1/2)+2*cos(d*x+c)*b^3*2^(1/2)+10*sin(d*x+c)*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+5*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*a^3-5*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*b^3+5*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^3-5*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-15*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+15*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))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*a^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+15*I*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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+15*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*a^2*b-15*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*a*b^2+15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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-15*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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)*(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"
819,1,2562,257,1.536000," ","int((a+b*tan(d*x+c))^3/cot(d*x+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/210/d*(-1+cos(d*x+c))*(-100*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)*b^3-756*cos(d*x+c)^3*2^(1/2)*a*b^2+126*cos(d*x+c)*2^(1/2)*a*b^2+756*2^(1/2)*cos(d*x+c)^4*a*b^2+100*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)*b^3-126*2^(1/2)*cos(d*x+c)^2*a*b^2-30*2^(1/2)*cos(d*x+c)*sin(d*x+c)*b^3+210*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*a^2*b-210*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)*a^2*b-105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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^3+105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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^3+105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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^3-210*2^(1/2)*cos(d*x+c)^4*a^3+30*sin(d*x+c)*2^(1/2)*b^3-105*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*a^3-105*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*b^3-105*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a^3-105*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*b^3+210*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a^3+210*cos(d*x+c)^3*2^(1/2)*a^3-105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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^3+315*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*a^2*b+315*EllipticPi(((1-cos(d*x+c)+sin(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))/sin(d*x+c))^(1/2)*((-1+cos(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*sin(d*x+c)*a*b^2+315*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a^2*b+315*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a*b^2-630*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a*b^2+315*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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*b-315*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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*b^2-315*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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*b+315*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(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*b^2)*(1+cos(d*x+c))^2/cos(d*x+c)^2/sin(d*x+c)^5/(cos(d*x+c)/sin(d*x+c))^(3/2)*2^(1/2)","C"
820,1,11153,227,2.304000," ","int(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"
821,1,10187,210,1.906000," ","int(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"
822,1,2238,194,2.019000," ","int(cot(d*x+c)^(1/2)/(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))*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*a*b^3-(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b-2*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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+I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^4-I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^4-I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2+2*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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+2*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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+3*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3*b+3*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b^2+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^3+3*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3*b+3*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b^2+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^3-4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*a^3*b-4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*a^2*b^2+I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3*b-I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b-I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3*b-I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^3+I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b^2-2*EllipticPi(((1-cos(d*x+c)+sin(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^2-2*EllipticPi(((1-cos(d*x+c)+sin(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^4+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(3/2)*a^2+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(3/2)*b^2+I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^3+I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*a^4-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2+b^2)^(1/2)*b^4-(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2-(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^4+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^4+2*EllipticPi(((1-cos(d*x+c)+sin(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^2+2*EllipticPi(((1-cos(d*x+c)+sin(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^4)*(1+cos(d*x+c))^2/cos(d*x+c)/sin(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"
823,1,1859,194,1.480000," ","int(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x)","-\frac{\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{1-\cos \left(d x +c \right)+\sin \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 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a}{a +b +\sqrt{a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{2} \sqrt{a^{2}+b^{2}}\, a -2 a^{2} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a}{-b +\sqrt{a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) b \sqrt{a^{2}+b^{2}}+2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a}{-b +\sqrt{a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) b^{2} \sqrt{a^{2}+b^{2}}\, a -2 a^{2} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a}{a +b +\sqrt{a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b \sqrt{a^{2}+b^{2}}+\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2} b -\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a \,b^{2}+\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2} b -\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a \,b^{2}-i \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -i \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -\left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +\left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -\left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +\left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b +\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{3}-\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{3}+\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{3}+3 i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2} b +3 i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a \,b^{2}-3 i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2} b -3 i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a \,b^{2}-i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{3}-i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{3}+i \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +i \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b +i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{3}+i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{3}+2 a^{3} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a}{a +b +\sqrt{a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b +2 a \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a}{a +b +\sqrt{a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{3}-2 a^{3} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a}{-b +\sqrt{a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) b -2 a \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a}{-b +\sqrt{a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) b^{3}-\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{3}\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)}}\, \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \left(a +b +\sqrt{a^{2}+b^{2}}\right) \left(-b +\sqrt{a^{2}+b^{2}}-a \right)}"," ",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)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(-(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3-(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3-(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3+2*a^3*EllipticPi(((1-cos(d*x+c)+sin(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*a*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3-2*a^3*EllipticPi(((1-cos(d*x+c)+sin(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*a*EllipticPi(((1-cos(d*x+c)+sin(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+2*EllipticPi(((1-cos(d*x+c)+sin(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*(a^2+b^2)^(1/2)*a-2*a^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b*(a^2+b^2)^(1/2)+2*EllipticPi(((1-cos(d*x+c)+sin(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*(a^2+b^2)^(1/2)*a+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2-I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3-I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3+I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3+I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3-2*a^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*b*(a^2+b^2)^(1/2)+3*I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2)/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"
824,1,1867,194,1.427000," ","int(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x)","-\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(2 \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a}{-b +\sqrt{a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) a^{3}-2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a}{a +b +\sqrt{a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) a^{2} b^{2}+2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a}{-b +\sqrt{a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) a^{2} b^{2}+2 \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a}{a +b +\sqrt{a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) a^{3}-2 a^{2} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a}{-b +\sqrt{a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) b \sqrt{a^{2}+b^{2}}-2 a^{2} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a}{a +b +\sqrt{a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b \sqrt{a^{2}+b^{2}}+3 \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2} b +3 \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a \,b^{2}+3 \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2} b +3 \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a \,b^{2}+i \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -i \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -\left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -\left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -\left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -\left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b +\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{3}+\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{3}+\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{3}-i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2} b +i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a \,b^{2}+i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2} b -i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a \,b^{2}+i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{3}-i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{3}-i \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +i \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{3}+i \sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{3}-2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a}{a +b +\sqrt{a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) a^{4}+2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a}{-b +\sqrt{a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) a^{4}+\sqrt{a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{3}\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{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) \left(-1+\cos \left(d x +c \right)\right) \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)^{4} \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \left(a +b +\sqrt{a^{2}+b^{2}}\right) \left(-b +\sqrt{a^{2}+b^{2}}-a \right)}"," ",0,"-1/2/d*(1+cos(d*x+c))^2*(I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3-I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3+I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+2*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^3-2*EllipticPi(((1-cos(d*x+c)+sin(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*EllipticPi(((1-cos(d*x+c)+sin(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+2*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(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-(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3+(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3-2*a^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-a/(-b+(a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b*(a^2+b^2)^(1/2)+3*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b+3*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2+3*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b+3*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2-I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3+I*(a^2+b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3-2*a^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),a/(a+b+(a^2+b^2)^(1/2)),1/2*2^(1/2))*b*(a^2+b^2)^(1/2)+I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2+I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b-I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b-I*(a^2+b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2-2*EllipticPi(((1-cos(d*x+c)+sin(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*EllipticPi(((1-cos(d*x+c)+sin(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)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))/(cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^4*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"
825,1,5450,210,1.533000," ","int(1/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"
826,1,36870,352,4.349000," ","int(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"
827,1,28581,315,2.825000," ","int(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"
828,1,18100,278,3.865000," ","int(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"
829,1,19992,275,1.972000," ","int(1/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"
830,1,19895,273,1.794000," ","int(1/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"
831,1,19988,279,1.795000," ","int(1/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"
832,1,21870,315,2.055000," ","int(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
833,1,99772,437,5.943000," ","int(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"
834,1,78085,392,5.885000," ","int(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"
835,1,50004,348,4.973000," ","int(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"
836,1,50074,344,4.199000," ","int(1/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"
837,1,50004,337,2.583000," ","int(1/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"
838,1,49971,337,2.638000," ","int(1/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"
839,1,50064,348,2.600000," ","int(1/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"
840,1,21305,215,1.896000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
841,1,10794,179,1.414000," ","int(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
842,1,10494,147,1.247000," ","int(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"
843,1,2587,125,1.394000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2),x)","\frac{\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)}}\, \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}{\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{a \left(-1+\cos \left(d x +c \right)\right)}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}\, \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}+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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}-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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}}+\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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}}+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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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} \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}}+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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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} \sqrt{a^{2}+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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) 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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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 -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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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^{3}-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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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 -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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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^{3}+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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) b^{3}\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)}"," ",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)*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*(a^2+b^2)^(1/2)-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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^3-2*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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+4*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^3)*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)","C"
844,1,5181,171,1.179000," ","int((a+b*tan(d*x+c))^(1/2)/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
845,1,12684,198,1.513000," ","int((a+b*tan(d*x+c))^(1/2)/cot(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
846,1,25428,254,2.012000," ","int(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
847,1,23629,216,1.737000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
848,1,12557,173,1.437000," ","int(cot(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","C"
849,1,11638,151,1.302000," ","int(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"
850,1,6261,172,1.237000," ","int(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"
851,1,13876,200,1.503000," ","int((a+b*tan(d*x+c))^(3/2)/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
852,1,16676,232,1.771000," ","int((a+b*tan(d*x+c))^(3/2)/cot(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
853,1,49804,300,2.707000," ","int(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
854,1,33758,256,2.180000," ","int(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
855,1,32909,213,1.906000," ","int(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
856,1,16676,180,1.544000," ","int(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"
857,1,27474,199,1.572000," ","int(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"
858,1,15064,202,1.515000," ","int(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"
859,1,17291,237,1.888000," ","int((a+b*tan(d*x+c))^(5/2)/cot(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
860,1,18203,275,2.297000," ","int((a+b*tan(d*x+c))^(5/2)/cot(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
861,1,8425,180,1.586000," ","int(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
862,1,6052,153,1.508000," ","int(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"
863,1,2048,121,1.363000," ","int(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x)","\frac{\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(-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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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 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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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 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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}}-\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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{2} b -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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) a^{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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) b^{3}-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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}}}{2}\right) b^{2}\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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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,"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)*(-I*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)-EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b^3-4*(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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"
864,1,1625,125,1.401000," ","int(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x)","-\frac{\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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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}{\left(-b +\sqrt{a^{2}+b^{2}}\right) \sin \left(d x +c \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{2}\, \sin \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}{\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)}}}{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,"-1/d*(I*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)*2^(1/2)*sin(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(1/cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)))^(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"
865,1,4632,172,1.350000," ","int(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-2/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)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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-4*I*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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^4-2*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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+4*I*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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^4-2*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)+3*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)^(1/2)*a^2*b-3*I*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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+3*I*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)+2*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)^(1/2)*a*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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)+4*I*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)+2*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)^(1/2)*a^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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)-EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)*(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"
866,1,11479,202,1.551000," ","int(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
867,1,9803,233,1.540000," ","int(cot(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","C"
868,1,9451,197,1.388000," ","int(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"
869,1,4831,165,1.354000," ","int(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-1/d*(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)*sin(d*x+c)*(3*I*sin(d*x+c)*(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*a^2*b+I*sin(d*x+c)*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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^4-I*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*a^4-3*I*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*a^2*b^2-3*I*sin(d*x+c)*(a^2+b^2)^(1/2)*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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+3*I*sin(d*x+c)*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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-sin(d*x+c)*a^3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))+2*sin(d*x+c)*b^2*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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-sin(d*x+c)*a^3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))+2*sin(d*x+c)*b^2*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*sin(d*x+c)*a^3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))+4*sin(d*x+c)*b^2*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a-2*sin(d*x+c)*b^3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*sin(d*x+c)*b^3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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-4*sin(d*x+c)*a^3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*b-4*sin(d*x+c)*b^3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*a-2*cos(d*x+c)*(a^2+b^2)^(1/2)*2^(1/2)*b^3+2*2^(1/2)*cos(d*x+c)*a^2*b^2+2*cos(d*x+c)*2^(1/2)*b^4+2*2^(1/2)*b^3*(a^2+b^2)^(1/2)-2*a^2*b^2*2^(1/2)-2*2^(1/2)*b^4)/(-1+cos(d*x+c))/(a*cos(d*x+c)+b*sin(d*x+c))*2^(1/2)/a/(a^2+b^2)/(I*a+(a^2+b^2)^(1/2)-b)/(I*a-(a^2+b^2)^(1/2)+b)","C"
870,1,4830,157,1.411000," ","int(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-1/d*(-2*I*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*a*b^3-2*I*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*(a^2+b^2)^(1/2)*a*b^2+I*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*(a^2+b^2)^(1/2)*a^3+2*I*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*(a^2+b^2)^(1/2)*a*b^2-I*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*(a^2+b^2)^(1/2)*a^3+2*I*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*a*b^3-3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*(a^2+b^2)^(1/2)*a^2*b+(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*a^4+3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*a^2*b^2-3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*(a^2+b^2)^(1/2)*a^2*b+(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*a^4+3*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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))*sin(d*x+c)*a^2*b^2+2*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*sin(d*x+c)*(a^2+b^2)^(1/2)*a^2*b+4*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*sin(d*x+c)*(a^2+b^2)^(1/2)*b^3-4*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*sin(d*x+c)*a^2*b^2-4*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2))^(1/2))*sin(d*x+c)*b^4+2*2^(1/2)*cos(d*x+c)*(a^2+b^2)^(1/2)*a*b^2-2*2^(1/2)*cos(d*x+c)*a^3*b-2*2^(1/2)*cos(d*x+c)*a*b^3-2*2^(1/2)*(a^2+b^2)^(1/2)*a*b^2+2*2^(1/2)*a^3*b+2*2^(1/2)*a*b^3)*cos(d*x+c)*(1/cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)))^(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)*2^(1/2)/(a^2+b^2)/(I*a+(a^2+b^2)^(1/2)-b)/(I*a-(a^2+b^2)^(1/2)+b)/a","C"
871,1,4817,160,1.383000," ","int(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"1/d*(-3*I*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*a-I*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)-3*I*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(a^2+b^2)^(1/2)*a*b+I*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)+3*I*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*a+3*I*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(a^2+b^2)^(1/2)*a*b-sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(a^2+b^2)^(1/2)+2*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-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)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(a^2+b^2)^(1/2)+2*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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*(((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(a^2+b^2)^(1/2)+2*sin(d*x+c)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(a^2+b^2)^(1/2)+4*sin(d*x+c)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(a^2+b^2)^(1/2)-2*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)-2*sin(d*x+c)*EllipticPi((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)-4*sin(d*x+c)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(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)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*b-4*sin(d*x+c)*EllipticF((((a^2+b^2)^(1/2)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),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)*sin(d*x+c)-a*cos(d*x+c)-b*sin(d*x+c)+a)/(-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*(-1+cos(d*x+c))/(-b+(a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)+2*cos(d*x+c)*2^(1/2)*(a^2+b^2)^(1/2)*a*b-2*cos(d*x+c)*2^(1/2)*a^3-2*cos(d*x+c)*2^(1/2)*a*b^2-2*a*b*(a^2+b^2)^(1/2)*2^(1/2)+2*2^(1/2)*a^3+2*2^(1/2)*a*b^2)*cos(d*x+c)^2*(1/cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)))^(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))^(3/2)/sin(d*x+c)*2^(1/2)/(a^2+b^2)/(I*a+(a^2+b^2)^(1/2)-b)/(I*a-(a^2+b^2)^(1/2)+b)","C"
872,1,14605,211,1.610000," ","int(1/cot(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","C"
873,1,15848,260,1.677000," ","int(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
874,1,41191,288,3.154000," ","int(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"
875,1,26414,259,2.523000," ","int(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"
876,1,20650,212,2.432000," ","int(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"
877,1,19740,209,2.247000," ","int(1/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"
878,1,20598,199,2.160000," ","int(1/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"
879,1,19701,212,2.053000," ","int(1/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"
880,0,0,198,1.486000," ","int((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^3,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^3,x)","F"
881,0,0,128,1.475000," ","int((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^2,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^2,x)","F"
882,0,0,92,1.918000," ","int((d*cot(f*x+e))^n*(a+b*tan(f*x+e)),x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(a +b \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*cot(f*x+e))^n*(a+b*tan(f*x+e)),x)","F"
883,0,0,180,1.629000," ","int((d*cot(f*x+e))^n/(a+b*tan(f*x+e)),x)","\int \frac{\left(d \cot \left(f x +e \right)\right)^{n}}{a +b \tan \left(f x +e \right)}\, dx"," ",0,"int((d*cot(f*x+e))^n/(a+b*tan(f*x+e)),x)","F"
884,0,0,248,1.782000," ","int((d*cot(f*x+e))^n/(a+b*tan(f*x+e))^2,x)","\int \frac{\left(d \cot \left(f x +e \right)\right)^{n}}{\left(a +b \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*cot(f*x+e))^n/(a+b*tan(f*x+e))^2,x)","F"
885,0,0,187,1.042000," ","int((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^m,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^m,x)","F"
886,0,0,141,1.179000," ","int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x)","\int \left(\cot^{\frac{3}{2}}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x)","F"
887,0,0,139,1.020000," ","int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n,x)","\int \left(\sqrt{\cot}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n,x)","F"
888,0,0,141,1.053000," ","int((a+b*tan(d*x+c))^n/cot(d*x+c)^(1/2),x)","\int \frac{\left(a +b \tan \left(d x +c \right)\right)^{n}}{\sqrt{\cot \left(d x +c \right)}}\, dx"," ",0,"int((a+b*tan(d*x+c))^n/cot(d*x+c)^(1/2),x)","F"
889,0,0,141,1.046000," ","int((a+b*tan(d*x+c))^n/cot(d*x+c)^(3/2),x)","\int \frac{\left(a +b \tan \left(d x +c \right)\right)^{n}}{\cot \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(d*x+c))^n/cot(d*x+c)^(3/2),x)","F"
890,1,37,21,0.019000," ","int((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e)),x)","\frac{a^{3} c \left(i \left(\tan^{2}\left(f x +e \right)\right)-\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}+\tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a^3*c*(I*tan(f*x+e)^2-1/3*tan(f*x+e)^3+tan(f*x+e))","A"
891,1,27,21,0.017000," ","int((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e)),x)","\frac{a^{2} c \left(\frac{i \left(\tan^{2}\left(f x +e \right)\right)}{2}+\tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a^2*c*(1/2*I*tan(f*x+e)^2+tan(f*x+e))","A"
892,1,13,12,0.020000," ","int((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e)),x)","\frac{a c \tan \left(f x +e \right)}{f}"," ",0,"a*c*tan(f*x+e)/f","A"
893,1,20,21,0.209000," ","int((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","\frac{c}{f a \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/f*c/a/(tan(f*x+e)-I)","A"
894,1,22,21,0.213000," ","int((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x)","-\frac{i c}{2 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}"," ",0,"-1/2*I/f*c/a^2/(tan(f*x+e)-I)^2","A"
895,1,21,21,0.224000," ","int((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x)","-\frac{c}{3 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}"," ",0,"-1/3/f*c/a^3/(tan(f*x+e)-I)^3","A"
896,1,50,50,0.020000," ","int((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^2,x)","\frac{a^{4} c^{2} \left(\tan \left(f x +e \right)-\frac{\left(\tan^{5}\left(f x +e \right)\right)}{5}+\frac{i \left(\tan^{4}\left(f x +e \right)\right)}{2}+i \left(\tan^{2}\left(f x +e \right)\right)\right)}{f}"," ",0,"1/f*a^4*c^2*(tan(f*x+e)-1/5*tan(f*x+e)^5+1/2*I*tan(f*x+e)^4+I*tan(f*x+e)^2)","A"
897,1,50,56,0.020000," ","int((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^2,x)","\frac{a^{3} c^{2} \left(\tan \left(f x +e \right)+\frac{i \left(\tan^{4}\left(f x +e \right)\right)}{4}+\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{i \left(\tan^{2}\left(f x +e \right)\right)}{2}\right)}{f}"," ",0,"1/f*a^3*c^2*(tan(f*x+e)+1/4*I*tan(f*x+e)^4+1/3*tan(f*x+e)^3+1/2*I*tan(f*x+e)^2)","A"
898,1,28,36,0.020000," ","int((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^2,x)","\frac{a^{2} c^{2} \left(\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}+\tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a^2*c^2*(1/3*tan(f*x+e)^3+tan(f*x+e))","A"
899,1,27,21,0.019000," ","int((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x)","\frac{a \,c^{2} \left(\tan \left(f x +e \right)-\frac{i \left(\tan^{2}\left(f x +e \right)\right)}{2}\right)}{f}"," ",0,"1/f*a*c^2*(tan(f*x+e)-1/2*I*tan(f*x+e)^2)","A"
900,1,46,52,0.211000," ","int((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x)","\frac{2 c^{2}}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{i c^{2} \ln \left(\tan \left(f x +e \right)-i\right)}{f a}"," ",0,"2/f*c^2/a/(tan(f*x+e)-I)+I/f*c^2/a*ln(tan(f*x+e)-I)","A"
901,1,39,27,0.224000," ","int((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x)","\frac{c^{2} \left(-\frac{1}{\tan \left(f x +e \right)-i}-\frac{i}{\left(\tan \left(f x +e \right)-i\right)^{2}}\right)}{f \,a^{2}}"," ",0,"1/f*c^2/a^2*(-1/(tan(f*x+e)-I)-I/(tan(f*x+e)-I)^2)","A"
902,1,39,50,0.221000," ","int((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x)","\frac{c^{2} \left(-\frac{2}{3 \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{i}{2 \left(\tan \left(f x +e \right)-i\right)^{2}}\right)}{f \,a^{3}}"," ",0,"1/f*c^2/a^3*(-2/3/(tan(f*x+e)-I)^3+1/2*I/(tan(f*x+e)-I)^2)","A"
903,1,39,54,0.227000," ","int((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^4,x)","\frac{c^{2} \left(\frac{1}{3 \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{i}{2 \left(\tan \left(f x +e \right)-i\right)^{4}}\right)}{f \,a^{4}}"," ",0,"1/f*c^2/a^4*(1/3/(tan(f*x+e)-I)^3+1/2*I/(tan(f*x+e)-I)^4)","A"
904,1,81,76,0.026000," ","int((a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^3,x)","\frac{a^{5} c^{3} \left(\tan \left(f x +e \right)-\frac{\left(\tan^{7}\left(f x +e \right)\right)}{7}+\frac{i \left(\tan^{6}\left(f x +e \right)\right)}{3}-\frac{\left(\tan^{5}\left(f x +e \right)\right)}{5}+i \left(\tan^{4}\left(f x +e \right)\right)+\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}+i \left(\tan^{2}\left(f x +e \right)\right)\right)}{f}"," ",0,"1/f*a^5*c^3*(tan(f*x+e)-1/7*tan(f*x+e)^7+1/3*I*tan(f*x+e)^6-1/5*tan(f*x+e)^5+I*tan(f*x+e)^4+1/3*tan(f*x+e)^3+I*tan(f*x+e)^2)","A"
905,1,71,75,0.018000," ","int((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^3,x)","\frac{a^{4} c^{3} \left(\tan \left(f x +e \right)+\frac{i \left(\tan^{6}\left(f x +e \right)\right)}{6}+\frac{\left(\tan^{5}\left(f x +e \right)\right)}{5}+\frac{i \left(\tan^{4}\left(f x +e \right)\right)}{2}+\frac{2 \left(\tan^{3}\left(f x +e \right)\right)}{3}+\frac{i \left(\tan^{2}\left(f x +e \right)\right)}{2}\right)}{f}"," ",0,"1/f*a^4*c^3*(tan(f*x+e)+1/6*I*tan(f*x+e)^6+1/5*tan(f*x+e)^5+1/2*I*tan(f*x+e)^4+2/3*tan(f*x+e)^3+1/2*I*tan(f*x+e)^2)","A"
906,1,38,55,0.023000," ","int((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^3,x)","\frac{a^{3} c^{3} \left(\frac{\left(\tan^{5}\left(f x +e \right)\right)}{5}+\frac{2 \left(\tan^{3}\left(f x +e \right)\right)}{3}+\tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a^3*c^3*(1/5*tan(f*x+e)^5+2/3*tan(f*x+e)^3+tan(f*x+e))","A"
907,1,50,56,0.019000," ","int((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^3,x)","\frac{a^{2} c^{3} \left(\tan \left(f x +e \right)-\frac{i \left(\tan^{4}\left(f x +e \right)\right)}{4}+\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}-\frac{i \left(\tan^{2}\left(f x +e \right)\right)}{2}\right)}{f}"," ",0,"1/f*a^2*c^3*(tan(f*x+e)-1/4*I*tan(f*x+e)^4+1/3*tan(f*x+e)^3-1/2*I*tan(f*x+e)^2)","A"
908,1,37,21,0.019000," ","int((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x)","\frac{a \,c^{3} \left(\tan \left(f x +e \right)-\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}-i \left(\tan^{2}\left(f x +e \right)\right)\right)}{f}"," ",0,"1/f*a*c^3*(tan(f*x+e)-1/3*tan(f*x+e)^3-I*tan(f*x+e)^2)","A"
909,1,62,68,0.177000," ","int((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x)","\frac{c^{3} \tan \left(f x +e \right)}{a f}+\frac{4 c^{3}}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{4 i c^{3} \ln \left(\tan \left(f x +e \right)-i\right)}{f a}"," ",0,"c^3*tan(f*x+e)/a/f+4/f*c^3/a/(tan(f*x+e)-I)+4*I/f*c^3/a*ln(tan(f*x+e)-I)","A"
910,1,69,78,0.220000," ","int((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x)","-\frac{4 c^{3}}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{2 i c^{3}}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i c^{3} \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{2}}"," ",0,"-4/f*c^3/a^2/(tan(f*x+e)-I)-2*I/f*c^3/a^2/(tan(f*x+e)-I)^2-I/f*c^3/a^2*ln(tan(f*x+e)-I)","A"
911,1,50,45,0.206000," ","int((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x)","\frac{c^{3} \left(\frac{1}{\tan \left(f x +e \right)-i}+\frac{2 i}{\left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{4}{3 \left(\tan \left(f x +e \right)-i\right)^{3}}\right)}{f \,a^{3}}"," ",0,"1/f*c^3/a^3*(1/(tan(f*x+e)-I)+2*I/(tan(f*x+e)-I)^2-4/3/(tan(f*x+e)-I)^3)","A"
912,1,53,77,0.215000," ","int((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^4,x)","\frac{c^{3} \left(-\frac{i}{2 \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{i}{\left(\tan \left(f x +e \right)-i\right)^{4}}+\frac{4}{3 \left(\tan \left(f x +e \right)-i\right)^{3}}\right)}{f \,a^{4}}"," ",0,"1/f*c^3/a^4*(-1/2*I/(tan(f*x+e)-I)^2+I/(tan(f*x+e)-I)^4+4/3/(tan(f*x+e)-I)^3)","A"
913,1,52,80,0.242000," ","int((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^5,x)","\frac{c^{3} \left(\frac{4}{5 \left(\tan \left(f x +e \right)-i\right)^{5}}-\frac{i}{\left(\tan \left(f x +e \right)-i\right)^{4}}-\frac{1}{3 \left(\tan \left(f x +e \right)-i\right)^{3}}\right)}{f \,a^{5}}"," ",0,"1/f*c^3/a^5*(4/5/(tan(f*x+e)-I)^5-I/(tan(f*x+e)-I)^4-1/3/(tan(f*x+e)-I)^3)","A"
914,1,90,93,0.018000," ","int((a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^4,x)","\frac{a^{5} c^{4} \left(\tan \left(f x +e \right)+\frac{i \left(\tan^{8}\left(f x +e \right)\right)}{8}+\frac{\left(\tan^{7}\left(f x +e \right)\right)}{7}+\frac{i \left(\tan^{6}\left(f x +e \right)\right)}{2}+\frac{3 \left(\tan^{5}\left(f x +e \right)\right)}{5}+\frac{3 i \left(\tan^{4}\left(f x +e \right)\right)}{4}+\tan^{3}\left(f x +e \right)+\frac{i \left(\tan^{2}\left(f x +e \right)\right)}{2}\right)}{f}"," ",0,"1/f*a^5*c^4*(tan(f*x+e)+1/8*I*tan(f*x+e)^8+1/7*tan(f*x+e)^7+1/2*I*tan(f*x+e)^6+3/5*tan(f*x+e)^5+3/4*I*tan(f*x+e)^4+tan(f*x+e)^3+1/2*I*tan(f*x+e)^2)","A"
915,1,46,73,0.017000," ","int((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^4,x)","\frac{a^{4} c^{4} \left(\frac{\left(\tan^{7}\left(f x +e \right)\right)}{7}+\frac{3 \left(\tan^{5}\left(f x +e \right)\right)}{5}+\tan^{3}\left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}"," ",0,"1/f*a^4*c^4*(1/7*tan(f*x+e)^7+3/5*tan(f*x+e)^5+tan(f*x+e)^3+tan(f*x+e))","A"
916,1,71,75,0.018000," ","int((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^4,x)","\frac{a^{3} c^{4} \left(\tan \left(f x +e \right)-\frac{i \left(\tan^{6}\left(f x +e \right)\right)}{6}+\frac{\left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{i \left(\tan^{4}\left(f x +e \right)\right)}{2}+\frac{2 \left(\tan^{3}\left(f x +e \right)\right)}{3}-\frac{i \left(\tan^{2}\left(f x +e \right)\right)}{2}\right)}{f}"," ",0,"1/f*a^3*c^4*(tan(f*x+e)-1/6*I*tan(f*x+e)^6+1/5*tan(f*x+e)^5-1/2*I*tan(f*x+e)^4+2/3*tan(f*x+e)^3-1/2*I*tan(f*x+e)^2)","A"
917,1,50,50,0.017000," ","int((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^4,x)","\frac{a^{2} c^{4} \left(\tan \left(f x +e \right)-\frac{\left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{i \left(\tan^{4}\left(f x +e \right)\right)}{2}-i \left(\tan^{2}\left(f x +e \right)\right)\right)}{f}"," ",0,"1/f*a^2*c^4*(tan(f*x+e)-1/5*tan(f*x+e)^5-1/2*I*tan(f*x+e)^4-I*tan(f*x+e)^2)","A"
918,1,48,21,0.018000," ","int((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x)","\frac{a \,c^{4} \left(\tan \left(f x +e \right)+\frac{i \left(\tan^{4}\left(f x +e \right)\right)}{4}-\left(\tan^{3}\left(f x +e \right)\right)-\frac{3 i \left(\tan^{2}\left(f x +e \right)\right)}{2}\right)}{f}"," ",0,"1/f*a*c^4*(tan(f*x+e)+1/4*I*tan(f*x+e)^4-tan(f*x+e)^3-3/2*I*tan(f*x+e)^2)","B"
919,1,83,89,0.181000," ","int((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e)),x)","\frac{5 c^{4} \tan \left(f x +e \right)}{a f}-\frac{i c^{4} \left(\tan^{2}\left(f x +e \right)\right)}{2 a f}+\frac{8 c^{4}}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{12 i c^{4} \ln \left(\tan \left(f x +e \right)-i\right)}{f a}"," ",0,"5*c^4*tan(f*x+e)/a/f-1/2*I*c^4*tan(f*x+e)^2/a/f+8/f*c^4/a/(tan(f*x+e)-I)+12*I/f*c^4/a*ln(tan(f*x+e)-I)","A"
920,1,86,96,0.177000," ","int((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^2,x)","-\frac{c^{4} \tan \left(f x +e \right)}{a^{2} f}-\frac{12 c^{4}}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{4 i c^{4}}{f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{6 i c^{4} \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{2}}"," ",0,"-c^4*tan(f*x+e)/a^2/f-12/f*c^4/a^2/(tan(f*x+e)-I)-4*I/f*c^4/a^2/(tan(f*x+e)-I)^2-6*I/f*c^4/a^2*ln(tan(f*x+e)-I)","A"
921,1,91,105,0.210000," ","int((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^3,x)","\frac{6 c^{4}}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{6 i c^{4}}{f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{i c^{4} \ln \left(\tan \left(f x +e \right)-i\right)}{f \,a^{3}}-\frac{8 c^{4}}{3 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}"," ",0,"6/f*c^4/a^3/(tan(f*x+e)-I)+6*I/f*c^4/a^3/(tan(f*x+e)-I)^2+I/f*c^4/a^3*ln(tan(f*x+e)-I)-8/3/f*c^4/a^3/(tan(f*x+e)-I)^3","A"
922,1,66,45,0.205000," ","int((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^4,x)","\frac{c^{4} \left(-\frac{1}{\tan \left(f x +e \right)-i}+\frac{4}{\left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{2 i}{\left(\tan \left(f x +e \right)-i\right)^{4}}-\frac{3 i}{\left(\tan \left(f x +e \right)-i\right)^{2}}\right)}{f \,a^{4}}"," ",0,"1/f*c^4/a^4*(-1/(tan(f*x+e)-I)+4/(tan(f*x+e)-I)^3+2*I/(tan(f*x+e)-I)^4-3*I/(tan(f*x+e)-I)^2)","A"
923,1,66,77,0.214000," ","int((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^5,x)","\frac{c^{4} \left(-\frac{3 i}{\left(\tan \left(f x +e \right)-i\right)^{4}}+\frac{8}{5 \left(\tan \left(f x +e \right)-i\right)^{5}}+\frac{i}{2 \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{2}{\left(\tan \left(f x +e \right)-i\right)^{3}}\right)}{f \,a^{5}}"," ",0,"1/f*c^4/a^5*(-3*I/(tan(f*x+e)-I)^4+8/5/(tan(f*x+e)-I)^5+1/2*I/(tan(f*x+e)-I)^2-2/(tan(f*x+e)-I)^3)","A"
924,1,83,89,0.204000," ","int((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e)),x)","\frac{5 a^{4} \tan \left(f x +e \right)}{c f}+\frac{i a^{4} \left(\tan^{2}\left(f x +e \right)\right)}{2 c f}+\frac{8 a^{4}}{f c \left(\tan \left(f x +e \right)+i\right)}-\frac{12 i a^{4} \ln \left(\tan \left(f x +e \right)+i\right)}{f c}"," ",0,"5*a^4*tan(f*x+e)/c/f+1/2*I*a^4*tan(f*x+e)^2/c/f+8/f*a^4/c/(tan(f*x+e)+I)-12*I/f*a^4/c*ln(tan(f*x+e)+I)","A"
925,1,62,68,0.198000," ","int((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x)","\frac{a^{3} \tan \left(f x +e \right)}{c f}+\frac{4 a^{3}}{f c \left(\tan \left(f x +e \right)+i\right)}-\frac{4 i a^{3} \ln \left(\tan \left(f x +e \right)+i\right)}{f c}"," ",0,"a^3*tan(f*x+e)/c/f+4/f*a^3/c/(tan(f*x+e)+I)-4*I/f*a^3/c*ln(tan(f*x+e)+I)","A"
926,1,46,52,0.199000," ","int((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x)","\frac{2 a^{2}}{f c \left(\tan \left(f x +e \right)+i\right)}-\frac{i a^{2} \ln \left(\tan \left(f x +e \right)+i\right)}{f c}"," ",0,"2/f*a^2/c/(tan(f*x+e)+I)-I/f*a^2/c*ln(tan(f*x+e)+I)","A"
927,1,20,21,0.229000," ","int((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","\frac{a}{f c \left(\tan \left(f x +e \right)+i\right)}"," ",0,"1/f*a/c/(tan(f*x+e)+I)","A"
928,1,90,33,0.280000," ","int(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{4 f c a}+\frac{1}{4 f c a \left(\tan \left(f x +e \right)+i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right)}{4 f c a}+\frac{1}{4 f c a \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/4*I/f/c/a*ln(tan(f*x+e)+I)+1/4/f/c/a/(tan(f*x+e)+I)-1/4*I/f/c/a*ln(tan(f*x+e)-I)+1/4/f/c/a/(tan(f*x+e)-I)","C"
929,1,113,78,0.306000," ","int(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x)","\frac{3 i \ln \left(\tan \left(f x +e \right)+i\right)}{16 f \,a^{2} c}+\frac{1}{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)}{16 f \,a^{2} c}-\frac{i}{8 f \,a^{2} c \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{1}{4 f \,a^{2} c \left(\tan \left(f x +e \right)-i\right)}"," ",0,"3/16*I/f/a^2/c*ln(tan(f*x+e)+I)+1/8/f/a^2/c/(tan(f*x+e)+I)-3/16*I/f/a^2/c*ln(tan(f*x+e)-I)-1/8*I/f/a^2/c/(tan(f*x+e)-I)^2+1/4/f/a^2/c/(tan(f*x+e)-I)","A"
930,1,135,106,0.353000," ","int(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x)","\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{8 f \,a^{3} c}+\frac{1}{16 f \,a^{3} c \left(\tan \left(f x +e \right)+i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right)}{8 f \,a^{3} c}-\frac{i}{8 f \,a^{3} c \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{1}{12 f \,a^{3} c \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{3}{16 f \,a^{3} c \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/8*I/f/a^3/c*ln(tan(f*x+e)+I)+1/16/f/a^3/c/(tan(f*x+e)+I)-1/8*I/f/a^3/c*ln(tan(f*x+e)-I)-1/8*I/f/a^3/c/(tan(f*x+e)-I)^2-1/12/f/a^3/c/(tan(f*x+e)-I)^3+3/16/f/a^3/c/(tan(f*x+e)-I)","A"
931,1,86,96,0.177000," ","int((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^2,x)","-\frac{a^{4} \tan \left(f x +e \right)}{c^{2} f}-\frac{12 a^{4}}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)}+\frac{6 i a^{4} \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{2}}+\frac{4 i a^{4}}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"-a^4*tan(f*x+e)/c^2/f-12/f*a^4/c^2/(tan(f*x+e)+I)+6*I/f*a^4/c^2*ln(tan(f*x+e)+I)+4*I/f*a^4/c^2/(tan(f*x+e)+I)^2","A"
932,1,69,78,0.207000," ","int((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x)","-\frac{4 a^{3}}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)}+\frac{i a^{3} \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{2}}+\frac{2 i a^{3}}{f \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"-4/f*a^3/c^2/(tan(f*x+e)+I)+I/f*a^3/c^2*ln(tan(f*x+e)+I)+2*I/f*a^3/c^2/(tan(f*x+e)+I)^2","A"
933,1,39,27,0.196000," ","int((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x)","\frac{a^{2} \left(-\frac{1}{\tan \left(f x +e \right)+i}+\frac{i}{\left(\tan \left(f x +e \right)+i\right)^{2}}\right)}{f \,c^{2}}"," ",0,"1/f*a^2/c^2*(-1/(tan(f*x+e)+I)+I/(tan(f*x+e)+I)^2)","A"
934,1,22,21,0.273000," ","int((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x)","\frac{i a}{2 f \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"1/2*I/f*a/c^2/(tan(f*x+e)+I)^2","A"
935,1,113,87,0.249000," ","int(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x)","\frac{i}{8 f a \,c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{3 i \ln \left(\tan \left(f x +e \right)+i\right)}{16 f a \,c^{2}}+\frac{1}{4 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)}{16 f a \,c^{2}}+\frac{1}{8 f a \,c^{2} \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/8*I/f/a/c^2/(tan(f*x+e)+I)^2+3/16*I/f/a/c^2*ln(tan(f*x+e)+I)+1/4/f/a/c^2/(tan(f*x+e)+I)-3/16*I/f/a/c^2*ln(tan(f*x+e)-I)+1/8/f/a/c^2/(tan(f*x+e)-I)","A"
936,1,136,58,0.270000," ","int(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x)","\frac{i}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{3 i \ln \left(\tan \left(f x +e \right)+i\right)}{16 f \,a^{2} c^{2}}+\frac{3}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)+i\right)}-\frac{3 i \ln \left(\tan \left(f x +e \right)-i\right)}{16 f \,a^{2} c^{2}}-\frac{i}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{3}{16 f \,a^{2} c^{2} \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/16*I/f/a^2/c^2/(tan(f*x+e)+I)^2+3/16*I/f/a^2/c^2*ln(tan(f*x+e)+I)+3/16/f/a^2/c^2/(tan(f*x+e)+I)-3/16*I/f/a^2/c^2*ln(tan(f*x+e)-I)-1/16*I/f/a^2/c^2/(tan(f*x+e)-I)^2+3/16/f/a^2/c^2/(tan(f*x+e)-I)","C"
937,1,158,103,0.250000," ","int(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x)","\frac{i}{32 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{5 i \ln \left(\tan \left(f x +e \right)+i\right)}{32 f \,a^{3} c^{2}}+\frac{1}{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)}{32 f \,a^{3} c^{2}}-\frac{3 i}{32 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{1}{24 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{3}{16 f \,a^{3} c^{2} \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/32*I/f/a^3/c^2/(tan(f*x+e)+I)^2+5/32*I/f/a^3/c^2*ln(tan(f*x+e)+I)+1/8/f/a^3/c^2/(tan(f*x+e)+I)-5/32*I/f/a^3/c^2*ln(tan(f*x+e)-I)-3/32*I/f/a^3/c^2/(tan(f*x+e)-I)^2-1/24/f/a^3/c^2/(tan(f*x+e)-I)^3+3/16/f/a^3/c^2/(tan(f*x+e)-I)","A"
938,1,128,142,0.173000," ","int((a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^3,x)","\frac{9 a^{6} \tan \left(f x +e \right)}{c^{3} f}+\frac{i a^{6} \left(\tan^{2}\left(f x +e \right)\right)}{2 c^{3} f}+\frac{80 a^{6}}{f \,c^{3} \left(\tan \left(f x +e \right)+i\right)}-\frac{40 i a^{6} \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{3}}-\frac{32 a^{6}}{3 f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{40 i a^{6}}{f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"9*a^6*tan(f*x+e)/c^3/f+1/2*I*a^6*tan(f*x+e)^2/c^3/f+80/f*a^6/c^3/(tan(f*x+e)+I)-40*I/f*a^6/c^3*ln(tan(f*x+e)+I)-32/3/f*a^6/c^3/(tan(f*x+e)+I)^3-40*I/f*a^6/c^3/(tan(f*x+e)+I)^2","A"
939,1,107,125,0.291000," ","int((a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^3,x)","\frac{a^{5} \tan \left(f x +e \right)}{c^{3} f}+\frac{24 a^{5}}{f \,c^{3} \left(\tan \left(f x +e \right)+i\right)}-\frac{8 i a^{5} \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{3}}-\frac{16 a^{5}}{3 f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{16 i a^{5}}{f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"a^5*tan(f*x+e)/c^3/f+24/f*a^5/c^3/(tan(f*x+e)+I)-8*I/f*a^5/c^3*ln(tan(f*x+e)+I)-16/3/f*a^5/c^3/(tan(f*x+e)+I)^3-16*I/f*a^5/c^3/(tan(f*x+e)+I)^2","A"
940,1,91,105,0.219000," ","int((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^3,x)","\frac{6 a^{4}}{f \,c^{3} \left(\tan \left(f x +e \right)+i\right)}-\frac{i a^{4} \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{3}}-\frac{8 a^{4}}{3 f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{6 i a^{4}}{f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"6/f*a^4/c^3/(tan(f*x+e)+I)-I/f*a^4/c^3*ln(tan(f*x+e)+I)-8/3/f*a^4/c^3/(tan(f*x+e)+I)^3-6*I/f*a^4/c^3/(tan(f*x+e)+I)^2","A"
941,1,50,45,0.228000," ","int((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x)","\frac{a^{3} \left(-\frac{2 i}{\left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{1}{\tan \left(f x +e \right)+i}-\frac{4}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}\right)}{f \,c^{3}}"," ",0,"1/f*a^3/c^3*(-2*I/(tan(f*x+e)+I)^2+1/(tan(f*x+e)+I)-4/3/(tan(f*x+e)+I)^3)","A"
942,1,39,50,0.216000," ","int((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x)","\frac{a^{2} \left(-\frac{2}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{i}{2 \left(\tan \left(f x +e \right)+i\right)^{2}}\right)}{f \,c^{3}}"," ",0,"1/f*a^2/c^3*(-2/3/(tan(f*x+e)+I)^3-1/2*I/(tan(f*x+e)+I)^2)","A"
943,1,21,21,0.206000," ","int((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x)","-\frac{a}{3 f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"-1/3/f*a/c^3/(tan(f*x+e)+I)^3","A"
944,1,135,113,0.344000," ","int(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x)","\frac{i}{8 f a \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{8 f a \,c^{3}}-\frac{1}{12 f a \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{3}{16 f a \,c^{3} \left(\tan \left(f x +e \right)+i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right)}{8 f a \,c^{3}}+\frac{1}{16 f a \,c^{3} \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/8*I/f/a/c^3/(tan(f*x+e)+I)^2+1/8*I/f/a/c^3*ln(tan(f*x+e)+I)-1/12/f/a/c^3/(tan(f*x+e)+I)^3+3/16/f/a/c^3/(tan(f*x+e)+I)-1/8*I/f/a/c^3*ln(tan(f*x+e)-I)+1/16/f/a/c^3/(tan(f*x+e)-I)","A"
945,1,158,139,0.346000," ","int(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x)","\frac{3 i}{32 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{5 i \ln \left(\tan \left(f x +e \right)+i\right)}{32 f \,a^{2} c^{3}}-\frac{1}{24 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{3}{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)}{32 f \,a^{2} c^{3}}-\frac{i}{32 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{1}{8 f \,a^{2} c^{3} \left(\tan \left(f x +e \right)-i\right)}"," ",0,"3/32*I/f/a^2/c^3/(tan(f*x+e)+I)^2+5/32*I/f/a^2/c^3*ln(tan(f*x+e)+I)-1/24/f/a^2/c^3/(tan(f*x+e)+I)^3+3/16/f/a^2/c^3/(tan(f*x+e)+I)-5/32*I/f/a^2/c^3*ln(tan(f*x+e)-I)-1/32*I/f/a^2/c^3/(tan(f*x+e)-I)^2+1/8/f/a^2/c^3/(tan(f*x+e)-I)","A"
946,1,180,83,0.362000," ","int(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x)","\frac{i}{16 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)+i\right)^{2}}+\frac{5 i \ln \left(\tan \left(f x +e \right)+i\right)}{32 f \,a^{3} c^{3}}-\frac{1}{48 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{5}{32 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)+i\right)}-\frac{5 i \ln \left(\tan \left(f x +e \right)-i\right)}{32 f \,a^{3} c^{3}}-\frac{i}{16 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{1}{48 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{5}{32 f \,a^{3} c^{3} \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/16*I/f/a^3/c^3/(tan(f*x+e)+I)^2+5/32*I/f/a^3/c^3*ln(tan(f*x+e)+I)-1/48/f/a^3/c^3/(tan(f*x+e)+I)^3+5/32/f/a^3/c^3/(tan(f*x+e)+I)-5/32*I/f/a^3/c^3*ln(tan(f*x+e)-I)-1/16*I/f/a^3/c^3/(tan(f*x+e)-I)^2-1/48/f/a^3/c^3/(tan(f*x+e)-I)^3+5/32/f/a^3/c^3/(tan(f*x+e)-I)","C"
947,1,131,149,0.175000," ","int((a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^4,x)","-\frac{a^{6} \tan \left(f x +e \right)}{c^{4} f}-\frac{40 a^{6}}{f \,c^{4} \left(\tan \left(f x +e \right)+i\right)}+\frac{10 i a^{6} \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{4}}+\frac{80 a^{6}}{3 f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{40 i a^{6}}{f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{8 i a^{6}}{f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"-a^6*tan(f*x+e)/c^4/f-40/f*a^6/c^4/(tan(f*x+e)+I)+10*I/f*a^6/c^4*ln(tan(f*x+e)+I)+80/3/f*a^6/c^4/(tan(f*x+e)+I)^3+40*I/f*a^6/c^4/(tan(f*x+e)+I)^2-8*I/f*a^6/c^4/(tan(f*x+e)+I)^4","A"
948,1,114,135,0.220000," ","int((a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^4,x)","-\frac{8 a^{5}}{f \,c^{4} \left(\tan \left(f x +e \right)+i\right)}+\frac{i a^{5} \ln \left(\tan \left(f x +e \right)+i\right)}{f \,c^{4}}+\frac{32 a^{5}}{3 f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{12 i a^{5}}{f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{4 i a^{5}}{f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"-8/f*a^5/c^4/(tan(f*x+e)+I)+I/f*a^5/c^4*ln(tan(f*x+e)+I)+32/3/f*a^5/c^4/(tan(f*x+e)+I)^3+12*I/f*a^5/c^4/(tan(f*x+e)+I)^2-4*I/f*a^5/c^4/(tan(f*x+e)+I)^4","A"
949,1,66,45,0.214000," ","int((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^4,x)","\frac{a^{4} \left(-\frac{1}{\tan \left(f x +e \right)+i}+\frac{4}{\left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{2 i}{\left(\tan \left(f x +e \right)+i\right)^{4}}+\frac{3 i}{\left(\tan \left(f x +e \right)+i\right)^{2}}\right)}{f \,c^{4}}"," ",0,"1/f*a^4/c^4*(-1/(tan(f*x+e)+I)+4/(tan(f*x+e)+I)^3-2*I/(tan(f*x+e)+I)^4+3*I/(tan(f*x+e)+I)^2)","A"
950,1,53,77,0.223000," ","int((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x)","\frac{a^{3} \left(\frac{4}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{i}{\left(\tan \left(f x +e \right)+i\right)^{4}}+\frac{i}{2 \left(\tan \left(f x +e \right)+i\right)^{2}}\right)}{f \,c^{4}}"," ",0,"1/f*a^3/c^4*(4/3/(tan(f*x+e)+I)^3-I/(tan(f*x+e)+I)^4+1/2*I/(tan(f*x+e)+I)^2)","A"
951,1,39,54,0.191000," ","int((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x)","\frac{a^{2} \left(\frac{1}{3 \left(\tan \left(f x +e \right)+i\right)^{3}}-\frac{i}{2 \left(\tan \left(f x +e \right)+i\right)^{4}}\right)}{f \,c^{4}}"," ",0,"1/f*a^2/c^4*(1/3/(tan(f*x+e)+I)^3-1/2*I/(tan(f*x+e)+I)^4)","A"
952,1,22,21,0.197000," ","int((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x)","-\frac{i a}{4 f \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"-1/4*I/f*a/c^4/(tan(f*x+e)+I)^4","A"
953,1,158,140,0.265000," ","int(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x)","\frac{3 i}{32 f a \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{i}{16 f a \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}+\frac{5 i \ln \left(\tan \left(f x +e \right)+i\right)}{64 f a \,c^{4}}-\frac{1}{12 f a \,c^{4} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{1}{8 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)}{64 f a \,c^{4}}+\frac{1}{32 f a \,c^{4} \left(\tan \left(f x +e \right)-i\right)}"," ",0,"3/32*I/f/a/c^4/(tan(f*x+e)+I)^2-1/16*I/f/a/c^4/(tan(f*x+e)+I)^4+5/64*I/f/a/c^4*ln(tan(f*x+e)+I)-1/12/f/a/c^4/(tan(f*x+e)+I)^3+1/8/f/a/c^4/(tan(f*x+e)+I)-5/64*I/f/a/c^4*ln(tan(f*x+e)-I)+1/32/f/a/c^4/(tan(f*x+e)-I)","A"
954,1,181,167,0.281000," ","int(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x)","\frac{3 i}{32 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{i}{32 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}+\frac{15 i \ln \left(\tan \left(f x +e \right)+i\right)}{128 f \,a^{2} c^{4}}-\frac{1}{16 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{5}{32 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)+i\right)}-\frac{15 i \ln \left(\tan \left(f x +e \right)-i\right)}{128 f \,a^{2} c^{4}}-\frac{i}{64 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{5}{64 f \,a^{2} c^{4} \left(\tan \left(f x +e \right)-i\right)}"," ",0,"3/32*I/f/a^2/c^4/(tan(f*x+e)+I)^2-1/32*I/f/a^2/c^4/(tan(f*x+e)+I)^4+15/128*I/f/a^2/c^4*ln(tan(f*x+e)+I)-1/16/f/a^2/c^4/(tan(f*x+e)+I)^3+5/32/f/a^2/c^4/(tan(f*x+e)+I)-15/128*I/f/a^2/c^4*ln(tan(f*x+e)-I)-1/64*I/f/a^2/c^4/(tan(f*x+e)-I)^2+5/64/f/a^2/c^4/(tan(f*x+e)-I)","A"
955,1,203,193,0.303000," ","int(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x)","\frac{5 i}{64 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)+i\right)^{2}}-\frac{i}{64 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)+i\right)^{4}}+\frac{35 i \ln \left(\tan \left(f x +e \right)+i\right)}{256 f \,a^{3} c^{4}}-\frac{1}{24 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)+i\right)^{3}}+\frac{5}{32 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)}{256 f \,a^{3} c^{4}}-\frac{5 i}{128 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{1}{96 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{15}{128 f \,a^{3} c^{4} \left(\tan \left(f x +e \right)-i\right)}"," ",0,"5/64*I/f/a^3/c^4/(tan(f*x+e)+I)^2-1/64*I/f/a^3/c^4/(tan(f*x+e)+I)^4+35/256*I/f/a^3/c^4*ln(tan(f*x+e)+I)-1/24/f/a^3/c^4/(tan(f*x+e)+I)^3+5/32/f/a^3/c^4/(tan(f*x+e)+I)-35/256*I/f/a^3/c^4*ln(tan(f*x+e)-I)-5/128*I/f/a^3/c^4/(tan(f*x+e)-I)^2-1/96/f/a^3/c^4/(tan(f*x+e)-I)^3+15/128/f/a^3/c^4/(tan(f*x+e)-I)","A"
956,1,66,76,0.885000," ","int((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x)","\frac{2 i a^{3} \left(\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}-\frac{4 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3}+4 c^{2} \sqrt{c -i c \tan \left(f x +e \right)}\right)}{f \,c^{2}}"," ",0,"2*I/f*a^3/c^2*(1/5*(c-I*c*tan(f*x+e))^(5/2)-4/3*(c-I*c*tan(f*x+e))^(3/2)*c+4*c^2*(c-I*c*tan(f*x+e))^(1/2))","A"
957,1,47,50,0.214000," ","int((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i a^{2} \left(\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}-2 \sqrt{c -i c \tan \left(f x +e \right)}\, c \right)}{f c}"," ",0,"-2*I/f*a^2/c*(1/3*(c-I*c*tan(f*x+e))^(3/2)-2*(c-I*c*tan(f*x+e))^(1/2)*c)","A"
958,1,22,21,0.173000," ","int((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x)","\frac{2 i a \sqrt{c -i c \tan \left(f x +e \right)}}{f}"," ",0,"2*I*a*(c-I*c*tan(f*x+e))^(1/2)/f","A"
959,1,80,75,0.336000," ","int((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x)","\frac{2 i c^{2} \left(-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{4 c \left(-c -i c \tan \left(f x +e \right)\right)}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{8 c^{\frac{3}{2}}}\right)}{f a}"," ",0,"2*I/f/a*c^2*(-1/4*(c-I*c*tan(f*x+e))^(1/2)/c/(-c-I*c*tan(f*x+e))+1/8/c^(3/2)*2^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
960,1,121,111,0.350000," ","int((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{3} \left(-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{8 c \left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{3 \left(-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{4 c \left(-c -i c \tan \left(f x +e \right)\right)}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{8 c^{\frac{3}{2}}}\right)}{8 c}\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^3*(-1/8*(c-I*c*tan(f*x+e))^(1/2)/c/(-c-I*c*tan(f*x+e))^2-3/8/c*(-1/4*(c-I*c*tan(f*x+e))^(1/2)/c/(-c-I*c*tan(f*x+e))+1/8/c^(3/2)*2^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2))))","A"
961,1,162,147,0.355000," ","int((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{4} \left(-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{12 c \left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{5 \left(-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{8 c \left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{3 \left(-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{4 c \left(-c -i c \tan \left(f x +e \right)\right)}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{8 c^{\frac{3}{2}}}\right)}{8 c}\right)}{12 c}\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^4*(-1/12*(c-I*c*tan(f*x+e))^(1/2)/c/(-c-I*c*tan(f*x+e))^3-5/12/c*(-1/8*(c-I*c*tan(f*x+e))^(1/2)/c/(-c-I*c*tan(f*x+e))^2-3/8/c*(-1/4*(c-I*c*tan(f*x+e))^(1/2)/c/(-c-I*c*tan(f*x+e))+1/8/c^(3/2)*2^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))))","A"
962,1,66,76,0.292000," ","int((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i a^{3} \left(\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}-\frac{4 c \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}+\frac{4 c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}\right)}{f \,c^{2}}"," ",0,"2*I/f*a^3/c^2*(1/7*(c-I*c*tan(f*x+e))^(7/2)-4/5*c*(c-I*c*tan(f*x+e))^(5/2)+4/3*c^2*(c-I*c*tan(f*x+e))^(3/2))","A"
963,1,47,50,0.200000," ","int((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{2 i a^{2} \left(\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}-\frac{2 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3}\right)}{f c}"," ",0,"-2*I/f*a^2/c*(1/5*(c-I*c*tan(f*x+e))^(5/2)-2/3*(c-I*c*tan(f*x+e))^(3/2)*c)","A"
964,1,22,21,0.194000," ","int((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i a \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}"," ",0,"2/3*I*a*(c-I*c*tan(f*x+e))^(3/2)/f","A"
965,1,77,79,0.282000," ","int((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x)","\frac{2 i c^{2} \left(-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{2 \left(-c -i c \tan \left(f x +e \right)\right)}-\frac{\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)}{f a}"," ",0,"2*I/f/a*c^2*(-1/2*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-1/4*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"
966,1,98,119,0.308000," ","int((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{3} \left(\frac{-\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{16 c}-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{8}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{32 c^{\frac{3}{2}}}\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^3*((-1/16/c*(c-I*c*tan(f*x+e))^(3/2)-1/8*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^2+1/32/c^(3/2)*2^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
967,1,117,159,0.352000," ","int((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{4} \left(\frac{\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{64 c^{2}}-\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 c}-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{16}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{128 c^{\frac{5}{2}}}\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^4*((1/64/c^2*(c-I*c*tan(f*x+e))^(5/2)-1/12/c*(c-I*c*tan(f*x+e))^(3/2)-1/16*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-1/128/c^(5/2)*2^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
968,1,66,76,0.313000," ","int((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i a^{3} \left(\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{9}-\frac{4 c \left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}+\frac{4 c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}\right)}{f \,c^{2}}"," ",0,"2*I/f*a^3/c^2*(1/9*(c-I*c*tan(f*x+e))^(9/2)-4/7*c*(c-I*c*tan(f*x+e))^(7/2)+4/5*c^2*(c-I*c*tan(f*x+e))^(5/2))","A"
969,1,47,50,0.210000," ","int((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{2 i a^{2} \left(\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7}-\frac{2 c \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5}\right)}{f c}"," ",0,"-2*I/f*a^2/c*(1/7*(c-I*c*tan(f*x+e))^(7/2)-2/5*c*(c-I*c*tan(f*x+e))^(5/2))","A"
970,1,22,21,0.179000," ","int((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i a \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}"," ",0,"2/5*I*a*(c-I*c*tan(f*x+e))^(5/2)/f","A"
971,1,95,105,0.349000," ","int((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x)","\frac{2 i c^{2} \left(\sqrt{c -i c \tan \left(f x +e \right)}+4 c \left(-\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{4 \left(-c -i c \tan \left(f x +e \right)\right)}-\frac{3 \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^2*((c-I*c*tan(f*x+e))^(1/2)+4*c*(-1/4*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-3/8*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"
972,1,96,119,0.299000," ","int((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{3} \left(\frac{-\frac{5 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8}+\frac{3 \sqrt{c -i c \tan \left(f x +e \right)}\, c}{4}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{3 \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)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^3*((-5/8*(c-I*c*tan(f*x+e))^(3/2)+3/4*(c-I*c*tan(f*x+e))^(1/2)*c)/(-c-I*c*tan(f*x+e))^2-3/16*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"
973,1,115,159,0.423000," ","int((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{4} \left(\frac{-\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{32 c}-\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{6}+\frac{\sqrt{c -i c \tan \left(f x +e \right)}\, c}{8}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}+\frac{\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^{3}}"," ",0,"2*I/f/a^3*c^4*((-1/32/c*(c-I*c*tan(f*x+e))^(5/2)-1/6*(c-I*c*tan(f*x+e))^(3/2)+1/8*(c-I*c*tan(f*x+e))^(1/2)*c)/(-c-I*c*tan(f*x+e))^3+1/64/c^(3/2)*2^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))","A"
974,1,66,76,0.252000," ","int((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(1/2),x)","\frac{2 i a^{3} \left(\frac{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3}-4 \sqrt{c -i c \tan \left(f x +e \right)}\, c -\frac{4 c^{2}}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{2}}"," ",0,"2*I/f*a^3/c^2*(1/3*(c-I*c*tan(f*x+e))^(3/2)-4*(c-I*c*tan(f*x+e))^(1/2)*c-4*c^2/(c-I*c*tan(f*x+e))^(1/2))","A"
975,1,45,50,0.232000," ","int((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(1/2),x)","-\frac{2 i a^{2} \left(\sqrt{c -i c \tan \left(f x +e \right)}+\frac{2 c}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f c}"," ",0,"-2*I/f*a^2/c*((c-I*c*tan(f*x+e))^(1/2)+2*c/(c-I*c*tan(f*x+e))^(1/2))","A"
976,1,22,21,0.196000," ","int((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x)","-\frac{2 i a}{f \sqrt{c -i c \tan \left(f x +e \right)}}"," ",0,"-2*I*a/f/(c-I*c*tan(f*x+e))^(1/2)","A"
977,1,102,98,0.328000," ","int(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x)","\frac{2 i c^{2} \left(-\frac{\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{-2 c -2 i c \tan \left(f x +e \right)}-\frac{3 \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^{2}}-\frac{1}{4 c^{2} \sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f a}"," ",0,"2*I/f/a*c^2*(-1/4/c^2*(1/2*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-3/4*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/(c-I*c*tan(f*x+e))^(1/2))","A"
978,1,121,134,0.405000," ","int(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{2 i c^{3} \left(\frac{\frac{\frac{7 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8}-\frac{9 \sqrt{c -i c \tan \left(f x +e \right)}\, c}{4}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{15 \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^{3}}+\frac{1}{8 c^{3} \sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,a^{2}}"," ",0,"-2*I/f/a^2*c^3*(1/8/c^3*((7/8*(c-I*c*tan(f*x+e))^(3/2)-9/4*(c-I*c*tan(f*x+e))^(1/2)*c)/(-c-I*c*tan(f*x+e))^2-15/16*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^3/(c-I*c*tan(f*x+e))^(1/2))","A"
979,1,140,170,0.438000," ","int(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i c^{4} \left(-\frac{\frac{\frac{19 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{16}-\frac{17 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3}+\frac{29 c^{2} \sqrt{c -i c \tan \left(f x +e \right)}}{4}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{35 \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{1}{16 c^{4} \sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,a^{3}}"," ",0,"2*I/f/a^3*c^4*(-1/16/c^4*((19/16*(c-I*c*tan(f*x+e))^(5/2)-17/3*(c-I*c*tan(f*x+e))^(3/2)*c+29/4*c^2*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-35/32*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/(c-I*c*tan(f*x+e))^(1/2))","A"
980,1,64,76,0.218000," ","int((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i a^{3} \left(\sqrt{c -i c \tan \left(f x +e \right)}-\frac{4 c^{2}}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{4 c}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{2}}"," ",0,"2*I/f*a^3/c^2*((c-I*c*tan(f*x+e))^(1/2)-4/3*c^2/(c-I*c*tan(f*x+e))^(3/2)+4*c/(c-I*c*tan(f*x+e))^(1/2))","A"
981,1,47,50,0.213000," ","int((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{2 i a^{2} \left(\frac{2 c}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{1}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f c}"," ",0,"-2*I/f*a^2/c*(2/3*c/(c-I*c*tan(f*x+e))^(3/2)-1/(c-I*c*tan(f*x+e))^(1/2))","A"
982,1,22,21,0.153000," ","int((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{2 i a}{3 f \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}"," ",0,"-2/3*I*a/f/(c-I*c*tan(f*x+e))^(3/2)","A"
983,1,121,124,0.279000," ","int(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i c^{2} \left(-\frac{\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{-4 c -4 i c \tan \left(f x +e \right)}-\frac{5 \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^{3}}-\frac{1}{4 c^{3} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{1}{12 c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\right)}{f a}"," ",0,"2*I/f/a*c^2*(-1/4/c^3*(1/4*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-5/8*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^3/(c-I*c*tan(f*x+e))^(1/2)-1/12/c^2/(c-I*c*tan(f*x+e))^(3/2))","A"
984,1,140,160,0.330000," ","int(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x)","-\frac{2 i c^{3} \left(\frac{\frac{\frac{11 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8}-\frac{13 \sqrt{c -i c \tan \left(f x +e \right)}\, c}{4}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{35 \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^{4}}+\frac{3}{16 c^{4} \sqrt{c -i c \tan \left(f x +e \right)}}+\frac{1}{24 c^{3} \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^3*(1/16/c^4*((11/8*(c-I*c*tan(f*x+e))^(3/2)-13/4*(c-I*c*tan(f*x+e))^(1/2)*c)/(-c-I*c*tan(f*x+e))^2-35/16*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/(c-I*c*tan(f*x+e))^(1/2)+1/24/c^3/(c-I*c*tan(f*x+e))^(3/2))","A"
985,1,159,196,0.399000," ","int(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x)","\frac{2 i c^{4} \left(-\frac{\frac{\frac{41 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{32}-\frac{35 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{6}+\frac{55 c^{2} \sqrt{c -i c \tan \left(f x +e \right)}}{8}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{105 \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^{5}}-\frac{1}{8 c^{5} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{1}{48 c^{4} \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^4*(-1/16/c^5*((41/32*(c-I*c*tan(f*x+e))^(5/2)-35/6*(c-I*c*tan(f*x+e))^(3/2)*c+55/8*c^2*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-105/64*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^5/(c-I*c*tan(f*x+e))^(1/2)-1/48/c^4/(c-I*c*tan(f*x+e))^(3/2))","A"
986,1,66,76,0.222000," ","int((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i a^{3} \left(\frac{4 c}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{4 c^{2}}{5 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}-\frac{1}{\sqrt{c -i c \tan \left(f x +e \right)}}\right)}{f \,c^{2}}"," ",0,"2*I/f*a^3/c^2*(4/3*c/(c-I*c*tan(f*x+e))^(3/2)-4/5*c^2/(c-I*c*tan(f*x+e))^(5/2)-1/(c-I*c*tan(f*x+e))^(1/2))","A"
987,1,47,50,0.196000," ","int((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{2 i a^{2} \left(-\frac{1}{3 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{2 c}{5 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\right)}{f c}"," ",0,"-2*I/f*a^2/c*(-1/3/(c-I*c*tan(f*x+e))^(3/2)+2/5*c/(c-I*c*tan(f*x+e))^(5/2))","A"
988,1,22,21,0.173000," ","int((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{2 i a}{5 f \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}"," ",0,"-2/5*I*a/f/(c-I*c*tan(f*x+e))^(5/2)","A"
989,1,140,150,0.277000," ","int(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i c^{2} \left(-\frac{\frac{\sqrt{c -i c \tan \left(f x +e \right)}}{-2 c -2 i c \tan \left(f x +e \right)}-\frac{7 \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^{4}}-\frac{3}{16 c^{4} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{1}{12 c^{3} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{1}{20 c^{2} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\right)}{f a}"," ",0,"2*I/f/a*c^2*(-1/16/c^4*(1/2*(c-I*c*tan(f*x+e))^(1/2)/(-c-I*c*tan(f*x+e))-7/4*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/(c-I*c*tan(f*x+e))^(1/2)-1/12/c^3/(c-I*c*tan(f*x+e))^(3/2)-1/20/c^2/(c-I*c*tan(f*x+e))^(5/2))","A"
990,1,159,186,0.336000," ","int(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x)","-\frac{2 i c^{3} \left(\frac{\frac{\frac{15 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{16}-\frac{17 \sqrt{c -i c \tan \left(f x +e \right)}\, c}{8}}{\left(-c -i c \tan \left(f x +e \right)\right)^{2}}-\frac{63 \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^{5}}+\frac{3}{16 c^{5} \sqrt{c -i c \tan \left(f x +e \right)}}+\frac{1}{16 c^{4} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{1}{40 c^{3} \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^3*(1/16/c^5*((15/16*(c-I*c*tan(f*x+e))^(3/2)-17/8*(c-I*c*tan(f*x+e))^(1/2)*c)/(-c-I*c*tan(f*x+e))^2-63/32*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^5/(c-I*c*tan(f*x+e))^(1/2)+1/16/c^4/(c-I*c*tan(f*x+e))^(3/2)+1/40/c^3/(c-I*c*tan(f*x+e))^(5/2))","A"
991,1,178,222,0.377000," ","int(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x)","\frac{2 i c^{4} \left(-\frac{\frac{\frac{71 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{32}-\frac{59 \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{6}+\frac{89 c^{2} \sqrt{c -i c \tan \left(f x +e \right)}}{8}}{\left(-c -i c \tan \left(f x +e \right)\right)^{3}}-\frac{231 \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^{6}}-\frac{5}{32 c^{6} \sqrt{c -i c \tan \left(f x +e \right)}}-\frac{1}{24 c^{5} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{1}{80 c^{4} \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^4*(-1/32/c^6*((71/32*(c-I*c*tan(f*x+e))^(5/2)-59/6*(c-I*c*tan(f*x+e))^(3/2)*c+89/8*c^2*(c-I*c*tan(f*x+e))^(1/2))/(-c-I*c*tan(f*x+e))^3-231/64*2^(1/2)/c^(1/2)*arctanh(1/2*(c-I*c*tan(f*x+e))^(1/2)*2^(1/2)/c^(1/2)))-5/32/c^6/(c-I*c*tan(f*x+e))^(1/2)-1/24/c^5/(c-I*c*tan(f*x+e))^(3/2)-1/80/c^4/(c-I*c*tan(f*x+e))^(5/2))","A"
992,1,154,121,0.327000," ","int((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)}\, a^{2} \left(4 i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-\tan \left(f x +e \right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+3 a c \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)\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^2*(4*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-tan(f*x+e)*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*a*c*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*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
993,1,122,84,0.289000," ","int((c-I*c*tan(f*x+e))^(1/2)*(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)}\, a \left(i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+a c \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)\right)}{f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*a*(I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+a*c*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*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
994,1,96,48,0.342000," ","int((c-I*c*tan(f*x+e))^(1/2)*(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)}\, a c \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)}{f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \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*(1+tan(f*x+e)^2))^(1/2)*a*c*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)^(1/2)","A"
995,1,65,34,0.382000," ","int((c-I*c*tan(f*x+e))^(1/2)/(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)}\, \left(1+i \tan \left(f x +e \right)\right)}{f a \left(-\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"-I/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a*(1+I*tan(f*x+e))/(-tan(f*x+e)+I)^2","A"
996,1,74,72,0.321000," ","int((c-I*c*tan(f*x+e))^(1/2)/(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)}\, \left(3 i \tan \left(f x +e \right)-\left(\tan^{2}\left(f x +e \right)\right)+2\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*(3*I*tan(f*x+e)-tan(f*x+e)^2+2)/(-tan(f*x+e)+I)^3","A"
997,1,85,109,0.327000," ","int((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(8 i \left(\tan^{2}\left(f x +e \right)\right)-2 \left(\tan^{3}\left(f x +e \right)\right)-7 i+13 \tan \left(f x +e \right)\right)}{15 f \,a^{3} \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)/a^3*(8*I*tan(f*x+e)^2-2*tan(f*x+e)^3-7*I+13*tan(f*x+e))/(-tan(f*x+e)+I)^4","A"
998,1,95,146,0.316000," ","int((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(7/2),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(10 i \left(\tan^{3}\left(f x +e \right)\right)-2 \left(\tan^{4}\left(f x +e \right)\right)-25 i \tan \left(f x +e \right)+21 \left(\tan^{2}\left(f x +e \right)\right)-12\right)}{35 f \,a^{4} \left(-\tan \left(f x +e \right)+i\right)^{5}}"," ",0,"1/35/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a^4*(10*I*tan(f*x+e)^3-2*tan(f*x+e)^4-25*I*tan(f*x+e)+21*tan(f*x+e)^2-12)/(-tan(f*x+e)+I)^5","A"
999,1,186,127,0.244000," ","int((a+I*a*tan(f*x+e))^(5/2)*(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)}\, a^{2} c \left(2 i \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 \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+3 a c \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)+3 \tan \left(f x +e \right) \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)*a^2*c*(2*I*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+2*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*a*c*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))+3*tan(f*x+e)*(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"
1000,1,128,90,0.232000," ","int((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)}\, c a \left(a c \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) \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*a*(a*c*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)*(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"
1001,1,122,84,0.396000," ","int((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(3/2),x)","\frac{\left(-i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+a c \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)\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)}\, c}{f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/f*(-I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+a*c*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*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*c/(c*a*(1+tan(f*x+e)^2))^(1/2)/(c*a)^(1/2)","A"
1002,1,269,84,0.301000," ","int((c-I*c*tan(f*x+e))^(3/2)/(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 \left(i \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 \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 \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+2 \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 \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)*c/a*(I*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*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*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+2*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*(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"
1003,1,64,34,0.221000," ","int((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(1+\tan^{2}\left(f x +e \right)\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)*c/a^2*(1+tan(f*x+e)^2)/(-tan(f*x+e)+I)^3","A"
1004,1,75,72,0.238000," ","int((c-I*c*tan(f*x+e))^(3/2)/(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 \left(1+\tan^{2}\left(f x +e \right)\right) \left(4 i-\tan \left(f x +e \right)\right)}{15 f \,a^{3} \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*(1+tan(f*x+e)^2)*(4*I-tan(f*x+e))/(-tan(f*x+e)+I)^4","A"
1005,1,85,109,0.248000," ","int((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(7/2),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(1+\tan^{2}\left(f x +e \right)\right) \left(10 i \tan \left(f x +e \right)-2 \left(\tan^{2}\left(f x +e \right)\right)+23\right)}{105 f \,a^{4} \left(-\tan \left(f x +e \right)+i\right)^{5}}"," ",0,"-1/105/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c/a^4*(1+tan(f*x+e)^2)*(10*I*tan(f*x+e)-2*tan(f*x+e)^2+23)/(-tan(f*x+e)+I)^5","A"
1006,1,97,146,0.363000," ","int((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(9/2),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(2 i \left(\tan^{3}\left(f x +e \right)\right)-33 i \tan \left(f x +e \right)+12 \left(\tan^{2}\left(f x +e \right)\right)-58\right)}{315 f \,a^{5} \left(-\tan \left(f x +e \right)+i\right)^{6}}"," ",0,"1/315*I/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c/a^5*(1+tan(f*x+e)^2)*(2*I*tan(f*x+e)^3-33*I*tan(f*x+e)+12*tan(f*x+e)^2-58)/(-tan(f*x+e)+I)^6","A"
1007,1,164,135,0.254000," ","int((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)}\, a^{2} c^{2} \left(2 \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}+3 a c \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)+5 \tan \left(f x +e \right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{8 f \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}}"," ",0,"1/8/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2*c^2*(2*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+3*a*c*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))+5*tan(f*x+e)*(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"
1008,1,186,127,0.231000," ","int((a+I*a*tan(f*x+e))^(3/2)*(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)}\, c^{2} a \left(2 i \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 \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-3 a c \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)-3 \tan \left(f x +e \right) \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^2*a*(2*I*tan(f*x+e)^2*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+2*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-3*a*c*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))-3*tan(f*x+e)*(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"
1009,1,154,121,0.301000," ","int((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)}\, c^{2} \left(3 a c \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)-4 i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-\tan \left(f x +e \right) \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^2*(3*a*c*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))-4*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-tan(f*x+e)*(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"
1010,1,300,124,0.301000," ","int((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(3 i \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 i \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 \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+6 \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 +\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)-5 \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)*c^2/a*(3*I*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*I*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*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)+6*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+(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-5*(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"
1011,1,350,124,0.229000," ","int((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(9 i \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 \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 \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 \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)+9 \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 \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)-4 \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*(9*I*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*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*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*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)+9*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*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-4*(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"
1012,1,75,34,0.241000," ","int((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(1+\tan^{2}\left(f x +e \right)\right) \left(\tan \left(f x +e \right)+i\right)}{5 f \,a^{3} \left(-\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"1/5/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^2/a^3*(1+tan(f*x+e)^2)*(tan(f*x+e)+I)/(-tan(f*x+e)+I)^4","B"
1013,1,87,72,0.266000," ","int((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(7/2),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(1+\tan^{2}\left(f x +e \right)\right) \left(5 i \tan \left(f x +e \right)-\left(\tan^{2}\left(f x +e \right)\right)-6\right)}{35 f \,a^{4} \left(-\tan \left(f x +e \right)+i\right)^{5}}"," ",0,"1/35/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^2/a^4*(1+tan(f*x+e)^2)*(5*I*tan(f*x+e)-tan(f*x+e)^2-6)/(-tan(f*x+e)+I)^5","A"
1014,1,99,109,0.367000," ","int((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(9/2),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(1+\tan^{2}\left(f x +e \right)\right) \left(2 i \left(\tan^{3}\left(f x +e \right)\right)-33 i \tan \left(f x +e \right)+12 \left(\tan^{2}\left(f x +e \right)\right)+47\right)}{315 f \,a^{5} \left(-\tan \left(f x +e \right)+i\right)^{6}}"," ",0,"-1/315*I/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^2/a^5*(1+tan(f*x+e)^2)*(2*I*tan(f*x+e)^3-33*I*tan(f*x+e)+12*tan(f*x+e)^2+47)/(-tan(f*x+e)+I)^6","A"
1015,1,110,146,0.266000," ","int((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(11/2),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(1+\tan^{2}\left(f x +e \right)\right) \left(2 i \left(\tan^{4}\left(f x +e \right)\right)-45 i \left(\tan^{2}\left(f x +e \right)\right)+14 \left(\tan^{3}\left(f x +e \right)\right)-152 i-91 \tan \left(f x +e \right)\right)}{1155 f \,a^{6} \left(-\tan \left(f x +e \right)+i\right)^{7}}"," ",0,"1/1155*I/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*c^2/a^6*(1+tan(f*x+e)^2)*(2*I*tan(f*x+e)^4-45*I*tan(f*x+e)^2+14*tan(f*x+e)^3-152*I-91*tan(f*x+e))/(-tan(f*x+e)+I)^7","A"
1016,1,328,164,0.312000," ","int((a+I*a*tan(f*x+e))^(7/2)/(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)}\, a^{3} \left(30 i \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 +6 i \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 \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 -\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 i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}-15 a c \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)-31 \tan \left(f x +e \right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{2 f c \left(\tan \left(f x +e \right)+i\right)^{2} \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}}"," ",0,"-1/2/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^3/c*(30*I*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+6*I*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^2+15*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-tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)-24*I*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)-15*a*c*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))-31*tan(f*x+e)*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2))/(tan(f*x+e)+I)^2/(c*a)^(1/2)/(c*a*(1+tan(f*x+e)^2))^(1/2)","A"
1017,1,299,124,0.313000," ","int((a+I*a*tan(f*x+e))^(5/2)/(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(3 i \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 i \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 \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-6 \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 -\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)+5 \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)*a^2/c*(3*I*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*I*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*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-6*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-(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2+5*(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"
1018,1,267,84,0.417000," ","int((a+I*a*tan(f*x+e))^(3/2)/(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 \left(i \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 \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 \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-2 \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 \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*a*(I*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*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*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-2*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*(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"
1019,1,63,34,0.339000," ","int((a+I*a*tan(f*x+e))^(1/2)/(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(-1+i \tan \left(f x +e \right)\right)}{f c \left(\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"-I/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c*(-1+I*tan(f*x+e))/(tan(f*x+e)+I)^2","A"
1020,1,82,38,0.355000," ","int(1/(c-I*c*tan(f*x+e))^(1/2)/(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)}\, \left(1+\tan^{2}\left(f x +e \right)\right) \tan \left(f x +e \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*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/c/a*(1+tan(f*x+e)^2)*tan(f*x+e)/(tan(f*x+e)+I)^2/(-tan(f*x+e)+I)^2","B"
1021,1,109,77,0.304000," ","int(1/(c-I*c*tan(f*x+e))^(1/2)/(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)}\, \left(2 i \left(\tan^{3}\left(f x +e \right)\right)-2 \left(\tan^{4}\left(f x +e \right)\right)+2 i \tan \left(f x +e \right)-3 \left(\tan^{2}\left(f x +e \right)\right)-1\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/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/c/a^2*(2*I*tan(f*x+e)^3-2*tan(f*x+e)^4+2*I*tan(f*x+e)-3*tan(f*x+e)^2-1)/(tan(f*x+e)+I)^2/(-tan(f*x+e)+I)^3","A"
1022,1,118,114,0.325000," ","int(1/(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 \left(\tan^{4}\left(f x +e \right)\right)-2 \left(\tan^{5}\left(f x +e \right)\right)+6 i \left(\tan^{2}\left(f x +e \right)\right)-\left(\tan^{3}\left(f x +e \right)\right)+2 i+\tan \left(f x +e \right)\right)}{5 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,"-1/5/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/c/a^3*(4*I*tan(f*x+e)^4-2*tan(f*x+e)^5+6*I*tan(f*x+e)^2-tan(f*x+e)^3+2*I+tan(f*x+e))/(tan(f*x+e)+I)^2/(-tan(f*x+e)+I)^4","A"
1023,1,130,151,0.318000," ","int(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(7/2),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(24 i \left(\tan^{5}\left(f x +e \right)\right)-8 \left(\tan^{6}\left(f x +e \right)\right)+28 i \left(\tan^{3}\left(f x +e \right)\right)+12 \left(\tan^{4}\left(f x +e \right)\right)+4 i \tan \left(f x +e \right)+33 \left(\tan^{2}\left(f x +e \right)\right)+13\right)}{35 f c \,a^{4} \left(\tan \left(f x +e \right)+i\right)^{2} \left(-\tan \left(f x +e \right)+i\right)^{5}}"," ",0,"1/35/f*(-c*(-1+I*tan(f*x+e)))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/c/a^4*(24*I*tan(f*x+e)^5-8*tan(f*x+e)^6+28*I*tan(f*x+e)^3+12*tan(f*x+e)^4+4*I*tan(f*x+e)+33*tan(f*x+e)^2+13)/(tan(f*x+e)+I)^2/(-tan(f*x+e)+I)^5","A"
1024,1,409,204,0.266000," ","int((a+I*a*tan(f*x+e))^(9/2)/(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)}\, a^{4} \left(315 i \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 +27 i \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan^{3}\left(f x +e \right)\right)+105 \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 \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)-105 i \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 -393 i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-315 \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 -259 \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)+164 \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^4/c^2*(315*I*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+27*I*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^3+105*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*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)^4-105*I*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-393*I*(c*a)^(1/2)*(c*a*(1+tan(f*x+e)^2))^(1/2)*tan(f*x+e)-315*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-259*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2+164*(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)","A"
1025,1,379,164,0.258000," ","int((a+I*a*tan(f*x+e))^(7/2)/(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)}\, a^{3} \left(45 i \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 i \sqrt{c a}\, \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \left(\tan^{3}\left(f x +e \right)\right)+15 \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 i \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 -57 i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-45 \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 -37 \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)+23 \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^3/c^2*(45*I*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*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^3+15*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*I*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-57*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-45*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-37*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2+23*(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"
1026,1,348,124,0.238000," ","int((a+I*a*tan(f*x+e))^(5/2)/(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)}\, a^{2} \left(9 i \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 \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 \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 \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \tan \left(f x +e \right)-9 \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 \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)+4 \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*(9*I*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*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*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*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)-9*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*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2+4*(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"
1027,1,62,34,0.221000," ","int((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)}\, a \left(1+\tan^{2}\left(f x +e \right)\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*a*(1+tan(f*x+e)^2)/(tan(f*x+e)+I)^3","A"
1028,1,70,72,0.291000," ","int((a+I*a*tan(f*x+e))^(1/2)/(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(3 i \tan \left(f x +e \right)+\tan^{2}\left(f x +e \right)-2\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*(3*I*tan(f*x+e)+tan(f*x+e)^2-2)/(tan(f*x+e)+I)^3","A"
1029,1,109,112,0.296000," ","int(1/(a+I*a*tan(f*x+e))^(1/2)/(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 i \left(\tan^{3}\left(f x +e \right)\right)+2 \left(\tan^{4}\left(f x +e \right)\right)+2 i \tan \left(f x +e \right)+3 \left(\tan^{2}\left(f x +e \right)\right)+1\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/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^2/a*(2*I*tan(f*x+e)^3+2*tan(f*x+e)^4+2*I*tan(f*x+e)+3*tan(f*x+e)^2+1)/(tan(f*x+e)+I)^3/(-tan(f*x+e)+I)^2","A"
1030,1,95,85,0.253000," ","int(1/(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(1+\tan^{2}\left(f x +e \right)\right) \tan \left(f x +e \right) \left(2 \left(\tan^{2}\left(f x +e \right)\right)+3\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*(1+tan(f*x+e)^2)*tan(f*x+e)*(2*tan(f*x+e)^2+3)/(tan(f*x+e)+I)^3/(-tan(f*x+e)+I)^3","A"
1031,1,130,122,0.263000," ","int(1/(a+I*a*tan(f*x+e))^(5/2)/(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(8 i \left(\tan^{5}\left(f x +e \right)\right)-8 \left(\tan^{6}\left(f x +e \right)\right)+20 i \left(\tan^{3}\left(f x +e \right)\right)-20 \left(\tan^{4}\left(f x +e \right)\right)+12 i \tan \left(f x +e \right)-15 \left(\tan^{2}\left(f x +e \right)\right)-3\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/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*tan(f*x+e)^5-8*tan(f*x+e)^6+20*I*tan(f*x+e)^3-20*tan(f*x+e)^4+12*I*tan(f*x+e)-15*tan(f*x+e)^2-3)/(tan(f*x+e)+I)^3/(-tan(f*x+e)+I)^4","A"
1032,1,141,159,0.270000," ","int(1/(a+I*a*tan(f*x+e))^(7/2)/(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(16 i \left(\tan^{6}\left(f x +e \right)\right)-8 \left(\tan^{7}\left(f x +e \right)\right)+40 i \left(\tan^{4}\left(f x +e \right)\right)-12 \left(\tan^{5}\left(f x +e \right)\right)+30 i \left(\tan^{2}\left(f x +e \right)\right)+5 \left(\tan^{3}\left(f x +e \right)\right)+6 i+9 \tan \left(f x +e \right)\right)}{21 f \,c^{2} a^{4} \left(\tan \left(f x +e \right)+i\right)^{3} \left(-\tan \left(f x +e \right)+i\right)^{5}}"," ",0,"1/21/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^2/a^4*(16*I*tan(f*x+e)^6-8*tan(f*x+e)^7+40*I*tan(f*x+e)^4-12*tan(f*x+e)^5+30*I*tan(f*x+e)^2+5*tan(f*x+e)^3+6*I+9*tan(f*x+e))/(tan(f*x+e)+I)^3/(-tan(f*x+e)+I)^5","A"
1033,1,490,244,0.258000," ","int((a+I*a*tan(f*x+e))^(11/2)/(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)}\, a^{5} \left(1260 i \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 +60 i \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)+315 \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 -5 \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\, \left(\tan^{5}\left(f x +e \right)\right)-1260 i \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 -1964 i \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}-1890 \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 -866 \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}+496 i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+315 a c \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)+1659 \tan \left(f x +e \right) \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}\right)}{10 f \,c^{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,"-1/10/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^5/c^3*(1260*I*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+60*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^4+315*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-5*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^5-1260*I*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-1964*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-1890*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-866*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+496*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+315*a*c*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))+1659*tan(f*x+e)*(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"
1034,1,460,204,0.285000," ","int((a+I*a*tan(f*x+e))^(9/2)/(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)}\, a^{4} \left(420 i \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 i \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)+105 \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 -420 i \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 -658 i \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}-630 \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 -292 \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}+167 i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+105 a c \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)+548 \tan \left(f x +e \right) \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^4/c^3*(420*I*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*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^4+105*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-420*I*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-658*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-630*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-292*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+167*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+105*a*c*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))+548*tan(f*x+e)*(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"
1035,1,429,164,0.250000," ","int((a+I*a*tan(f*x+e))^(7/2)/(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)}\, a^{3} \left(60 i \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 \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 -60 i \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 -94 i \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 \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 \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}+26 i \sqrt{c a \left(1+\tan^{2}\left(f x +e \right)\right)}\, \sqrt{c a}+15 a c \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)+74 \tan \left(f x +e \right) \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*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*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-60*I*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-94*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)*tan(f*x+e)^2-90*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*tan(f*x+e)^3*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+26*I*(c*a*(1+tan(f*x+e)^2))^(1/2)*(c*a)^(1/2)+15*a*c*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))+74*tan(f*x+e)*(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"
1036,1,75,34,0.246000," ","int((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)}\, a^{2} \left(1+\tan^{2}\left(f x +e \right)\right) \left(-\tan \left(f x +e \right)+i\right)}{5 f \,c^{3} \left(\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"-1/5/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)*a^2/c^3*(1+tan(f*x+e)^2)*(-tan(f*x+e)+I)/(tan(f*x+e)+I)^4","B"
1037,1,71,72,0.220000," ","int((a+I*a*tan(f*x+e))^(3/2)/(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)}\, a \left(1+\tan^{2}\left(f x +e \right)\right) \left(4 i+\tan \left(f x +e \right)\right)}{15 f \,c^{3} \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*(1+tan(f*x+e)^2)*(4*I+tan(f*x+e))/(tan(f*x+e)+I)^4","A"
1038,1,83,109,0.316000," ","int((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(8 i \left(\tan^{2}\left(f x +e \right)\right)+2 \left(\tan^{3}\left(f x +e \right)\right)-7 i-13 \tan \left(f x +e \right)\right)}{15 f \,c^{3} \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*(8*I*tan(f*x+e)^2+2*tan(f*x+e)^3-7*I-13*tan(f*x+e))/(tan(f*x+e)+I)^4","A"
1039,1,118,152,0.321000," ","int(1/(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 \left(\tan^{4}\left(f x +e \right)\right)+2 \left(\tan^{5}\left(f x +e \right)\right)+6 i \left(\tan^{2}\left(f x +e \right)\right)+\tan^{3}\left(f x +e \right)+2 i-\tan \left(f x +e \right)\right)}{5 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,"1/5/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^3/a*(4*I*tan(f*x+e)^4+2*tan(f*x+e)^5+6*I*tan(f*x+e)^2+tan(f*x+e)^3+2*I-tan(f*x+e))/(tan(f*x+e)+I)^4/(-tan(f*x+e)+I)^2","A"
1040,1,130,189,0.276000," ","int(1/(a+I*a*tan(f*x+e))^(3/2)/(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 i \left(\tan^{5}\left(f x +e \right)\right)+8 \left(\tan^{6}\left(f x +e \right)\right)+20 i \left(\tan^{3}\left(f x +e \right)\right)+20 \left(\tan^{4}\left(f x +e \right)\right)+12 i \tan \left(f x +e \right)+15 \left(\tan^{2}\left(f x +e \right)\right)+3\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/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*tan(f*x+e)^5+8*tan(f*x+e)^6+20*I*tan(f*x+e)^3+20*tan(f*x+e)^4+12*I*tan(f*x+e)+15*tan(f*x+e)^2+3)/(tan(f*x+e)+I)^4/(-tan(f*x+e)+I)^3","A"
1041,1,105,130,0.283000," ","int(1/(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(1+\tan^{2}\left(f x +e \right)\right) \tan \left(f x +e \right) \left(8 \left(\tan^{4}\left(f x +e \right)\right)+20 \left(\tan^{2}\left(f x +e \right)\right)+15\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*(1+tan(f*x+e)^2)*tan(f*x+e)*(8*tan(f*x+e)^4+20*tan(f*x+e)^2+15)/(tan(f*x+e)+I)^4/(-tan(f*x+e)+I)^4","A"
1042,1,151,167,0.278000," ","int(1/(a+I*a*tan(f*x+e))^(7/2)/(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(16 i \left(\tan^{7}\left(f x +e \right)\right)-16 \left(\tan^{8}\left(f x +e \right)\right)+56 i \left(\tan^{5}\left(f x +e \right)\right)-56 \left(\tan^{6}\left(f x +e \right)\right)+70 i \left(\tan^{3}\left(f x +e \right)\right)-70 \left(\tan^{4}\left(f x +e \right)\right)+30 i \tan \left(f x +e \right)-35 \left(\tan^{2}\left(f x +e \right)\right)-5\right)}{35 f \,c^{3} a^{4} \left(\tan \left(f x +e \right)+i\right)^{4} \left(-\tan \left(f x +e \right)+i\right)^{5}}"," ",0,"1/35/f*(a*(1+I*tan(f*x+e)))^(1/2)*(-c*(-1+I*tan(f*x+e)))^(1/2)/c^3/a^4*(16*I*tan(f*x+e)^7-16*tan(f*x+e)^8+56*I*tan(f*x+e)^5-56*tan(f*x+e)^6+70*I*tan(f*x+e)^3-70*tan(f*x+e)^4+30*I*tan(f*x+e)-35*tan(f*x+e)^2-5)/(tan(f*x+e)+I)^4/(-tan(f*x+e)+I)^5","A"
1043,1,1784,126,3.961000," ","int((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^n,x)","\frac{8 i a^{4} \left(n^{3} \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i c \right) n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{6 i f x} {\mathrm e}^{6 i e}+6 n^{2} \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i c \right) n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{6 i f x} {\mathrm e}^{6 i e}+11 n \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i c \right) n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{6 i f x} {\mathrm e}^{6 i e}+3 n^{2} \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i c \right) n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{4 i f x} {\mathrm e}^{4 i e}+6 \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i c \right) n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{6 i f x} {\mathrm e}^{6 i e}+15 n \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i c \right) n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{4 i f x} {\mathrm e}^{4 i e}+18 \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i c \right) n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{4 i f x} {\mathrm e}^{4 i e}+6 n \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i c \right) n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{2 i f x} {\mathrm e}^{2 i e}+18 \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i c \right) n}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n}{2}} {\mathrm e}^{2 i f x} {\mathrm e}^{2 i e}+6 \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} c^{n} 2^{n} {\mathrm e}^{\frac{i \pi  \,\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) n \left(\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)-\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)\right) \left(-\mathrm{csgn}\left(\frac{i c}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)+\mathrm{csgn}\left(i c \right)\right)}{2}}\right)}{\left(1+n \right) f \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{3} \left(3+n \right) n \left(2+n \right)}"," ",0,"8*I*a^4/(1+n)/f/(exp(2*I*(f*x+e))+1)^3/(3+n)/n/(2+n)*(n^3/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(6*I*f*x)*exp(6*I*e)+6*n^2/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(6*I*f*x)*exp(6*I*e)+11*n/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(6*I*f*x)*exp(6*I*e)+3*n^2/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(4*I*f*x)*exp(4*I*e)+6/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(6*I*f*x)*exp(6*I*e)+15*n/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(4*I*f*x)*exp(4*I*e)+18/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(4*I*f*x)*exp(4*I*e)+6*n/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(2*I*f*x)*exp(2*I*e)+18/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^3*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I*c)*n)*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(-1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*csgn(I*c)*csgn(I/(exp(2*I*(f*x+e))+1))*n)*exp(2*I*f*x)*exp(2*I*e)+6/((exp(2*I*(f*x+e))+1)^n)*c^n*2^n*exp(1/2*I*Pi*csgn(I*c/(exp(2*I*(f*x+e))+1))*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))))","C"
1044,1,192,93,2.108000," ","int((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^n,x)","\frac{i a^{3} n \,{\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)}}{\left(1+n \right) \left(2+n \right) f}+\frac{5 i a^{3} {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)}}{\left(1+n \right) \left(2+n \right) f}+\frac{8 i a^{3} {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)}}{\left(1+n \right) \left(2+n \right) f n}-\frac{i a^{3} \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{2 a^{3} \left(3+n \right) \tan \left(f x +e \right) {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)}}{\left(1+n \right) f \left(2+n \right)}"," ",0,"I*a^3/(1+n)/(2+n)/f*n*exp(n*ln(c-I*c*tan(f*x+e)))+5*I*a^3/(1+n)/(2+n)/f*exp(n*ln(c-I*c*tan(f*x+e)))+8*I*a^3/(1+n)/(2+n)/f/n*exp(n*ln(c-I*c*tan(f*x+e)))-I/f/(2+n)*a^3*tan(f*x+e)^2*exp(n*ln(c-I*c*tan(f*x+e)))-2*a^3*(3+n)/(1+n)/f/(2+n)*tan(f*x+e)*exp(n*ln(c-I*c*tan(f*x+e)))","B"
1045,1,100,60,1.737000," ","int((a+I*a*tan(f*x+e))^2*(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^{2}}{f \left(1+n \right)}+\frac{2 i {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)} a^{2}}{f n \left(1+n \right)}-\frac{a^{2} \tan \left(f x +e \right) {\mathrm e}^{n \ln \left(c -i c \tan \left(f x +e \right)\right)}}{\left(1+n \right) f}"," ",0,"I/f/(1+n)*exp(n*ln(c-I*c*tan(f*x+e)))*a^2+2*I/f/n/(1+n)*exp(n*ln(c-I*c*tan(f*x+e)))*a^2-a^2/(1+n)/f*tan(f*x+e)*exp(n*ln(c-I*c*tan(f*x+e)))","A"
1046,1,25,24,0.164000," ","int((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x)","\frac{i a \left(c -i c \tan \left(f x +e \right)\right)^{n}}{f n}"," ",0,"I*a*(c-I*c*tan(f*x+e))^n/f/n","A"
1047,0,0,45,3.900000," ","int((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","\int \frac{\left(c -i c \tan \left(f x +e \right)\right)^{n}}{a +i a \tan \left(f x +e \right)}\, dx"," ",0,"int((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","F"
1048,0,0,45,3.920000," ","int((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","\int \frac{\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((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","F"
1049,0,0,45,4.292000," ","int((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x)","\int \frac{\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((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x)","F"
1050,0,0,58,4.028000," ","int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^n,x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \left(c -i c \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^n,x)","F"
1051,1,5385,126,2.347000," ","int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
1052,1,192,93,1.910000," ","int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^3,x)","\frac{i c^{3} \left(\tan^{2}\left(f x +e \right)\right) {\mathrm e}^{m \ln \left(a +i a \tan \left(f x +e \right)\right)}}{f \left(2+m \right)}-\frac{2 c^{3} \left(3+m \right) \tan \left(f x +e \right) {\mathrm e}^{m \ln \left(a +i a \tan \left(f x +e \right)\right)}}{f \left(1+m \right) \left(2+m \right)}-\frac{i c^{3} m \,{\mathrm e}^{m \ln \left(a +i a \tan \left(f x +e \right)\right)}}{f \left(1+m \right) \left(2+m \right)}-\frac{5 i c^{3} {\mathrm e}^{m \ln \left(a +i a \tan \left(f x +e \right)\right)}}{f \left(1+m \right) \left(2+m \right)}-\frac{8 i c^{3} {\mathrm e}^{m \ln \left(a +i a \tan \left(f x +e \right)\right)}}{f m \left(1+m \right) \left(2+m \right)}"," ",0,"I/f/(2+m)*c^3*tan(f*x+e)^2*exp(m*ln(a+I*a*tan(f*x+e)))-2*c^3*(3+m)/f/(1+m)/(2+m)*tan(f*x+e)*exp(m*ln(a+I*a*tan(f*x+e)))-I*c^3/f*m/(1+m)/(2+m)*exp(m*ln(a+I*a*tan(f*x+e)))-5*I*c^3/f/(1+m)/(2+m)*exp(m*ln(a+I*a*tan(f*x+e)))-8*I*c^3/f/m/(1+m)/(2+m)*exp(m*ln(a+I*a*tan(f*x+e)))","B"
1053,1,100,60,1.589000," ","int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^2,x)","-\frac{c^{2} \tan \left(f x +e \right) {\mathrm e}^{m \ln \left(a +i a \tan \left(f x +e \right)\right)}}{f \left(1+m \right)}-\frac{i {\mathrm e}^{m \ln \left(a +i a \tan \left(f x +e \right)\right)} c^{2}}{f \left(1+m \right)}-\frac{2 i {\mathrm e}^{m \ln \left(a +i a \tan \left(f x +e \right)\right)} c^{2}}{f m \left(1+m \right)}"," ",0,"-c^2/f/(1+m)*tan(f*x+e)*exp(m*ln(a+I*a*tan(f*x+e)))-I/f/(1+m)*exp(m*ln(a+I*a*tan(f*x+e)))*c^2-2*I/f/m/(1+m)*exp(m*ln(a+I*a*tan(f*x+e)))*c^2","A"
1054,1,25,24,0.137000," ","int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e)),x)","-\frac{i c \left(a +i a \tan \left(f x +e \right)\right)^{m}}{f m}"," ",0,"-I*c*(a+I*a*tan(f*x+e))^m/f/m","A"
1055,0,0,45,4.863000," ","int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e)),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{c -i c \tan \left(f x +e \right)}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e)),x)","F"
1056,0,0,45,1.724000," ","int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^2,x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\left(c -i c \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^2,x)","F"
1057,0,0,45,3.925000," ","int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^3,x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\left(c -i c \tan \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^3,x)","F"
1058,0,0,45,1.681000," ","int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^4,x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\left(c -i c \tan \left(f x +e \right)\right)^{4}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^4,x)","F"
1059,0,0,53,4.478000," ","int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(5/2),x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(5/2),x)","F"
1060,0,0,53,3.610000," ","int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(3/2),x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(3/2),x)","F"
1061,0,0,53,4.077000," ","int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(1/2),x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \sqrt{c -i c \tan \left(f x +e \right)}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(1/2),x)","F"
1062,0,0,53,3.430000," ","int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(1/2),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\sqrt{c -i c \tan \left(f x +e \right)}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(1/2),x)","F"
1063,0,0,53,3.532000," ","int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(3/2),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(3/2),x)","F"
1064,0,0,53,3.533000," ","int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(5/2),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\left(c -i c \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(5/2),x)","F"
1065,1,160,100,0.024000," ","int((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e)),x)","-\frac{i a^{3} \left(\tan^{3}\left(f x +e \right)\right) d}{3 f}-\frac{i a^{3} c \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{4 i a^{3} d \tan \left(f x +e \right)}{f}-\frac{3 a^{3} \left(\tan^{2}\left(f x +e \right)\right) d}{2 f}-\frac{3 a^{3} c \tan \left(f x +e \right)}{f}+\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c}{f}+\frac{2 a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d}{f}-\frac{4 i a^{3} \arctan \left(\tan \left(f x +e \right)\right) d}{f}+\frac{4 a^{3} \arctan \left(\tan \left(f x +e \right)\right) c}{f}"," ",0,"-1/3*I/f*a^3*tan(f*x+e)^3*d-1/2*I/f*a^3*c*tan(f*x+e)^2+4*I/f*a^3*d*tan(f*x+e)-3/2/f*a^3*tan(f*x+e)^2*d-3/f*a^3*c*tan(f*x+e)+2*I/f*a^3*ln(1+tan(f*x+e)^2)*c+2/f*a^3*ln(1+tan(f*x+e)^2)*d-4*I/f*a^3*arctan(tan(f*x+e))*d+4/f*a^3*arctan(tan(f*x+e))*c","A"
1066,1,123,74,0.023000," ","int((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e)),x)","-\frac{a^{2} \left(\tan^{2}\left(f x +e \right)\right) d}{2 f}-\frac{a^{2} c \tan \left(f x +e \right)}{f}+\frac{2 i a^{2} \tan \left(f x +e \right) d}{f}+\frac{i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c}{f}+\frac{a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d}{f}-\frac{2 i a^{2} \arctan \left(\tan \left(f x +e \right)\right) d}{f}+\frac{2 a^{2} \arctan \left(\tan \left(f x +e \right)\right) c}{f}"," ",0,"-1/2/f*a^2*tan(f*x+e)^2*d-a^2*c*tan(f*x+e)/f+2*I/f*a^2*tan(f*x+e)*d+I/f*a^2*ln(1+tan(f*x+e)^2)*c+1/f*a^2*ln(1+tan(f*x+e)^2)*d-2*I/f*a^2*arctan(tan(f*x+e))*d+2/f*a^2*arctan(tan(f*x+e))*c","A"
1067,1,81,43,0.022000," ","int((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e)),x)","\frac{i a d \tan \left(f x +e \right)}{f}+\frac{i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c}{2 f}+\frac{a \ln \left(1+\tan^{2}\left(f x +e \right)\right) d}{2 f}-\frac{i a \arctan \left(\tan \left(f x +e \right)\right) d}{f}+\frac{a \arctan \left(\tan \left(f x +e \right)\right) c}{f}"," ",0,"I*a*d*tan(f*x+e)/f+1/2*I/f*a*ln(1+tan(f*x+e)^2)*c+1/2/f*a*ln(1+tan(f*x+e)^2)*d-I/f*a*arctan(tan(f*x+e))*d+1/f*a*arctan(tan(f*x+e))*c","A"
1068,1,121,40,0.208000," ","int((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","\frac{\ln \left(\tan \left(f x +e \right)+i\right) d}{4 f a}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) c}{4 f a}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c}{4 f a}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) d}{4 f a}+\frac{c}{2 f a \left(\tan \left(f x +e \right)-i\right)}+\frac{i d}{2 f a \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/4/f/a*ln(tan(f*x+e)+I)*d+1/4*I/f/a*ln(tan(f*x+e)+I)*c-1/4*I/f/a*ln(tan(f*x+e)-I)*c-1/4/f/a*ln(tan(f*x+e)-I)*d+1/2/f/a/(tan(f*x+e)-I)*c+1/2*I/f/a/(tan(f*x+e)-I)*d","B"
1069,1,162,69,0.220000," ","int((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x)","\frac{\ln \left(\tan \left(f x +e \right)+i\right) d}{8 f \,a^{2}}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) c}{8 f \,a^{2}}+\frac{c}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{i d}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{i c}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{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) c}{8 f \,a^{2}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) d}{8 f \,a^{2}}"," ",0,"1/8/f/a^2*ln(tan(f*x+e)+I)*d+1/8*I/f/a^2*ln(tan(f*x+e)+I)*c+1/4/f/a^2/(tan(f*x+e)-I)*c-1/4*I/f/a^2/(tan(f*x+e)-I)*d-1/4*I/f/a^2/(tan(f*x+e)-I)^2*c+1/4/f/a^2/(tan(f*x+e)-I)^2*d-1/8*I/f/a^2*ln(tan(f*x+e)-I)*c-1/8/f/a^2*ln(tan(f*x+e)-I)*d","B"
1070,1,203,97,0.221000," ","int((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x)","\frac{\ln \left(\tan \left(f x +e \right)+i\right) d}{16 f \,a^{3}}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) c}{16 f \,a^{3}}-\frac{c}{6 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i d}{6 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{c}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{i d}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{i c}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{d}{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) c}{16 f \,a^{3}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) d}{16 f \,a^{3}}"," ",0,"1/16/f/a^3*ln(tan(f*x+e)+I)*d+1/16*I/f/a^3*ln(tan(f*x+e)+I)*c-1/6/f*c/a^3/(tan(f*x+e)-I)^3-1/6*I/f/a^3/(tan(f*x+e)-I)^3*d+1/8/f/a^3/(tan(f*x+e)-I)*c-1/8*I/f/a^3/(tan(f*x+e)-I)*d-1/8*I/f/a^3/(tan(f*x+e)-I)^2*c-1/8/f/a^3/(tan(f*x+e)-I)^2*d-1/16*I/f/a^3*ln(tan(f*x+e)-I)*c-1/16/f/a^3*ln(tan(f*x+e)-I)*d","B"
1071,1,290,137,0.023000," ","int((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x)","-\frac{i a^{3} d^{2} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}-\frac{2 i a^{3} \left(\tan^{3}\left(f x +e \right)\right) c d}{3 f}-\frac{i a^{3} \left(\tan^{2}\left(f x +e \right)\right) c^{2}}{2 f}+\frac{2 i a^{3} \left(\tan^{2}\left(f x +e \right)\right) d^{2}}{f}-\frac{a^{3} d^{2} \left(\tan^{3}\left(f x +e \right)\right)}{f}+\frac{8 i a^{3} c d \tan \left(f x +e \right)}{f}-\frac{3 a^{3} \left(\tan^{2}\left(f x +e \right)\right) c d}{f}-\frac{3 a^{3} c^{2} \tan \left(f x +e \right)}{f}+\frac{4 a^{3} \tan \left(f x +e \right) d^{2}}{f}+\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2}}{f}-\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{2}}{f}+\frac{4 a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c d}{f}-\frac{8 i a^{3} \arctan \left(\tan \left(f x +e \right)\right) c d}{f}+\frac{4 a^{3} \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f}-\frac{4 a^{3} \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f}"," ",0,"-1/4*I/f*a^3*d^2*tan(f*x+e)^4-2/3*I/f*a^3*tan(f*x+e)^3*c*d-1/2*I/f*a^3*tan(f*x+e)^2*c^2+2*I/f*a^3*tan(f*x+e)^2*d^2-1/f*a^3*d^2*tan(f*x+e)^3+8*I/f*a^3*c*d*tan(f*x+e)-3/f*a^3*tan(f*x+e)^2*c*d-3*a^3*c^2*tan(f*x+e)/f+4/f*a^3*tan(f*x+e)*d^2+2*I/f*a^3*ln(1+tan(f*x+e)^2)*c^2-2*I/f*a^3*ln(1+tan(f*x+e)^2)*d^2+4/f*a^3*ln(1+tan(f*x+e)^2)*c*d-8*I/f*a^3*arctan(tan(f*x+e))*c*d+4/f*a^3*arctan(tan(f*x+e))*c^2-4/f*a^3*arctan(tan(f*x+e))*d^2","B"
1072,1,231,107,0.023000," ","int((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x)","\frac{i a^{2} \left(\tan^{2}\left(f x +e \right)\right) d^{2}}{f}-\frac{a^{2} d^{2} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{4 i a^{2} c d \tan \left(f x +e \right)}{f}-\frac{a^{2} \left(\tan^{2}\left(f x +e \right)\right) c d}{f}-\frac{a^{2} c^{2} \tan \left(f x +e \right)}{f}+\frac{2 a^{2} \tan \left(f x +e \right) d^{2}}{f}+\frac{i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2}}{f}-\frac{i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{2}}{f}+\frac{2 a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c d}{f}-\frac{4 i a^{2} \arctan \left(\tan \left(f x +e \right)\right) c d}{f}+\frac{2 a^{2} \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f}-\frac{2 a^{2} \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f}"," ",0,"I/f*a^2*tan(f*x+e)^2*d^2-1/3/f*a^2*d^2*tan(f*x+e)^3+4*I/f*a^2*c*d*tan(f*x+e)-1/f*a^2*tan(f*x+e)^2*c*d-a^2*c^2*tan(f*x+e)/f+2/f*a^2*tan(f*x+e)*d^2+I/f*a^2*ln(1+tan(f*x+e)^2)*c^2-I/f*a^2*ln(1+tan(f*x+e)^2)*d^2+2/f*a^2*ln(1+tan(f*x+e)^2)*c*d-4*I/f*a^2*arctan(tan(f*x+e))*c*d+2/f*a^2*arctan(tan(f*x+e))*c^2-2/f*a^2*arctan(tan(f*x+e))*d^2","B"
1073,1,156,71,0.021000," ","int((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^2,x)","\frac{i a \,d^{2} \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{2 i a c d \tan \left(f x +e \right)}{f}+\frac{a \tan \left(f x +e \right) d^{2}}{f}-\frac{i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{2}}{2 f}+\frac{i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2}}{2 f}+\frac{a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c d}{f}-\frac{2 i a \arctan \left(\tan \left(f x +e \right)\right) c d}{f}+\frac{a \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f}-\frac{a \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f}"," ",0,"1/2*I/f*a*d^2*tan(f*x+e)^2+2*I/f*a*c*d*tan(f*x+e)+1/f*a*tan(f*x+e)*d^2-1/2*I/f*a*ln(1+tan(f*x+e)^2)*d^2+1/2*I/f*a*ln(1+tan(f*x+e)^2)*c^2+1/f*a*ln(1+tan(f*x+e)^2)*c*d-2*I/f*a*arctan(tan(f*x+e))*c*d+1/f*a*arctan(tan(f*x+e))*c^2-1/f*a*arctan(tan(f*x+e))*d^2","B"
1074,1,196,66,0.220000," ","int((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x)","\frac{\ln \left(\tan \left(f x +e \right)+i\right) c d}{2 f a}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) c^{2}}{4 f a}-\frac{i \ln \left(\tan \left(f x +e \right)+i\right) d^{2}}{4 f a}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) c d}{2 f a}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{2}}{4 f a}-\frac{3 i \ln \left(\tan \left(f x +e \right)-i\right) d^{2}}{4 f a}+\frac{i c d}{f a \left(\tan \left(f x +e \right)-i\right)}+\frac{c^{2}}{2 f a \left(\tan \left(f x +e \right)-i\right)}-\frac{d^{2}}{2 f a \left(\tan \left(f x +e \right)-i\right)}"," ",0,"1/2/f/a*ln(tan(f*x+e)+I)*c*d+1/4*I/f/a*ln(tan(f*x+e)+I)*c^2-1/4*I/f/a*ln(tan(f*x+e)+I)*d^2-1/2/f/a*ln(tan(f*x+e)-I)*c*d-1/4*I/f/a*ln(tan(f*x+e)-I)*c^2-3/4*I/f/a*ln(tan(f*x+e)-I)*d^2+I/f/a/(tan(f*x+e)-I)*c*d+1/2/f/a/(tan(f*x+e)-I)*c^2-1/2/f/a/(tan(f*x+e)-I)*d^2","B"
1075,1,263,78,0.218000," ","int((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x)","\frac{\ln \left(\tan \left(f x +e \right)+i\right) c d}{4 f \,a^{2}}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) c^{2}}{8 f \,a^{2}}-\frac{i \ln \left(\tan \left(f x +e \right)+i\right) d^{2}}{8 f \,a^{2}}-\frac{i c d}{2 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{c^{2}}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{3 d^{2}}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{c d}{2 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i c^{2}}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{i d^{2}}{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) d^{2}}{8 f \,a^{2}}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{2}}{8 f \,a^{2}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) c d}{4 f \,a^{2}}"," ",0,"1/4/f/a^2*ln(tan(f*x+e)+I)*c*d+1/8*I/f/a^2*ln(tan(f*x+e)+I)*c^2-1/8*I/f/a^2*ln(tan(f*x+e)+I)*d^2-1/2*I/f/a^2/(tan(f*x+e)-I)*c*d+1/4/f/a^2/(tan(f*x+e)-I)*c^2+3/4/f/a^2/(tan(f*x+e)-I)*d^2+1/2/f/a^2/(tan(f*x+e)-I)^2*c*d-1/4*I/f/a^2/(tan(f*x+e)-I)^2*c^2+1/4*I/f/a^2/(tan(f*x+e)-I)^2*d^2+1/8*I/f/a^2*ln(tan(f*x+e)-I)*d^2-1/8*I/f/a^2*ln(tan(f*x+e)-I)*c^2-1/4/f/a^2*ln(tan(f*x+e)-I)*c*d","B"
1076,1,329,111,0.211000," ","int((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x)","\frac{\ln \left(\tan \left(f x +e \right)+i\right) c d}{8 f \,a^{3}}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) c^{2}}{16 f \,a^{3}}-\frac{i \ln \left(\tan \left(f x +e \right)+i\right) d^{2}}{16 f \,a^{3}}-\frac{c d}{4 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i c^{2}}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{3 i d^{2}}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i c d}{4 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{c^{2}}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{d^{2}}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{d^{2}}{6 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i c d}{3 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{c^{2}}{6 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{2}}{16 f \,a^{3}}+\frac{i \ln \left(\tan \left(f x +e \right)-i\right) d^{2}}{16 f \,a^{3}}-\frac{\ln \left(\tan \left(f x +e \right)-i\right) c d}{8 f \,a^{3}}"," ",0,"1/8/f/a^3*ln(tan(f*x+e)+I)*c*d+1/16*I/f/a^3*ln(tan(f*x+e)+I)*c^2-1/16*I/f/a^3*ln(tan(f*x+e)+I)*d^2-1/4/f/a^3/(tan(f*x+e)-I)^2*c*d-1/8*I/f/a^3/(tan(f*x+e)-I)^2*c^2-3/8*I/f/a^3/(tan(f*x+e)-I)^2*d^2-1/4*I/f/a^3/(tan(f*x+e)-I)*c*d+1/8/f/a^3/(tan(f*x+e)-I)*c^2-1/8/f/a^3/(tan(f*x+e)-I)*d^2+1/6/f/a^3/(tan(f*x+e)-I)^3*d^2-1/3*I/f/a^3/(tan(f*x+e)-I)^3*c*d-1/6/f/a^3/(tan(f*x+e)-I)^3*c^2-1/16*I/f/a^3*ln(tan(f*x+e)-I)*c^2+1/16*I/f/a^3*ln(tan(f*x+e)-I)*d^2-1/8/f/a^3*ln(tan(f*x+e)-I)*c*d","B"
1077,1,443,176,0.025000," ","int((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x)","-\frac{4 i a^{3} d^{3} \tan \left(f x +e \right)}{f}-\frac{i a^{3} d^{3} \left(\tan^{5}\left(f x +e \right)\right)}{5 f}+\frac{4 i a^{3} \arctan \left(\tan \left(f x +e \right)\right) d^{3}}{f}-\frac{i a^{3} \left(\tan^{2}\left(f x +e \right)\right) c^{3}}{2 f}-\frac{3 a^{3} d^{3} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{12 i a^{3} c^{2} d \tan \left(f x +e \right)}{f}-\frac{i a^{3} \left(\tan^{3}\left(f x +e \right)\right) c^{2} d}{f}-\frac{3 a^{3} \left(\tan^{3}\left(f x +e \right)\right) c \,d^{2}}{f}-\frac{3 i a^{3} \left(\tan^{4}\left(f x +e \right)\right) c \,d^{2}}{4 f}+\frac{4 i a^{3} \left(\tan^{3}\left(f x +e \right)\right) d^{3}}{3 f}-\frac{9 a^{3} \left(\tan^{2}\left(f x +e \right)\right) c^{2} d}{2 f}+\frac{2 a^{3} \left(\tan^{2}\left(f x +e \right)\right) d^{3}}{f}-\frac{3 a^{3} c^{3} \tan \left(f x +e \right)}{f}+\frac{12 a^{3} \tan \left(f x +e \right) c \,d^{2}}{f}-\frac{12 i a^{3} \arctan \left(\tan \left(f x +e \right)\right) c^{2} d}{f}+\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3}}{f}+\frac{6 a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} d}{f}-\frac{2 a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{3}}{f}-\frac{6 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{f}+\frac{6 i a^{3} \left(\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{f}+\frac{4 a^{3} \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f}-\frac{12 a^{3} \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f}"," ",0,"-4*I/f*a^3*d^3*tan(f*x+e)-1/5*I/f*a^3*d^3*tan(f*x+e)^5+4*I/f*a^3*arctan(tan(f*x+e))*d^3-1/2*I/f*a^3*tan(f*x+e)^2*c^3-3/4/f*a^3*d^3*tan(f*x+e)^4+12*I/f*a^3*c^2*d*tan(f*x+e)-I/f*a^3*tan(f*x+e)^3*c^2*d-3/f*a^3*tan(f*x+e)^3*c*d^2-3/4*I/f*a^3*tan(f*x+e)^4*c*d^2+4/3*I/f*a^3*tan(f*x+e)^3*d^3-9/2/f*a^3*tan(f*x+e)^2*c^2*d+2/f*a^3*tan(f*x+e)^2*d^3-3*a^3*c^3*tan(f*x+e)/f+12/f*a^3*tan(f*x+e)*c*d^2-12*I/f*a^3*arctan(tan(f*x+e))*c^2*d+2*I/f*a^3*ln(1+tan(f*x+e)^2)*c^3+6/f*a^3*ln(1+tan(f*x+e)^2)*c^2*d-2/f*a^3*ln(1+tan(f*x+e)^2)*d^3-6*I/f*a^3*ln(1+tan(f*x+e)^2)*c*d^2+6*I/f*a^3*tan(f*x+e)^2*c*d^2+4/f*a^3*arctan(tan(f*x+e))*c^3-12/f*a^3*arctan(tan(f*x+e))*c*d^2","B"
1078,1,360,131,0.024000," ","int((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x)","\frac{3 i a^{2} \left(\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{f}-\frac{a^{2} d^{3} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{2 i a^{2} \arctan \left(\tan \left(f x +e \right)\right) d^{3}}{f}-\frac{a^{2} \left(\tan^{3}\left(f x +e \right)\right) c \,d^{2}}{f}+\frac{2 i a^{2} \left(\tan^{3}\left(f x +e \right)\right) d^{3}}{3 f}+\frac{i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3}}{f}-\frac{3 a^{2} \left(\tan^{2}\left(f x +e \right)\right) c^{2} d}{2 f}+\frac{a^{2} \left(\tan^{2}\left(f x +e \right)\right) d^{3}}{f}-\frac{a^{2} c^{3} \tan \left(f x +e \right)}{f}+\frac{6 a^{2} \tan \left(f x +e \right) c \,d^{2}}{f}-\frac{2 i a^{2} d^{3} \tan \left(f x +e \right)}{f}+\frac{6 i a^{2} c^{2} d \tan \left(f x +e \right)}{f}+\frac{3 a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} d}{f}-\frac{a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{3}}{f}-\frac{3 i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{f}-\frac{6 i a^{2} \arctan \left(\tan \left(f x +e \right)\right) c^{2} d}{f}+\frac{2 a^{2} \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f}-\frac{6 a^{2} \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f}"," ",0,"3*I/f*a^2*tan(f*x+e)^2*c*d^2-1/4/f*a^2*d^3*tan(f*x+e)^4+2*I/f*a^2*arctan(tan(f*x+e))*d^3-1/f*a^2*tan(f*x+e)^3*c*d^2+2/3*I/f*a^2*tan(f*x+e)^3*d^3+I/f*a^2*ln(1+tan(f*x+e)^2)*c^3-3/2/f*a^2*tan(f*x+e)^2*c^2*d+1/f*a^2*tan(f*x+e)^2*d^3-a^2*c^3*tan(f*x+e)/f+6/f*a^2*tan(f*x+e)*c*d^2-2*I/f*a^2*d^3*tan(f*x+e)+6*I/f*a^2*c^2*d*tan(f*x+e)+3/f*a^2*ln(1+tan(f*x+e)^2)*c^2*d-1/f*a^2*ln(1+tan(f*x+e)^2)*d^3-3*I/f*a^2*ln(1+tan(f*x+e)^2)*c*d^2-6*I/f*a^2*arctan(tan(f*x+e))*c^2*d+2/f*a^2*arctan(tan(f*x+e))*c^3-6/f*a^2*arctan(tan(f*x+e))*c*d^2","B"
1079,1,256,97,0.024000," ","int((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^3,x)","\frac{i a \,d^{3} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{3 i a \left(\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{2 f}+\frac{3 i a \,c^{2} d \tan \left(f x +e \right)}{f}-\frac{i a \,d^{3} \tan \left(f x +e \right)}{f}+\frac{a \left(\tan^{2}\left(f x +e \right)\right) d^{3}}{2 f}+\frac{3 a \tan \left(f x +e \right) c \,d^{2}}{f}-\frac{3 i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{2 f}-\frac{a \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{3}}{2 f}+\frac{i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3}}{2 f}+\frac{3 a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} d}{2 f}-\frac{3 i a \arctan \left(\tan \left(f x +e \right)\right) c^{2} d}{f}+\frac{i a \arctan \left(\tan \left(f x +e \right)\right) d^{3}}{f}+\frac{a \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f}-\frac{3 a \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f}"," ",0,"1/3*I/f*a*d^3*tan(f*x+e)^3+3/2*I/f*a*tan(f*x+e)^2*c*d^2+3*I/f*a*c^2*d*tan(f*x+e)-I/f*a*d^3*tan(f*x+e)+1/2/f*a*tan(f*x+e)^2*d^3+3/f*a*tan(f*x+e)*c*d^2-3/2*I/f*a*ln(1+tan(f*x+e)^2)*c*d^2-1/2/f*a*ln(1+tan(f*x+e)^2)*d^3+1/2*I/f*a*ln(1+tan(f*x+e)^2)*c^3+3/2/f*a*ln(1+tan(f*x+e)^2)*c^2*d-3*I/f*a*arctan(tan(f*x+e))*c^2*d+I/f*a*arctan(tan(f*x+e))*d^3+1/f*a*arctan(tan(f*x+e))*c^3-3/f*a*arctan(tan(f*x+e))*c*d^2","B"
1080,1,288,117,0.187000," ","int((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x)","-\frac{i d^{3} \tan \left(f x +e \right)}{f a}+\frac{3 \ln \left(\tan \left(f x +e \right)+i\right) c^{2} d}{4 f a}-\frac{\ln \left(\tan \left(f x +e \right)+i\right) d^{3}}{4 f a}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) c^{3}}{4 f a}-\frac{3 i \ln \left(\tan \left(f x +e \right)+i\right) c \,d^{2}}{4 f a}-\frac{3 \ln \left(\tan \left(f x +e \right)-i\right) c^{2} d}{4 f a}+\frac{5 \ln \left(\tan \left(f x +e \right)-i\right) d^{3}}{4 f a}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{3}}{4 f a}-\frac{9 i \ln \left(\tan \left(f x +e \right)-i\right) c \,d^{2}}{4 f a}+\frac{3 i c^{2} d}{2 f a \left(\tan \left(f x +e \right)-i\right)}-\frac{i d^{3}}{2 f a \left(\tan \left(f x +e \right)-i\right)}+\frac{c^{3}}{2 f a \left(\tan \left(f x +e \right)-i\right)}-\frac{3 c \,d^{2}}{2 f a \left(\tan \left(f x +e \right)-i\right)}"," ",0,"-I/f/a*d^3*tan(f*x+e)+3/4/f/a*ln(tan(f*x+e)+I)*c^2*d-1/4/f/a*ln(tan(f*x+e)+I)*d^3+1/4*I/f/a*ln(tan(f*x+e)+I)*c^3-3/4*I/f/a*ln(tan(f*x+e)+I)*c*d^2-3/4/f/a*ln(tan(f*x+e)-I)*c^2*d+5/4/f/a*ln(tan(f*x+e)-I)*d^3-1/4*I/f/a*ln(tan(f*x+e)-I)*c^3-9/4*I/f/a*ln(tan(f*x+e)-I)*c*d^2+3/2*I/f/a/(tan(f*x+e)-I)*c^2*d-1/2*I/f/a/(tan(f*x+e)-I)*d^3+1/2/f/a/(tan(f*x+e)-I)*c^3-3/2/f/a/(tan(f*x+e)-I)*c*d^2","B"
1081,1,362,123,0.289000," ","int((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x)","\frac{3 \ln \left(\tan \left(f x +e \right)+i\right) c^{2} d}{8 f \,a^{2}}-\frac{\ln \left(\tan \left(f x +e \right)+i\right) d^{3}}{8 f \,a^{2}}-\frac{3 i c^{2} d}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{3 i c \,d^{2}}{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) c^{3}}{8 f \,a^{2}}+\frac{5 i d^{3}}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{c^{3}}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{9 c \,d^{2}}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)}+\frac{3 c^{2} d}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{d^{3}}{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) c^{3}}{8 f \,a^{2}}+\frac{3 i \ln \left(\tan \left(f x +e \right)-i\right) c \,d^{2}}{8 f \,a^{2}}-\frac{3 i \ln \left(\tan \left(f x +e \right)+i\right) c \,d^{2}}{8 f \,a^{2}}-\frac{i c^{3}}{4 f \,a^{2} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{3 \ln \left(\tan \left(f x +e \right)-i\right) c^{2} d}{8 f \,a^{2}}-\frac{7 \ln \left(\tan \left(f x +e \right)-i\right) d^{3}}{8 f \,a^{2}}"," ",0,"3/8/f/a^2*ln(tan(f*x+e)+I)*c^2*d-1/8/f/a^2*ln(tan(f*x+e)+I)*d^3-3/4*I/f/a^2/(tan(f*x+e)-I)*c^2*d+3/4*I/f/a^2/(tan(f*x+e)-I)^2*c*d^2+1/8*I/f/a^2*ln(tan(f*x+e)+I)*c^3+5/4*I/f/a^2/(tan(f*x+e)-I)*d^3+1/4/f/a^2/(tan(f*x+e)-I)*c^3+9/4/f/a^2/(tan(f*x+e)-I)*c*d^2+3/4/f/a^2/(tan(f*x+e)-I)^2*c^2*d-1/4/f/a^2/(tan(f*x+e)-I)^2*d^3-1/8*I/f/a^2*ln(tan(f*x+e)-I)*c^3+3/8*I/f/a^2*ln(tan(f*x+e)-I)*c*d^2-3/8*I/f/a^2*ln(tan(f*x+e)+I)*c*d^2-1/4*I/f/a^2/(tan(f*x+e)-I)^2*c^3-3/8/f/a^2*ln(tan(f*x+e)-I)*c^2*d-7/8/f/a^2*ln(tan(f*x+e)-I)*d^3","B"
1082,1,454,122,0.249000," ","int((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x)","\frac{3 \ln \left(\tan \left(f x +e \right)+i\right) c^{2} d}{16 f \,a^{3}}-\frac{\ln \left(\tan \left(f x +e \right)+i\right) d^{3}}{16 f \,a^{3}}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right) c^{3}}{16 f \,a^{3}}-\frac{i c^{2} d}{2 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{c^{3}}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{3 c \,d^{2}}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{3 i c^{2} d}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{i d^{3}}{6 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{3 i \ln \left(\tan \left(f x +e \right)-i\right) c \,d^{2}}{16 f \,a^{3}}+\frac{c \,d^{2}}{2 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{9 i c \,d^{2}}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{c^{3}}{6 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{7 i d^{3}}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{\ln \left(\tan \left(f x +e \right)-i\right) d^{3}}{16 f \,a^{3}}-\frac{3 i \ln \left(\tan \left(f x +e \right)+i\right) c \,d^{2}}{16 f \,a^{3}}-\frac{3 \ln \left(\tan \left(f x +e \right)-i\right) c^{2} d}{16 f \,a^{3}}-\frac{3 c^{2} d}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{5 d^{3}}{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) c^{3}}{16 f \,a^{3}}-\frac{i c^{3}}{8 f \,a^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}"," ",0,"3/16/f/a^3*ln(tan(f*x+e)+I)*c^2*d-1/16/f/a^3*ln(tan(f*x+e)+I)*d^3+1/16*I/f/a^3*ln(tan(f*x+e)+I)*c^3-1/2*I/f/a^3/(tan(f*x+e)-I)^3*c^2*d+1/8/f/a^3/(tan(f*x+e)-I)*c^3-3/8/f/a^3/(tan(f*x+e)-I)*c*d^2-3/8*I/f/a^3/(tan(f*x+e)-I)*c^2*d+1/6*I/f/a^3/(tan(f*x+e)-I)^3*d^3+3/16*I/f/a^3*ln(tan(f*x+e)-I)*c*d^2+1/2/f/a^3/(tan(f*x+e)-I)^3*c*d^2-9/8*I/f/a^3/(tan(f*x+e)-I)^2*c*d^2-1/6/f/a^3/(tan(f*x+e)-I)^3*c^3-7/8*I/f/a^3/(tan(f*x+e)-I)*d^3+1/16/f/a^3*ln(tan(f*x+e)-I)*d^3-3/16*I/f/a^3*ln(tan(f*x+e)+I)*c*d^2-3/16/f/a^3*ln(tan(f*x+e)-I)*c^2*d-3/8/f/a^3/(tan(f*x+e)-I)^2*c^2*d+5/8/f/a^3/(tan(f*x+e)-I)^2*d^3-1/16*I/f/a^3*ln(tan(f*x+e)-I)*c^3-1/8*I/f/a^3/(tan(f*x+e)-I)^2*c^3","B"
1083,1,257,111,0.207000," ","int((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x)","-\frac{i a^{3} \tan \left(f x +e \right)}{f d}+\frac{i a^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right)}-\frac{3 i a^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}-\frac{3 a^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2}}{f d \left(c^{2}+d^{2}\right)}+\frac{a^{3} d \ln \left(c +d \tan \left(f x +e \right)\right)}{f \left(c^{2}+d^{2}\right)}+\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}+\frac{4 i a^{3} \arctan \left(\tan \left(f x +e \right)\right) d}{f \left(c^{2}+d^{2}\right)}-\frac{2 a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d}{f \left(c^{2}+d^{2}\right)}+\frac{4 a^{3} \arctan \left(\tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}"," ",0,"-I/f*a^3/d*tan(f*x+e)+I/f*a^3/d^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*c^3-3*I/f*a^3/(c^2+d^2)*ln(c+d*tan(f*x+e))*c-3/f*a^3/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*c^2+1/f*a^3*d/(c^2+d^2)*ln(c+d*tan(f*x+e))+2*I/f*a^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*c+4*I/f*a^3/(c^2+d^2)*arctan(tan(f*x+e))*d-2/f*a^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*d+4/f*a^3/(c^2+d^2)*arctan(tan(f*x+e))*c","B"
1084,1,204,101,0.241000," ","int((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x)","-\frac{2 i a^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}-\frac{a^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right) d}+\frac{a^{2} d \ln \left(c +d \tan \left(f x +e \right)\right)}{f \left(c^{2}+d^{2}\right)}+\frac{2 i a^{2} \arctan \left(\tan \left(f x +e \right)\right) d}{f \left(c^{2}+d^{2}\right)}+\frac{i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}+\frac{2 a^{2} \arctan \left(\tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}-\frac{a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d}{f \left(c^{2}+d^{2}\right)}"," ",0,"-2*I/f*a^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*c-1/f*a^2/(c^2+d^2)/d*ln(c+d*tan(f*x+e))*c^2+1/f*a^2/(c^2+d^2)*d*ln(c+d*tan(f*x+e))+2*I/f*a^2/(c^2+d^2)*arctan(tan(f*x+e))*d+I/f*a^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*c+2/f*a^2/(c^2+d^2)*arctan(tan(f*x+e))*c-1/f*a^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*d","B"
1085,1,157,43,0.220000," ","int((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x)","-\frac{i a \ln \left(c +d \tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}+\frac{a \ln \left(c +d \tan \left(f x +e \right)\right) d}{f \left(c^{2}+d^{2}\right)}+\frac{i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c}{2 f \left(c^{2}+d^{2}\right)}-\frac{a \ln \left(1+\tan^{2}\left(f x +e \right)\right) d}{2 f \left(c^{2}+d^{2}\right)}+\frac{i a \arctan \left(\tan \left(f x +e \right)\right) d}{f \left(c^{2}+d^{2}\right)}+\frac{a \arctan \left(\tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}"," ",0,"-I/f*a/(c^2+d^2)*ln(c+d*tan(f*x+e))*c+1/f*a/(c^2+d^2)*ln(c+d*tan(f*x+e))*d+1/2*I/f*a/(c^2+d^2)*ln(1+tan(f*x+e)^2)*c-1/2/f*a/(c^2+d^2)*ln(1+tan(f*x+e)^2)*d+I/f*a/(c^2+d^2)*arctan(tan(f*x+e))*d+1/f*a/(c^2+d^2)*arctan(tan(f*x+e))*c","B"
1086,1,155,119,0.285000," ","int(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x)","-\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{f a \left(4 i d -4 c \right)}-\frac{i d^{2} \ln \left(c +d \tan \left(f x +e \right)\right)}{f a \left(i d -c \right) \left(i d +c \right)^{2}}+\frac{1}{f a \left(2 i d +2 c \right) \left(\tan \left(f x +e \right)-i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c}{4 f a \left(i d +c \right)^{2}}+\frac{3 \ln \left(\tan \left(f x +e \right)-i\right) d}{4 f a \left(i d +c \right)^{2}}"," ",0,"-I/f/a/(4*I*d-4*c)*ln(tan(f*x+e)+I)-I/f/a*d^2/(I*d-c)/(c+I*d)^2*ln(c+d*tan(f*x+e))+1/f/a/(2*I*d+2*c)/(tan(f*x+e)-I)-1/4*I/f/a/(c+I*d)^2*ln(tan(f*x+e)-I)*c+3/4/f/a/(c+I*d)^2*ln(tan(f*x+e)-I)*d","A"
1087,1,339,157,0.337000," ","int(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x)","-\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{f \,a^{2} \left(8 i d -8 c \right)}+\frac{d^{3} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \,a^{2} \left(i d -c \right) \left(i d +c \right)^{3}}+\frac{i c d}{f \,a^{2} \left(i d +c \right)^{3} \left(\tan \left(f x +e \right)-i\right)}+\frac{c^{2}}{4 f \,a^{2} \left(i d +c \right)^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{3 d^{2}}{4 f \,a^{2} \left(i d +c \right)^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{i c^{2}}{4 f \,a^{2} \left(i d +c \right)^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{i d^{2}}{4 f \,a^{2} \left(i d +c \right)^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{c d}{2 f \,a^{2} \left(i d +c \right)^{3} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{2}}{8 f \,a^{2} \left(i d +c \right)^{3}}+\frac{7 i \ln \left(\tan \left(f x +e \right)-i\right) d^{2}}{8 f \,a^{2} \left(i d +c \right)^{3}}+\frac{\ln \left(\tan \left(f x +e \right)-i\right) c d}{2 f \,a^{2} \left(i d +c \right)^{3}}"," ",0,"-I/f/a^2/(8*I*d-8*c)*ln(tan(f*x+e)+I)+1/f/a^2*d^3/(I*d-c)/(c+I*d)^3*ln(c+d*tan(f*x+e))+I/f/a^2/(c+I*d)^3/(tan(f*x+e)-I)*c*d+1/4/f/a^2/(c+I*d)^3/(tan(f*x+e)-I)*c^2-3/4/f/a^2/(c+I*d)^3/(tan(f*x+e)-I)*d^2-1/4*I/f/a^2/(c+I*d)^3/(tan(f*x+e)-I)^2*c^2+1/4*I/f/a^2/(c+I*d)^3/(tan(f*x+e)-I)^2*d^2+1/2/f/a^2/(c+I*d)^3/(tan(f*x+e)-I)^2*c*d-1/8*I/f/a^2/(c+I*d)^3*ln(tan(f*x+e)-I)*c^2+7/8*I/f/a^2/(c+I*d)^3*ln(tan(f*x+e)-I)*d^2+1/2/f/a^2/(c+I*d)^3*ln(tan(f*x+e)-I)*c*d","B"
1088,1,564,212,0.355000," ","int(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x)","\frac{5 i c^{2} d}{8 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)}+\frac{i d^{4} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \,a^{3} \left(i d -c \right) \left(i d +c \right)^{4}}-\frac{i c^{3}}{8 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{7 i d^{3}}{8 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)}-\frac{c^{3}}{6 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{c \,d^{2}}{2 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i c^{2} d}{2 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{3}}{16 f \,a^{3} \left(i d +c \right)^{4}}+\frac{c^{3}}{8 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)}-\frac{11 c \,d^{2}}{8 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)}+\frac{i d^{3}}{6 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{f \,a^{3} \left(16 i d -16 c \right)}+\frac{5 c^{2} d}{8 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{3 d^{3}}{8 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{7 i c \,d^{2}}{8 f \,a^{3} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{11 i \ln \left(\tan \left(f x +e \right)-i\right) c \,d^{2}}{16 f \,a^{3} \left(i d +c \right)^{4}}+\frac{5 \ln \left(\tan \left(f x +e \right)-i\right) c^{2} d}{16 f \,a^{3} \left(i d +c \right)^{4}}-\frac{15 \ln \left(\tan \left(f x +e \right)-i\right) d^{3}}{16 f \,a^{3} \left(i d +c \right)^{4}}"," ",0,"5/8*I/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)*c^2*d+I/f/a^3*d^4/(I*d-c)/(c+I*d)^4*ln(c+d*tan(f*x+e))-1/8*I/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)^2*c^3-7/8*I/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)*d^3-1/6/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)^3*c^3+1/2/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)^3*c*d^2-1/2*I/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)^3*c^2*d-1/16*I/f/a^3/(c+I*d)^4*ln(tan(f*x+e)-I)*c^3+1/8/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)*c^3-11/8/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)*c*d^2+1/6*I/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)^3*d^3-I/f/a^3/(16*I*d-16*c)*ln(tan(f*x+e)+I)+5/8/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)^2*c^2*d-3/8/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)^2*d^3+7/8*I/f/a^3/(c+I*d)^4/(tan(f*x+e)-I)^2*c*d^2+11/16*I/f/a^3/(c+I*d)^4*ln(tan(f*x+e)-I)*c*d^2+5/16/f/a^3/(c+I*d)^4*ln(tan(f*x+e)-I)*c^2*d-15/16/f/a^3/(c+I*d)^4*ln(tan(f*x+e)-I)*d^3","B"
1089,1,438,134,0.300000," ","int((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x)","-\frac{i a^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c^{4}}{f \left(c^{2}+d^{2}\right)^{2} d^{2}}-\frac{6 i a^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 i a^{3} d^{2} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{8 a^{3} d \ln \left(c +d \tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{i a^{3} c^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 i a^{3} c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 a^{3} c^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{a^{3} d}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{8 i a^{3} \arctan \left(\tan \left(f x +e \right)\right) c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{4 a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{4 a^{3} \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{4 a^{3} \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"-I/f*a^3/(c^2+d^2)^2/d^2*ln(c+d*tan(f*x+e))*c^4-6*I/f*a^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c^2+3*I/f*a^3/(c^2+d^2)^2*d^2*ln(c+d*tan(f*x+e))+8/f*a^3/(c^2+d^2)^2*d*ln(c+d*tan(f*x+e))*c-I/f*a^3/d^2/(c^2+d^2)/(c+d*tan(f*x+e))*c^3+3*I/f*a^3/(c^2+d^2)/(c+d*tan(f*x+e))*c+3/f*a^3/d/(c^2+d^2)/(c+d*tan(f*x+e))*c^2-1/f*a^3*d/(c^2+d^2)/(c+d*tan(f*x+e))+2*I/f*a^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*c^2-2*I/f*a^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*d^2+8*I/f*a^3/(c^2+d^2)^2*arctan(tan(f*x+e))*c*d-4/f*a^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*c*d+4/f*a^3/(c^2+d^2)^2*arctan(tan(f*x+e))*c^2-4/f*a^3/(c^2+d^2)^2*arctan(tan(f*x+e))*d^2","B"
1090,1,366,88,0.240000," ","int((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x)","\frac{2 i a^{2} c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{a^{2} c^{2}}{f \left(c^{2}+d^{2}\right) d \left(c +d \tan \left(f x +e \right)\right)}-\frac{a^{2} d}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{2 i a^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 i a^{2} \ln \left(c +d \tan \left(f x +e \right)\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{4 a^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{4 i a^{2} \arctan \left(\tan \left(f x +e \right)\right) c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 a^{2} \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 a^{2} \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c d}{f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"2*I/f*a^2/(c^2+d^2)/(c+d*tan(f*x+e))*c+1/f*a^2/(c^2+d^2)/d/(c+d*tan(f*x+e))*c^2-1/f*a^2/(c^2+d^2)*d/(c+d*tan(f*x+e))-2*I/f*a^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c^2+2*I/f*a^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*d^2+4/f*a^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c*d+4*I/f*a^2/(c^2+d^2)^2*arctan(tan(f*x+e))*c*d+I/f*a^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*c^2-I/f*a^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*d^2+2/f*a^2/(c^2+d^2)^2*arctan(tan(f*x+e))*c^2-2/f*a^2/(c^2+d^2)^2*arctan(tan(f*x+e))*d^2-2/f*a^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*c*d","B"
1091,1,309,71,0.266000," ","int((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x)","-\frac{i a \ln \left(c +d \tan \left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{i a \ln \left(c +d \tan \left(f x +e \right)\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 a \ln \left(c +d \tan \left(f x +e \right)\right) c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{i a c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{a d}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 i a \arctan \left(\tan \left(f x +e \right)\right) c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{a \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{a \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"-I/f*a/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c^2+I/f*a/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*d^2+2/f*a/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c*d+I/f*a/(c^2+d^2)/(c+d*tan(f*x+e))*c-1/f*a/(c^2+d^2)/(c+d*tan(f*x+e))*d-1/f*a/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*c*d+1/2*I/f*a/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*c^2-1/2*I/f*a/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*d^2+2*I/f*a/(c^2+d^2)^2*arctan(tan(f*x+e))*c*d+1/f*a/(c^2+d^2)^2*arctan(tan(f*x+e))*c^2-1/f*a/(c^2+d^2)^2*arctan(tan(f*x+e))*d^2","B"
1092,1,281,184,0.319000," ","int(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x)","\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{4 f a \left(i d -c \right)^{2}}+\frac{3 i d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{3}}+\frac{d^{3} \ln \left(c +d \tan \left(f x +e \right)\right)}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{3}}-\frac{i d^{2} c^{2}}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{3} \left(c +d \tan \left(f x +e \right)\right)}-\frac{i d^{4}}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{3} \left(c +d \tan \left(f x +e \right)\right)}+\frac{1}{2 f a \left(i d +c \right)^{2} \left(\tan \left(f x +e \right)-i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c}{4 f a \left(i d +c \right)^{3}}+\frac{5 \ln \left(\tan \left(f x +e \right)-i\right) d}{4 f a \left(i d +c \right)^{3}}"," ",0,"1/4*I/f/a/(I*d-c)^2*ln(tan(f*x+e)+I)+3*I/f/a*d^2/(I*d-c)^2/(c+I*d)^3*ln(c+d*tan(f*x+e))*c+1/f/a*d^3/(I*d-c)^2/(c+I*d)^3*ln(c+d*tan(f*x+e))-I/f/a*d^2/(I*d-c)^2/(c+I*d)^3/(c+d*tan(f*x+e))*c^2-I/f/a*d^4/(I*d-c)^2/(c+I*d)^3/(c+d*tan(f*x+e))+1/2/f/a/(c+I*d)^2/(tan(f*x+e)-I)-1/4*I/f/a/(c+I*d)^3*ln(tan(f*x+e)-I)*c+5/4/f/a/(c+I*d)^3*ln(tan(f*x+e)-I)*d","A"
1093,1,465,248,0.348000," ","int(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x)","\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{8 f \,a^{2} \left(i d -c \right)^{2}}+\frac{2 i d^{4} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{4}}-\frac{4 d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{4}}+\frac{d^{3} c^{2}}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)}+\frac{d^{5}}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)}-\frac{i c^{2}}{4 f \,a^{2} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{i d^{2}}{4 f \,a^{2} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{c d}{2 f \,a^{2} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{3 i c d}{2 f \,a^{2} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)}+\frac{c^{2}}{4 f \,a^{2} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)}-\frac{5 d^{2}}{4 f \,a^{2} \left(i d +c \right)^{4} \left(\tan \left(f x +e \right)-i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{2}}{8 f \,a^{2} \left(i d +c \right)^{4}}+\frac{17 i \ln \left(\tan \left(f x +e \right)-i\right) d^{2}}{8 f \,a^{2} \left(i d +c \right)^{4}}+\frac{3 \ln \left(\tan \left(f x +e \right)-i\right) c d}{4 f \,a^{2} \left(i d +c \right)^{4}}"," ",0,"1/8*I/f/a^2/(I*d-c)^2*ln(tan(f*x+e)+I)+2*I/f/a^2*d^4/(I*d-c)^2/(c+I*d)^4*ln(c+d*tan(f*x+e))-4/f/a^2*d^3/(I*d-c)^2/(c+I*d)^4*ln(c+d*tan(f*x+e))*c+1/f/a^2*d^3/(I*d-c)^2/(c+I*d)^4/(c+d*tan(f*x+e))*c^2+1/f/a^2*d^5/(I*d-c)^2/(c+I*d)^4/(c+d*tan(f*x+e))-1/4*I/f/a^2/(c+I*d)^4/(tan(f*x+e)-I)^2*c^2+1/4*I/f/a^2/(c+I*d)^4/(tan(f*x+e)-I)^2*d^2+1/2/f/a^2/(c+I*d)^4/(tan(f*x+e)-I)^2*c*d+3/2*I/f/a^2/(c+I*d)^4/(tan(f*x+e)-I)*c*d+1/4/f/a^2/(c+I*d)^4/(tan(f*x+e)-I)*c^2-5/4/f/a^2/(c+I*d)^4/(tan(f*x+e)-I)*d^2-1/8*I/f/a^2/(c+I*d)^4*ln(tan(f*x+e)-I)*c^2+17/8*I/f/a^2/(c+I*d)^4*ln(tan(f*x+e)-I)*d^2+3/4/f/a^2/(c+I*d)^4*ln(tan(f*x+e)-I)*c*d","A"
1094,1,692,327,0.341000," ","int(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x)","-\frac{5 i d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) c}{f \,a^{3} \left(i d -c \right)^{2} \left(i d +c \right)^{5}}+\frac{7 i c^{2} d}{8 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)}-\frac{3 d^{5} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \,a^{3} \left(i d -c \right)^{2} \left(i d +c \right)^{5}}-\frac{17 i d^{3}}{8 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)}+\frac{i d^{3}}{6 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{23 i \ln \left(\tan \left(f x +e \right)-i\right) c \,d^{2}}{16 f \,a^{3} \left(i d +c \right)^{5}}+\frac{i d^{6}}{f \,a^{3} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(c +d \tan \left(f x +e \right)\right)}+\frac{7 c^{2} d}{8 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{5 d^{3}}{8 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i c^{3}}{8 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i c^{2} d}{2 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{c^{3}}{8 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)}-\frac{23 c \,d^{2}}{8 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{3}}{16 f \,a^{3} \left(i d +c \right)^{5}}+\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{16 f \,a^{3} \left(i d -c \right)^{2}}+\frac{7 \ln \left(\tan \left(f x +e \right)-i\right) c^{2} d}{16 f \,a^{3} \left(i d +c \right)^{5}}-\frac{49 \ln \left(\tan \left(f x +e \right)-i\right) d^{3}}{16 f \,a^{3} \left(i d +c \right)^{5}}+\frac{11 i c \,d^{2}}{8 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{i d^{4} c^{2}}{f \,a^{3} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(c +d \tan \left(f x +e \right)\right)}-\frac{c^{3}}{6 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{c \,d^{2}}{2 f \,a^{3} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{3}}"," ",0,"-5*I/f/a^3*d^4/(I*d-c)^2/(c+I*d)^5*ln(c+d*tan(f*x+e))*c+7/8*I/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)*c^2*d-3/f/a^3*d^5/(I*d-c)^2/(c+I*d)^5*ln(c+d*tan(f*x+e))-17/8*I/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)*d^3+1/6*I/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)^3*d^3+23/16*I/f/a^3/(c+I*d)^5*ln(tan(f*x+e)-I)*c*d^2+I/f/a^3*d^6/(I*d-c)^2/(c+I*d)^5/(c+d*tan(f*x+e))+7/8/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)^2*c^2*d-5/8/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)^2*d^3-1/8*I/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)^2*c^3-1/2*I/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)^3*c^2*d+1/8/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)*c^3-23/8/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)*c*d^2-1/16*I/f/a^3/(c+I*d)^5*ln(tan(f*x+e)-I)*c^3+1/16*I/f/a^3/(I*d-c)^2*ln(tan(f*x+e)+I)+7/16/f/a^3/(c+I*d)^5*ln(tan(f*x+e)-I)*c^2*d-49/16/f/a^3/(c+I*d)^5*ln(tan(f*x+e)-I)*d^3+11/8*I/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)^2*c*d^2+I/f/a^3*d^4/(I*d-c)^2/(c+I*d)^5/(c+d*tan(f*x+e))*c^2-1/6/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)^3*c^3+1/2/f/a^3/(c+I*d)^5/(tan(f*x+e)-I)^3*c*d^2","B"
1095,1,635,126,0.292000," ","int((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x)","-\frac{6 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 i a^{3} d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{8 a^{3} d c}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{i a^{3} c^{3}}{2 f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{12 i a^{3} \arctan \left(\tan \left(f x +e \right)\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 a^{3} c^{2}}{2 f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{a^{3} d}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{3 i a^{3} c}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{i a^{3} c^{4}}{f \left(c^{2}+d^{2}\right)^{2} d^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{12 a^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{4 a^{3} \ln \left(c +d \tan \left(f x +e \right)\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{12 i a^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{4 i a^{3} \arctan \left(\tan \left(f x +e \right)\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{4 i a^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{6 i a^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{6 a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{2 a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{4 a^{3} \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{12 a^{3} \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}"," ",0,"-6*I/f*a^3/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c*d^2-3*I/f*a^3/(c^2+d^2)^2*d^2/(c+d*tan(f*x+e))+2*I/f*a^3/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c^3-8/f*a^3/(c^2+d^2)^2*d/(c+d*tan(f*x+e))*c-1/2*I/f*a^3/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*c^3+12*I/f*a^3/(c^2+d^2)^3*arctan(tan(f*x+e))*c^2*d+3/2/f*a^3/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*c^2-1/2/f*a^3*d/(c^2+d^2)/(c+d*tan(f*x+e))^2+3/2*I/f*a^3/(c^2+d^2)/(c+d*tan(f*x+e))^2*c+I/f*a^3/(c^2+d^2)^2/d^2/(c+d*tan(f*x+e))*c^4+12/f*a^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c^2*d-4/f*a^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*d^3+12*I/f*a^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c*d^2-4*I/f*a^3/(c^2+d^2)^3*arctan(tan(f*x+e))*d^3-4*I/f*a^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c^3+6*I/f*a^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*c^2-6/f*a^3/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c^2*d+2/f*a^3/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*d^3+4/f*a^3/(c^2+d^2)^3*arctan(tan(f*x+e))*c^3-12/f*a^3/(c^2+d^2)^3*arctan(tan(f*x+e))*c*d^2","B"
1096,1,562,117,0.293000," ","int((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x)","-\frac{3 i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{a^{2} c^{2}}{2 f \left(c^{2}+d^{2}\right) d \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{a^{2} d}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{2 i a^{2} \arctan \left(\tan \left(f x +e \right)\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{2 i a^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{4 a^{2} c d}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{6 i a^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{i a^{2} c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{6 a^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{2 a^{2} \ln \left(c +d \tan \left(f x +e \right)\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{i a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{6 i a^{2} \arctan \left(\tan \left(f x +e \right)\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{2 i a^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{2 i a^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{2 a^{2} \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{6 a^{2} \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}"," ",0,"-3*I/f*a^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c*d^2+1/2/f*a^2/(c^2+d^2)/d/(c+d*tan(f*x+e))^2*c^2-1/2/f*a^2/(c^2+d^2)*d/(c+d*tan(f*x+e))^2-2*I/f*a^2/(c^2+d^2)^3*arctan(tan(f*x+e))*d^3-2*I/f*a^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*d^2-4/f*a^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*c*d+6*I/f*a^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c*d^2+I/f*a^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*c+6/f*a^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c^2*d-2/f*a^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*d^3+I/f*a^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c^3+6*I/f*a^2/(c^2+d^2)^3*arctan(tan(f*x+e))*c^2*d+2*I/f*a^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*c^2-2*I/f*a^2/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c^3+2/f*a^2/(c^2+d^2)^3*arctan(tan(f*x+e))*c^3-6/f*a^2/(c^2+d^2)^3*arctan(tan(f*x+e))*c*d^2-3/f*a^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c^2*d+1/f*a^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*d^3","B"
1097,1,493,97,0.274000," ","int((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x)","\frac{3 i a \arctan \left(\tan \left(f x +e \right)\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{i a \arctan \left(\tan \left(f x +e \right)\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{2 a c d}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{i a \ln \left(c +d \tan \left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{a d}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 i a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 a \ln \left(c +d \tan \left(f x +e \right)\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{a \ln \left(c +d \tan \left(f x +e \right)\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 a \ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{a \ln \left(1+\tan^{2}\left(f x +e \right)\right) d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{i a \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{i a \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 i a \ln \left(c +d \tan \left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{i a c}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{a \arctan \left(\tan \left(f x +e \right)\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 a \arctan \left(\tan \left(f x +e \right)\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}"," ",0,"3*I/f*a/(c^2+d^2)^3*arctan(tan(f*x+e))*c^2*d-I/f*a/(c^2+d^2)^3*arctan(tan(f*x+e))*d^3-2/f*a/(c^2+d^2)^2/(c+d*tan(f*x+e))*c*d-I/f*a/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c^3-1/2/f*a/(c^2+d^2)/(c+d*tan(f*x+e))^2*d+1/2*I/f*a/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c^3-3/2*I/f*a/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c*d^2+3/f*a/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c^2*d-1/f*a/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*d^3-3/2/f*a/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c^2*d+1/2/f*a/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*d^3-I/f*a/(c^2+d^2)^2/(c+d*tan(f*x+e))*d^2+I/f*a/(c^2+d^2)^2/(c+d*tan(f*x+e))*c^2+3*I/f*a/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c*d^2+1/2*I/f*a/(c^2+d^2)/(c+d*tan(f*x+e))^2*c+1/f*a/(c^2+d^2)^3*arctan(tan(f*x+e))*c^3-3/f*a/(c^2+d^2)^3*arctan(tan(f*x+e))*c*d^2","B"
1098,1,542,250,0.343000," ","int(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x)","-\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{4 f a \left(i d -c \right)^{3}}-\frac{6 i d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2}}{f a \left(i d -c \right)^{3} \left(i d +c \right)^{4}}+\frac{2 i d^{4} \ln \left(c +d \tan \left(f x +e \right)\right)}{f a \left(i d -c \right)^{3} \left(i d +c \right)^{4}}-\frac{4 d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c}{f a \left(i d -c \right)^{3} \left(i d +c \right)^{4}}+\frac{3 i d^{2} c^{3}}{f a \left(i d -c \right)^{3} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 i d^{4} c}{f a \left(i d -c \right)^{3} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)}+\frac{d^{3} c^{2}}{f a \left(i d -c \right)^{3} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)}+\frac{d^{5}}{f a \left(i d -c \right)^{3} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)}+\frac{i d^{2} c^{4}}{2 f a \left(i d -c \right)^{3} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{i d^{4} c^{2}}{f a \left(i d -c \right)^{3} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{i d^{6}}{2 f a \left(i d -c \right)^{3} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{1}{2 f a \left(i d +c \right)^{3} \left(\tan \left(f x +e \right)-i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c}{4 f a \left(i d +c \right)^{4}}+\frac{7 \ln \left(\tan \left(f x +e \right)-i\right) d}{4 f a \left(i d +c \right)^{4}}"," ",0,"-1/4*I/f/a/(I*d-c)^3*ln(tan(f*x+e)+I)-6*I/f/a*d^2/(I*d-c)^3/(c+I*d)^4*ln(c+d*tan(f*x+e))*c^2+2*I/f/a*d^4/(I*d-c)^3/(c+I*d)^4*ln(c+d*tan(f*x+e))-4/f/a*d^3/(I*d-c)^3/(c+I*d)^4*ln(c+d*tan(f*x+e))*c+3*I/f/a*d^2/(I*d-c)^3/(c+I*d)^4/(c+d*tan(f*x+e))*c^3+3*I/f/a*d^4/(I*d-c)^3/(c+I*d)^4/(c+d*tan(f*x+e))*c+1/f/a*d^3/(I*d-c)^3/(c+I*d)^4/(c+d*tan(f*x+e))*c^2+1/f/a*d^5/(I*d-c)^3/(c+I*d)^4/(c+d*tan(f*x+e))+1/2*I/f/a*d^2/(I*d-c)^3/(c+I*d)^4/(c+d*tan(f*x+e))^2*c^4+I/f/a*d^4/(I*d-c)^3/(c+I*d)^4/(c+d*tan(f*x+e))^2*c^2+1/2*I/f/a*d^6/(I*d-c)^3/(c+I*d)^4/(c+d*tan(f*x+e))^2+1/2/f/a/(c+I*d)^3/(tan(f*x+e)-I)-1/4*I/f/a/(c+I*d)^4*ln(tan(f*x+e)-I)*c+7/4/f/a/(c+I*d)^4*ln(tan(f*x+e)-I)*d","B"
1099,1,726,324,0.399000," ","int(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x)","-\frac{10 i d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) c}{f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5}}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{2}}{8 f \,a^{2} \left(i d +c \right)^{5}}+\frac{10 d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2}}{f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5}}-\frac{4 d^{5} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5}}+\frac{31 i \ln \left(\tan \left(f x +e \right)-i\right) d^{2}}{8 f \,a^{2} \left(i d +c \right)^{5}}+\frac{i d^{2}}{4 f \,a^{2} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{4 d^{3} c^{3}}{f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5} \left(c +d \tan \left(f x +e \right)\right)}-\frac{4 d^{5} c}{f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5} \left(c +d \tan \left(f x +e \right)\right)}-\frac{d^{3} c^{4}}{2 f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5} \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{d^{5} c^{2}}{f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5} \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{d^{7}}{2 f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5} \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{2 i d^{6}}{f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5} \left(c +d \tan \left(f x +e \right)\right)}+\frac{c^{2}}{4 f \,a^{2} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)}-\frac{7 d^{2}}{4 f \,a^{2} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)}-\frac{i c^{2}}{4 f \,a^{2} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{2 i c d}{f \,a^{2} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)}+\frac{c d}{2 f \,a^{2} \left(i d +c \right)^{5} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{8 f \,a^{2} \left(i d -c \right)^{3}}+\frac{2 i d^{4} c^{2}}{f \,a^{2} \left(i d -c \right)^{3} \left(i d +c \right)^{5} \left(c +d \tan \left(f x +e \right)\right)}+\frac{\ln \left(\tan \left(f x +e \right)-i\right) c d}{f \,a^{2} \left(i d +c \right)^{5}}"," ",0,"-10*I/f/a^2*d^4/(I*d-c)^3/(c+I*d)^5*ln(c+d*tan(f*x+e))*c-1/8*I/f/a^2/(c+I*d)^5*ln(tan(f*x+e)-I)*c^2+10/f/a^2*d^3/(I*d-c)^3/(c+I*d)^5*ln(c+d*tan(f*x+e))*c^2-4/f/a^2*d^5/(I*d-c)^3/(c+I*d)^5*ln(c+d*tan(f*x+e))+31/8*I/f/a^2/(c+I*d)^5*ln(tan(f*x+e)-I)*d^2+1/4*I/f/a^2/(c+I*d)^5/(tan(f*x+e)-I)^2*d^2-4/f/a^2*d^3/(I*d-c)^3/(c+I*d)^5/(c+d*tan(f*x+e))*c^3-4/f/a^2*d^5/(I*d-c)^3/(c+I*d)^5/(c+d*tan(f*x+e))*c-1/2/f/a^2*d^3/(I*d-c)^3/(c+I*d)^5/(c+d*tan(f*x+e))^2*c^4-1/f/a^2*d^5/(I*d-c)^3/(c+I*d)^5/(c+d*tan(f*x+e))^2*c^2-1/2/f/a^2*d^7/(I*d-c)^3/(c+I*d)^5/(c+d*tan(f*x+e))^2+2*I/f/a^2*d^6/(I*d-c)^3/(c+I*d)^5/(c+d*tan(f*x+e))+1/4/f/a^2/(c+I*d)^5/(tan(f*x+e)-I)*c^2-7/4/f/a^2/(c+I*d)^5/(tan(f*x+e)-I)*d^2-1/4*I/f/a^2/(c+I*d)^5/(tan(f*x+e)-I)^2*c^2+2*I/f/a^2/(c+I*d)^5/(tan(f*x+e)-I)*c*d+1/2/f/a^2/(c+I*d)^5/(tan(f*x+e)-I)^2*c*d-1/8*I/f/a^2/(I*d-c)^3*ln(tan(f*x+e)+I)+2*I/f/a^2*d^4/(I*d-c)^3/(c+I*d)^5/(c+d*tan(f*x+e))*c^2+1/f/a^2/(c+I*d)^5*ln(tan(f*x+e)-I)*c*d","B"
1100,1,954,412,0.384000," ","int(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x)","-\frac{c^{3}}{6 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{111 \ln \left(\tan \left(f x +e \right)-i\right) d^{3}}{16 f \,a^{3} \left(i d +c \right)^{6}}-\frac{7 d^{3}}{8 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)^{2}}+\frac{9 c^{2} d}{8 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{39 c \,d^{2}}{8 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)}+\frac{c \,d^{2}}{2 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{9 \ln \left(\tan \left(f x +e \right)-i\right) c^{2} d}{16 f \,a^{3} \left(i d +c \right)^{6}}-\frac{3 d^{7}}{f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6} \left(c +d \tan \left(f x +e \right)\right)}-\frac{31 i d^{3}}{8 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)}+\frac{15 i d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2}}{f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6}}-\frac{i d^{4} c^{4}}{2 f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6} \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{i d^{6} c^{2}}{f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6} \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{5 i d^{4} c^{3}}{f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6} \left(c +d \tan \left(f x +e \right)\right)}-\frac{5 i d^{6} c}{f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6} \left(c +d \tan \left(f x +e \right)\right)}+\frac{15 i c \,d^{2}}{8 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{7 i d^{6} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6}}+\frac{9 i c^{2} d}{8 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)}-\frac{i c^{2} d}{2 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)^{3}}+\frac{39 i \ln \left(\tan \left(f x +e \right)-i\right) c \,d^{2}}{16 f \,a^{3} \left(i d +c \right)^{6}}-\frac{3 d^{5} c^{2}}{f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6} \left(c +d \tan \left(f x +e \right)\right)}+\frac{18 d^{5} \ln \left(c +d \tan \left(f x +e \right)\right) c}{f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6}}-\frac{i d^{8}}{2 f \,a^{3} \left(i d -c \right)^{3} \left(i d +c \right)^{6} \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{i d^{3}}{6 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)^{3}}-\frac{i c^{3}}{8 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)^{2}}-\frac{i \ln \left(\tan \left(f x +e \right)+i\right)}{16 f \,a^{3} \left(i d -c \right)^{3}}+\frac{c^{3}}{8 f \,a^{3} \left(i d +c \right)^{6} \left(\tan \left(f x +e \right)-i\right)}-\frac{i \ln \left(\tan \left(f x +e \right)-i\right) c^{3}}{16 f \,a^{3} \left(i d +c \right)^{6}}"," ",0,"-1/8*I/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)^2*c^3-31/8*I/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)*d^3-1/16*I/f/a^3/(c+I*d)^6*ln(tan(f*x+e)-I)*c^3+1/6*I/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)^3*d^3+15*I/f/a^3*d^4/(I*d-c)^3/(c+I*d)^6*ln(c+d*tan(f*x+e))*c^2-1/2*I/f/a^3*d^4/(I*d-c)^3/(c+I*d)^6/(c+d*tan(f*x+e))^2*c^4-I/f/a^3*d^6/(I*d-c)^3/(c+I*d)^6/(c+d*tan(f*x+e))^2*c^2-5*I/f/a^3*d^4/(I*d-c)^3/(c+I*d)^6/(c+d*tan(f*x+e))*c^3-5*I/f/a^3*d^6/(I*d-c)^3/(c+I*d)^6/(c+d*tan(f*x+e))*c-3/f/a^3*d^5/(I*d-c)^3/(c+I*d)^6/(c+d*tan(f*x+e))*c^2+18/f/a^3*d^5/(I*d-c)^3/(c+I*d)^6*ln(c+d*tan(f*x+e))*c-1/2*I/f/a^3*d^8/(I*d-c)^3/(c+I*d)^6/(c+d*tan(f*x+e))^2-7*I/f/a^3*d^6/(I*d-c)^3/(c+I*d)^6*ln(c+d*tan(f*x+e))+9/8*I/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)*c^2*d-1/2*I/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)^3*c^2*d+39/16*I/f/a^3/(c+I*d)^6*ln(tan(f*x+e)-I)*c*d^2+15/8*I/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)^2*c*d^2+9/8/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)^2*c^2*d-39/8/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)*c*d^2+1/2/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)^3*c*d^2+9/16/f/a^3/(c+I*d)^6*ln(tan(f*x+e)-I)*c^2*d-3/f/a^3*d^7/(I*d-c)^3/(c+I*d)^6/(c+d*tan(f*x+e))-1/6/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)^3*c^3-111/16/f/a^3/(c+I*d)^6*ln(tan(f*x+e)-I)*d^3-7/8/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)^2*d^3-1/16*I/f/a^3/(I*d-c)^3*ln(tan(f*x+e)+I)+1/8/f/a^3/(c+I*d)^6/(tan(f*x+e)-I)*c^3","B"
1101,1,1272,128,0.436000," ","int((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x)","\frac{4 i a^{3} \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}-\frac{16 i a^{3} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}-\frac{2 a^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{f d}-\frac{2 i a^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f \,d^{2}}-\frac{4 a^{3} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{8 i a^{3} \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{16 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{16 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{16 i a^{3} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{4 a^{3} d \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{4 i a^{3} \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{2 i a^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3 f \,d^{2}}+\frac{16 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{16 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"4*I/f*a^3/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-16*I/f*a^3*d^2/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-4*I/f*a^3/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-2/f*a^3/d*(c+d*tan(f*x+e))^(3/2)-2/5*I/f*a^3/d^2*(c+d*tan(f*x+e))^(5/2)-4/f*a^3*d/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+8*I*a^3*(c+d*tan(f*x+e))^(1/2)/f+16/f*a^3*d/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)+16/f*a^3*d/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-16*I/f*a^3*d^2/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-4*I/f*a^3/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+4/f*a^3*d/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+4*I/f*a^3/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+2/3*I/f*a^3/d^2*(c+d*tan(f*x+e))^(3/2)*c+16/f*a^3*d/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)+16/f*a^3*d/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c","B"
1102,1,1229,84,0.251000," ","int((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x)","-\frac{2 a^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 d f}+\frac{4 i a^{2} \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{2 i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}-\frac{2 a^{2} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}-\frac{2 i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}-\frac{8 i a^{2} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{8 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{8 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{2 i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{2 a^{2} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{8 i a^{2} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{8 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{8 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"-2/3*a^2*(c+d*tan(f*x+e))^(3/2)/d/f+4*I*a^2*(c+d*tan(f*x+e))^(1/2)/f-2*I/f*a^2/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)-2/f*a^2*d/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*I/f*a^2/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-8*I/f*a^2*d^2/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+8/f*a^2*d/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)+8/f*a^2*d/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+2*I/f*a^2/(4*(c^2+d^2)^(1/2)+4*c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c+2*I/f*a^2/(4*(c^2+d^2)^(1/2)+4*c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+2/f*a^2*d/(4*(c^2+d^2)^(1/2)+4*c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+8*I/f*a^2*d^2/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-8/f*a^2*d/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)-8/f*a^2*d/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c","B"
1103,1,1173,57,0.209000," ","int((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x)","\frac{i a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{2 i a \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{i a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}-\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, d}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}-\frac{4 i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{2}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{2}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, d}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right)}+\frac{4 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d \sqrt{c^{2}+d^{2}}}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d c}{f \left(4 \sqrt{c^{2}+d^{2}}+4 c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"I/f*a/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+2*I*a*(c+d*tan(f*x+e))^(1/2)/f+I/f*a/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-1/f*a/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*d-4*I/f*a/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^2-4*I/f*a/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^2+4/f*a/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d*(c^2+d^2)^(1/2)+4/f*a/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d*c-I/f*a/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c+1/f*a/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*d-I/f*a/(4*(c^2+d^2)^(1/2)+4*c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)+4/f*a/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d*(c^2+d^2)^(1/2)+4/f*a/(4*(c^2+d^2)^(1/2)+4*c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d*c","B"
1104,1,125,112,0.487000," ","int((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x)","-\frac{i \sqrt{i d -c}\, \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{2 f a}+\frac{d \sqrt{c +d \tan \left(f x +e \right)}}{2 f a \left(d \tan \left(f x +e \right)-i d \right)}-\frac{i c \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{2 f a \sqrt{-i d -c}}"," ",0,"-1/2*I/f/a*(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))+1/2/f/a*d*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)-1/2*I/f/a*c/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))","A"
1105,1,715,176,0.422000," ","int((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x)","-\frac{i \sqrt{i d -c}\, \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{4 f \,a^{2}}+\frac{i d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{2}}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(i c^{2}-i d^{2}-2 c d \right)}-\frac{i d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(i c^{2}-i d^{2}-2 c d \right)}-\frac{3 d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(i c^{2}-i d^{2}-2 c d \right)}+\frac{7 d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(i c^{2}-i d^{2}-2 c d \right)}-\frac{3 d^{4} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(i c^{2}-i d^{2}-2 c d \right)}-\frac{i d \sqrt{c +d \tan \left(f x +e \right)}\, c^{3}}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(i c^{2}-i d^{2}-2 c d \right)}+\frac{i d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c}{f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(i c^{2}-i d^{2}-2 c d \right)}+\frac{\arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{4 f \,a^{2} \left(i c^{2}-i d^{2}-2 c d \right) \sqrt{-i d -c}}-\frac{d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{8 f \,a^{2} \left(i c^{2}-i d^{2}-2 c d \right) \sqrt{-i d -c}}+\frac{i d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{2 f \,a^{2} \left(i c^{2}-i d^{2}-2 c d \right) \sqrt{-i d -c}}+\frac{i d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{2} \left(i c^{2}-i d^{2}-2 c d \right) \sqrt{-i d -c}}"," ",0,"-1/4*I/f/a^2*(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))+1/4*I/f/a^2*d/(d*tan(f*x+e)-I*d)^2/(I*c^2-I*d^2-2*c*d)*(c+d*tan(f*x+e))^(3/2)*c^2-1/8*I/f/a^2*d^3/(d*tan(f*x+e)-I*d)^2/(I*c^2-I*d^2-2*c*d)*(c+d*tan(f*x+e))^(3/2)-3/8/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2/(I*c^2-I*d^2-2*c*d)*(c+d*tan(f*x+e))^(3/2)*c+7/8/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2/(I*c^2-I*d^2-2*c*d)*(c+d*tan(f*x+e))^(1/2)*c^2-3/8/f/a^2*d^4/(d*tan(f*x+e)-I*d)^2/(I*c^2-I*d^2-2*c*d)*(c+d*tan(f*x+e))^(1/2)-1/4*I/f/a^2*d/(d*tan(f*x+e)-I*d)^2/(I*c^2-I*d^2-2*c*d)*(c+d*tan(f*x+e))^(1/2)*c^3+I/f/a^2*d^3/(d*tan(f*x+e)-I*d)^2/(I*c^2-I*d^2-2*c*d)*(c+d*tan(f*x+e))^(1/2)*c+1/4/f/a^2/(I*c^2-I*d^2-2*c*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3-1/8/f/a^2*d^2/(I*c^2-I*d^2-2*c*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+1/2*I/f/a^2*d/(I*c^2-I*d^2-2*c*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+1/8*I/f/a^2*d^3/(I*c^2-I*d^2-2*c*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))","B"
1106,1,1315,237,0.441000," ","int((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{2 i d^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{3}}{f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d \,c^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{3 d^{3} c \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{5 i d^{2} c^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{4}}{8 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}-\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{4}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{4 d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{2}}{3 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{d^{5} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{i d^{6} \sqrt{c +d \tan \left(f x +e \right)}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{5 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{16 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{5}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{25 d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c^{3}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{17 d^{5} \sqrt{c +d \tan \left(f x +e \right)}\, c}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{11 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c^{4}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{i \sqrt{i d -c}\, \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{8 f \,a^{3}}-\frac{29 i d^{4} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{3 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{8 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{16 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}"," ",0,"2/3*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c-I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^3+1/8/f/a^3*d/(d*tan(f*x+e)-I*d)^3*c^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)-3/16/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3*c/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)+5/16*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3*c^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)-1/8*I/f/a^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^4-1/4/f/a^3*d/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^4+4/3/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^2-1/12/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)+1/4*I/f/a^3*d^6/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)+5/16*I/f/a^3*d^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+1/8*I/f/a^3*d^4/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+1/8/f/a^3*d/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^5-25/16/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^3+17/16/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c+11/16*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^4-1/8*I/f/a^3*(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))-29/16*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^2+3/8/f/a^3*d/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3+1/16/f/a^3*d^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c","B"
1107,1,2535,154,0.244000," ","int((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2),x)","\frac{8 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 a^{3} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{4 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 a^{3} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a^{3} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{2 a^{3} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{4 i a^{3} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 i a^{3} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 i a^{3} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{2 i a^{3} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{2 i a^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 f \,d^{2}}+\frac{8 i a^{3} c \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{8 i a^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{8 a^{3} d \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{6 a^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f d}+\frac{4 i a^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 i a^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{2 i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{8 a^{3} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{3} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 i a^{3} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 i a^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c}{5 f \,d^{2}}-\frac{4 i a^{3} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 i a^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{3} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{4 a^{3} d^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a^{3} d^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{4 a^{3} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{4 a^{3} d^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a^{3} d^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}"," ",0,"8/f*a^3*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-4/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c-2*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+2*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-4/f*a^3*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+4/f*a^3*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-2/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2-2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3+4*I/f*a^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-4*I/f*a^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+2/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2+2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3-2/7*I/f*a^3/d^2*(c+d*tan(f*x+e))^(7/2)+8*I/f*a^3*c*(c+d*tan(f*x+e))^(1/2)+2*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c-4*I/f*a^3*d^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-2*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c+4*I/f*a^3*d^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+8/f*a^3*d*(c+d*tan(f*x+e))^(1/2)-6/5/f*a^3/d*(c+d*tan(f*x+e))^(5/2)+4*I/f*a^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2+4*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+2/5*I/f*a^3/d^2*(c+d*tan(f*x+e))^(5/2)*c-8/f*a^3*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+8/3*I*a^3*(c+d*tan(f*x+e))^(3/2)/f-4/f*a^3*d^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+2/f*a^3*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+4/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c+4/f*a^3*d^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-4*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-4*I/f*a^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-2/f*a^3*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))","B"
1108,1,2484,110,0.228000," ","int((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x)","\frac{4 i a^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{2 i a^{2} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a^{2} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{2 i a^{2} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a^{2} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{4 i a^{2} c \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{4 a^{2} d \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{2 i a^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 i a^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{2 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{a^{2} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{2 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a^{2} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{2 a^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d f}-\frac{a^{2} d^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{2 a^{2} d^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a^{2} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{4 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a^{2} d^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 i a^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a^{2} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{4 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a^{2} d^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a^{2} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{i a^{2} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 i a^{2} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"-I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c+2*I/f*a^2*d^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-2*I/f*a^2*d^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+4/3*I*a^2*(c+d*tan(f*x+e))^(3/2)/f+2*I/f*a^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-2*I/f*a^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3+I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c+4/f*a^2*d*(c+d*tan(f*x+e))^(1/2)+2/f*a^2*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3+4*I/f*a^2*c*(c+d*tan(f*x+e))^(1/2)-1/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2-2/f*a^2*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+1/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-2/5*a^2*(c+d*tan(f*x+e))^(5/2)/d/f-1/f*a^2*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-2/f*a^2*d^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+2/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c+I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-4/f*a^2*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))+1/f*a^2*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))-2*I/f*a^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+2*I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+4/f*a^2*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+2*I/f*a^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+2/f*a^2*d^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-2/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c-I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2-I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))-2*I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))","B"
1109,1,2398,81,0.206000," ","int((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x)","\frac{2 i a \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) d^{2}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2} d}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2} d}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) d^{2}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c \,d^{2}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{2}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c \,d^{2}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{2}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) d^{3}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) d^{3}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 a \sqrt{c +d \tan \left(f x +e \right)}\, d}{f}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{3}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{2 i a c \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"-1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2*d-1/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d+I/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+I/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+2/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d-1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*d^2+1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2+1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3+1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*d^2-I/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+1/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d+1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2*d-1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3-I/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-I/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^2+I/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^2-1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c*d^2+1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c*d^2+I/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^2-2/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d+1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*d^3+1/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c*d+1/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^3-1/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^3-1/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c*d-1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*d^3+2/3*I*a*(c+d*tan(f*x+e))^(3/2)/f+2/f*a*(c+d*tan(f*x+e))^(1/2)*d+2*I/f*a*c*(c+d*tan(f*x+e))^(1/2)-I/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^2","B"
1110,1,257,125,0.355000," ","int((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x)","\frac{i d^{2} \sqrt{c +d \tan \left(f x +e \right)}}{2 f a \left(d \tan \left(f x +e \right)-i d \right)}+\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c}{2 f a \left(d \tan \left(f x +e \right)-i d \right)}-\frac{d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{2 f a \sqrt{-i d -c}}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{2 f a \sqrt{-i d -c}}-\frac{i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{f a \sqrt{-i d -c}}+\frac{i \left(i d -c \right)^{\frac{3}{2}} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{2 f a}"," ",0,"1/2*I/f/a*d^2*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)+1/2/f/a*d*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)*c-1/2/f/a*d/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c-1/2*I/f/a/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2-I/f/a*d^2/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+1/2*I/f/a*(I*d-c)^(3/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))","B"
1111,1,861,175,0.394000," ","int((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x)","\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{3}}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{2 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{2}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{3 i d^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{4}}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{3 d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{d^{5} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{5 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c^{3}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{i d^{4} \sqrt{c +d \tan \left(f x +e \right)}\, c}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{4 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{2 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{4}}{4 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}-\frac{3 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{8 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{i \left(i d -c \right)^{\frac{3}{2}} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{4 f \,a^{2}}"," ",0,"1/4/f/a^2*d/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^3+1/2/f/a^2*d^3/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c+1/8*I/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^2+3/8*I/f/a^2*d^4/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)-1/4/f/a^2*d/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^4+3/8/f/a^2*d^3/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^2+1/8/f/a^2*d^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)-5/8*I/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^3-1/8*I/f/a^2*d^4/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c+1/4/f/a^2*d/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3+1/2/f/a^2*d^3/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c-1/4*I/f/a^2/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^4-3/8*I/f/a^2*d^2/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+1/8*I/f/a^2*d^4/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+1/4*I/f/a^2*(I*d-c)^(3/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))","B"
1112,1,1266,233,0.453000," ","int((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x)","\frac{3 i d^{4} c \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{16 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}-\frac{i c^{5} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c^{4}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c^{2}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{d^{5} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{2}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{5 d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3}}-\frac{i d^{2} c^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{16 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}-\frac{7 i d^{6} \sqrt{c +d \tan \left(f x +e \right)}\, c}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{9 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c^{5}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{6}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{7 d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c^{4}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{3 d^{5} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d^{7} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{3 i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c^{3}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{i \left(i d -c \right)^{\frac{3}{2}} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{8 f \,a^{3}}-\frac{3 i d^{4} \sqrt{c +d \tan \left(f x +e \right)}\, c^{3}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d \,c^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{4 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{3 d^{3} c^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{5 i d^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}"," ",0,"3/16*I/f/a^3*d^4*c/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))-1/8*I/f/a^3*c^5/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+1/8/f/a^3*d/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^4+1/8/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^2-1/8/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)-1/4/f/a^3*d/(d*tan(f*x+e)-I*d)^3*(c+d*tan(f*x+e))^(3/2)*c^2-5/12/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3*(c+d*tan(f*x+e))^(3/2)-1/16*I/f/a^3*d^2*c^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))-7/16*I/f/a^3*d^6/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c+9/16*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^5+1/8/f/a^3*d/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^6-7/8/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^4-3/8/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^2+1/8/f/a^3*d^7/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)+3/16*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^3+1/8*I/f/a^3*(I*d-c)^(3/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))-3/8*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^3+1/4/f/a^3*d*c^4/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+3/8/f/a^3*d^3*c^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+5/16*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c","B"
1113,1,2936,183,0.243000," ","int((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"8/5*I*a^3*(c+d*tan(f*x+e))^(5/2)/f-8*I/f*a^3*d^2*(c+d*tan(f*x+e))^(1/2)+8*I/f*a^3*c^2*(c+d*tan(f*x+e))^(1/2)+8/3*I/f*a^3*(c+d*tan(f*x+e))^(3/2)*c-2/9*I/f*a^3/d^2*(c+d*tan(f*x+e))^(9/2)+8/3/f*a^3*d*(c+d*tan(f*x+e))^(3/2)-6/7/f*a^3/d*(c+d*tan(f*x+e))^(7/2)+12/f*a^3*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-12/f*a^3*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-6/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2+4*I/f*a^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3-4*I/f*a^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3+2/7*I/f*a^3/d^2*(c+d*tan(f*x+e))^(7/2)*c+6/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-2/f*a^3*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+2/f*a^3*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-4/f*a^3*d^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+4/f*a^3*d^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+16/f*a^3*d*c*(c+d*tan(f*x+e))^(1/2)+4*I/f*a^3*d^4/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+12*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+6*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c-12*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-2*I/f*a^3*d^4/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))-6*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c+2*I/f*a^3*d^4/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-4*I/f*a^3*d^4/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-4*I/f*a^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^4+4*I/f*a^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^4-2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^4+2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^4+8/f*a^3*d^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-4/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3-4/f*a^3*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c+4/f*a^3*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c-8/f*a^3*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-8/f*a^3*d^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+4/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3+8/f*a^3*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3","B"
1114,1,2886,139,0.223000," ","int((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"-6*I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+6*I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-I/f*a^2*d^4/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+4/5*I*a^2*(c+d*tan(f*x+e))^(5/2)/f+2/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3+2/f*a^2*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c-2/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3-2/f*a^2*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c-4/f*a^2*d^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+4/f*a^2*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+4/f*a^2*d^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+I/f*a^2*d^4/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-2/7*a^2*(c+d*tan(f*x+e))^(7/2)/d/f-2/f*a^2*d^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+1/f*a^2*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))+2/f*a^2*d^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+8/f*a^2*d*(c+d*tan(f*x+e))^(1/2)*c+4/3*I/f*a^2*(c+d*tan(f*x+e))^(3/2)*c-4*I/f*a^2*d^2*(c+d*tan(f*x+e))^(1/2)+4*I/f*a^2*c^2*(c+d*tan(f*x+e))^(1/2)+4/3/f*a^2*d*(c+d*tan(f*x+e))^(3/2)+I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^4-3*I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c-2*I/f*a^2*d^4/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-4/f*a^2*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+2*I/f*a^2*d^4/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+3*I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c+2*I/f*a^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^4-I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^4-2*I/f*a^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^4+I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3-6/f*a^2*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-3/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2-1/f*a^2*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+6/f*a^2*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+3/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3-2*I/f*a^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+2*I/f*a^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3","B"
1115,1,2785,108,0.207000," ","int((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x)","\frac{3 a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2} d}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 a \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} d}{3 f}-\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{3} d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c \,d^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{2 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3} d}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3} d}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 a c d \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) d^{3}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) d^{3}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{4}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{4}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{4}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{3}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 i a \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}+\frac{3 i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c \,d^{2}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 i a \,c^{2} \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{2 i a \,d^{2} \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{2 i a \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{3 f}+\frac{2 a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{4}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c \,d^{2}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) d^{4}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) d^{4}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{4}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{3 i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{4}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{3}}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3} d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c \,d^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{3 i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2} d}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{3 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"I/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-I/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+3/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2*d-1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3+2/3/f*a*(c+d*tan(f*x+e))^(3/2)*d-3*I/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^2-1/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3*d-1/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c*d^3-2/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3*d+2/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3*d+1/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^3+4/f*a*c*d*(c+d*tan(f*x+e))^(1/2)+2*I/f*a*c^2*(c+d*tan(f*x+e))^(1/2)-2*I/f*a*d^2*(c+d*tan(f*x+e))^(1/2)+2/3*I/f*a*(c+d*tan(f*x+e))^(3/2)*c-1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*d^3-1/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^3+1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*d^3+I/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^4+2/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^3-1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*d^4+1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*d^4+2/5*I*a*(c+d*tan(f*x+e))^(5/2)/f-1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^4-I/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^4-3/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c*d^2+3/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c*d^2+3*I/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^2-I/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^4+1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^4-2/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^3+1/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3*d+1/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c*d^3+I/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^4+1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3-3/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d-3/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2*d+3/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d","B"
1116,1,674,152,0.384000," ","int((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x)","-\frac{2 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}}{f a}+\frac{3 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{2 f a \left(i d +c \right) \left(d \tan \left(f x +e \right)-i d \right)}-\frac{i d^{4} \sqrt{c +d \tan \left(f x +e \right)}}{2 f a \left(i d +c \right) \left(d \tan \left(f x +e \right)-i d \right)}+\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{3}}{2 f a \left(i d +c \right) \left(d \tan \left(f x +e \right)-i d \right)}-\frac{3 d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c}{2 f a \left(i d +c \right) \left(d \tan \left(f x +e \right)-i d \right)}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{4}}{2 f a \left(i d +c \right) \sqrt{-i d -c}}-\frac{9 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{2 f a \left(i d +c \right) \sqrt{-i d -c}}+\frac{2 i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{f a \left(i d +c \right) \sqrt{-i d -c}}-\frac{d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{2 f a \left(i d +c \right) \sqrt{-i d -c}}+\frac{11 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{2 f a \left(i d +c \right) \sqrt{-i d -c}}+\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{3}}{2 f a \sqrt{i d -c}}-\frac{3 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c}{2 f a \sqrt{i d -c}}+\frac{3 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{2}}{2 f a \sqrt{i d -c}}-\frac{d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{2 f a \sqrt{i d -c}}"," ",0,"-2*I/f/a*d^2*(c+d*tan(f*x+e))^(1/2)+3/2*I/f/a*d^2/(c+I*d)*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)*c^2-1/2*I/f/a*d^4/(c+I*d)*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)+1/2/f/a*d/(c+I*d)*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)*c^3-3/2/f/a*d^3/(c+I*d)*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)*c-1/2*I/f/a/(c+I*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^4-9/2*I/f/a*d^2/(c+I*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+2*I/f/a*d^4/(c+I*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))-1/2/f/a*d/(c+I*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3+11/2/f/a*d^3/(c+I*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+1/2*I/f/a/(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^3-3/2*I/f/a*d^2/(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c+3/2/f/a*d/(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^2-1/2/f/a*d^3/(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))","B"
1117,1,978,181,0.395000," ","int((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x)","\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{4}}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{15 d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{2}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{7 d^{5} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{5 i d^{6} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{3}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{5}}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c^{3}}{f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{9 d^{5} \sqrt{c +d \tan \left(f x +e \right)}\, c}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{5 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{8 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}-\frac{15 i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{8 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{5}}{4 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}-\frac{5 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{8 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{7 d^{5} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{19 i d^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{3 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c^{4}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{11 i d^{4} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{i \left(i d -c \right)^{\frac{5}{2}} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{4 f \,a^{2}}"," ",0,"1/4/f/a^2*d/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^4+15/8/f/a^2*d^3/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^2-7/8/f/a^2*d^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)+5/8*I/f/a^2*d^6/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)-1/8*I/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^3-1/4/f/a^2*d/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^5-1/f/a^2*d^3/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^3+9/4/f/a^2*d^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c-5/8*I/f/a^2*d^2/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3-15/8*I/f/a^2*d^4/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c-1/4*I/f/a^2/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^5-5/8/f/a^2*d^3/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+7/8/f/a^2*d^5/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+19/8*I/f/a^2*d^4/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c-3/8*I/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^4-11/4*I/f/a^2*d^4/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^2-1/4*I/f/a^2*(I*d-c)^(5/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))","B"
1118,1,1861,242,0.448000," ","int((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x)","-\frac{i \left(i d -c \right)^{\frac{5}{2}} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{8 f \,a^{3}}-\frac{i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{5}}{2 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{7 i d^{2} c^{6} \sqrt{c +d \tan \left(f x +e \right)}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{5 i d^{4} c^{4} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{i d^{6} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{6 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{i d^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c^{2}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c^{4}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{5 i d^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{3}}{3 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{5 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{4}}{16 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}-\frac{5 i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{16 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}-\frac{13 i d^{6} c^{2} \sqrt{c +d \tan \left(f x +e \right)}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{6}}{8 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{i d^{6} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{i d^{6} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d \,c^{7} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{5 d^{3} c^{5} \sqrt{c +d \tan \left(f x +e \right)}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{5 d^{5} c^{3} \sqrt{c +d \tan \left(f x +e \right)}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{5 d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{4}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{5 d^{5} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{2}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{3 d^{7} c \sqrt{c +d \tan \left(f x +e \right)}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{7 d^{5} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{16 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{5}}{8 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}-\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{6}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{5 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{16 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c^{5}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{5 d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c^{3}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{7 d^{5} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d^{7} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}"," ",0,"-1/4/f/a^3*d/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^6-5/12/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^4+5/4/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^2-1/8*I/f/a^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^6+1/8*I/f/a^3*d^6/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))-1/8*I/f/a^3*(I*d-c)^(5/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))+1/4*I/f/a^3*d^6/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)+1/8/f/a^3*d/(d*tan(f*x+e)-I*d)^3*c^7/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)-5/16/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3*c^5/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)-5/4/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3*c^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)+3/16/f/a^3*d^7/(d*tan(f*x+e)-I*d)^3*c/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)+7/16/f/a^3*d^5/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+1/8/f/a^3*d/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^5+5/16/f/a^3*d^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3-13/16*I/f/a^3*d^6/(d*tan(f*x+e)-I*d)^3*c^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)+1/16*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^4-5/3*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^3-5/16*I/f/a^3*d^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^4-5/16*I/f/a^3*d^4/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+7/16*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3*c^6/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)+5/8*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3*c^4/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)+1/6*I/f/a^3*d^6/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c+1/16*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^2-1/2*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^5+1/8/f/a^3*d/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^5+5/16/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^3+7/16/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c+1/12/f/a^3*d^7/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)","B"
1119,1,1748,107,0.298000," ","int((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(1/2),x)","-\frac{2 i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{4 i a^{3} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{6 a^{3} \sqrt{c +d \tan \left(f x +e \right)}}{f d}+\frac{4 i a^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{4 i a^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a^{3} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{2 i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 i a^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f \,d^{2}}+\frac{4 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{3} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{4 i a^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{2 i a^{3} c \sqrt{c +d \tan \left(f x +e \right)}}{f \,d^{2}}-\frac{2 a^{3} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{2 a^{3} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{2 a^{3} d^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{2 i a^{3} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{4 a^{3} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 a^{3} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 a^{3} d^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"-2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c-4*I/f*a^3*d^2/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-6/f*a^3/d*(c+d*tan(f*x+e))^(1/2)+4*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2+4*I/f*a^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+2/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-2*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-2/3*I/f*a^3/d^2*(c+d*tan(f*x+e))^(3/2)+4/f*a^3*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+4*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c-4*I/f*a^3/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+4*I/f*a^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3+2*I/f*a^3/d^2*c*(c+d*tan(f*x+e))^(1/2)-2/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c-2/f*a^3*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-2/f*a^3*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+2*I/f*a^3*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))-4/f*a^3*d/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-4/f*a^3*d/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-4/f*a^3*d^3/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))","B"
1120,1,1698,63,0.224000," ","int((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(1/2),x)","-\frac{2 a^{2} \sqrt{c +d \tan \left(f x +e \right)}}{d f}-\frac{2 i a^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{a^{2} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{2 i a^{2} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a^{2} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{2 i a^{2} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{a^{2} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{a^{2} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{a^{2} d^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{2 i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{2 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a^{2} d^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"-2*a^2*(c+d*tan(f*x+e))^(1/2)/d/f-2*I/f*a^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+2*I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3+1/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-2*I/f*a^2*d^2/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))+2/f*a^2*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+2*I/f*a^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+2*I/f*a^2*d^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c-I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c-1/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c-1/f*a^2*d/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-1/f*a^2*d^3/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+2*I/f*a^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-2/f*a^2*d/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-2/f*a^2*d/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-2/f*a^2*d^3/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))","B"
1121,1,1618,37,0.200000," ","int((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(1/2),x)","\frac{i a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{i a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) d}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}+\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{2}}{f \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) d^{2}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}}-\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c d}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2} d}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}-\frac{a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) d^{3}}{2 f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{i a \ln \left(d \tan \left(f x +e \right)+c -\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c \,d^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right)}+\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c d}{f \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}-\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{3}}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}\, c +c^{2}+d^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3+I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2+1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*d+I/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+I/f*a/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^2+1/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d-1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))+1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*d^2-1/2*I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c-I/f*a/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c*d-1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2*d-1/2/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*d^3+I/f*a/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c*d^2+1/f*a/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d+1/f*a/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d+1/f*a/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)*c+c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^3","B"
1122,1,191,127,0.378000," ","int(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x)","\frac{d \sqrt{c +d \tan \left(f x +e \right)}}{2 f a \left(i d +c \right) \left(d \tan \left(f x +e \right)-i d \right)}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{2 f a \left(i d +c \right) \sqrt{-i d -c}}+\frac{d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{f a \left(i d +c \right) \sqrt{-i d -c}}+\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{2 f a \sqrt{i d -c}}"," ",0,"1/2/f/a*d/(c+I*d)*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)-1/2*I/f/a/(c+I*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+1/f/a*d/(c+I*d)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+1/2*I/f/a/(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))","A"
1123,1,502,185,0.444000," ","int(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x)","\frac{5 i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{9 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{4 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{7 d^{3} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{4 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{7 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{3 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{4 f \,a^{2} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{4 f \,a^{2} \sqrt{i d -c}}"," ",0,"5/8*I/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)+1/4/f/a^2*d/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c-9/8*I/f/a^2*d^2/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c-1/4/f/a^2*d/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^2+7/8/f/a^2*d^3/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)-1/4*I/f/a^2/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+7/8*I/f/a^2*d^2/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+3/4/f/a^2*d/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+1/4*I/f/a^2/(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))","B"
1124,1,1105,255,0.440000," ","int(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x)","-\frac{45 i d^{4} \sqrt{c +d \tan \left(f x +e \right)}\, c}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c^{2}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{5 d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{13 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{16 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{8 f \,a^{3} \sqrt{i d -c}}-\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{3}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{31 d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{19 i d^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{12 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{7 i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}} c}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{4}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{19 d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{9 d^{5} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{8 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}-\frac{5 i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{2}}{4 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}+\frac{d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{2 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}-\frac{3 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{4 f \,a^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right) \sqrt{-i d -c}}+\frac{13 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c^{3}}{16 f \,a^{3} \left(d \tan \left(f x +e \right)-i d \right)^{3} \left(3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right)}"," ",0,"-45/16*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c+1/8/f/a^3*d/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^2-5/8/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)+13/16*I/f/a^3*d^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+1/8*I/f/a^3/(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))-1/4/f/a^3*d/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^3+31/12/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c+19/12*I/f/a^3*d^4/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)+7/16*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c+1/8/f/a^3*d/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^4-19/8/f/a^3*d^3/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^2+9/8/f/a^3*d^5/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)-1/8*I/f/a^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3-5/4*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^2+1/2/f/a^3*d/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2-3/4/f/a^3*d^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+13/16*I/f/a^3*d^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^3","B"
1125,1,2594,122,0.327000," ","int((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x)","-\frac{2 i a^{3} \sqrt{c +d \tan \left(f x +e \right)}}{f \,d^{2}}-\frac{2 i a^{3} c^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right) \sqrt{c +d \tan \left(f x +e \right)}}-\frac{2 a^{3} d}{f \left(c^{2}+d^{2}\right) \sqrt{c +d \tan \left(f x +e \right)}}+\frac{4 i a^{3} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{4 i a^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{c^{2}+d^{2}}\, \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 i a^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{4 i a^{3} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a^{3} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{i a^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{i a^{3} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{4 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 a^{3} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{8 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a^{3} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{2 a^{3} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{8 a^{3} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a^{3} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{a^{3} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{4 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 a^{3} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{3} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 i a^{3} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{6 a^{3} c^{2}}{f d \left(c^{2}+d^{2}\right) \sqrt{c +d \tan \left(f x +e \right)}}+\frac{6 i a^{3} c}{f \left(c^{2}+d^{2}\right) \sqrt{c +d \tan \left(f x +e \right)}}"," ",0,"4*I/f*a^3*d^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-4*I/f*a^3*d^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-2*I/f*a^3/d^2*(c+d*tan(f*x+e))^(1/2)-2/f*a^3*d/(c^2+d^2)/(c+d*tan(f*x+e))^(1/2)+I/f*a^3/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2+4/f*a^3*d/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-4/f*a^3*d/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+I/f*a^3*d^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+8/f*a^3*d/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+2/f*a^3*d/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-2/f*a^3*d/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-8/f*a^3*d/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-I/f*a^3/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2+4*I/f*a^3/((c^2+d^2)^(1/2)+c)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-4*I/f*a^3/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+4*I/f*a^3/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+I/f*a^3/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-4*I/f*a^3*d^2/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-I/f*a^3*d^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+4*I/f*a^3*d^2/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-I/f*a^3/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-4*I/f*a^3/((c^2+d^2)^(1/2)+c)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+1/f*a^3*d/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-1/f*a^3*d/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-4/f*a^3*d/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+4/f*a^3*d/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-2*I/f*a^3/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^(1/2)*c^3+6/f*a^3/d/(c^2+d^2)/(c+d*tan(f*x+e))^(1/2)*c^2+6*I/f*a^3/(c^2+d^2)/(c+d*tan(f*x+e))^(1/2)*c","B"
1126,1,2534,79,0.285000," ","int((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x)","-\frac{2 a^{2} d}{f \left(c^{2}+d^{2}\right) \sqrt{c +d \tan \left(f x +e \right)}}-\frac{2 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 i a^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{2 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{2 i a^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{2 f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{i a^{2} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{2 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{2 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{2 i a^{2} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a^{2} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{2 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{2 i a^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{2 f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{a^{2} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{a^{2} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{4 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{2} c}{f \left(c^{2}+d^{2}\right) \sqrt{c +d \tan \left(f x +e \right)}}-\frac{2 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a^{2} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{2 f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{a^{2} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{2 f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{2 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 i a^{2} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a^{2} c^{2}}{f d \left(c^{2}+d^{2}\right) \sqrt{c +d \tan \left(f x +e \right)}}"," ",0,"-2/f*a^2*d/(c^2+d^2)/(c+d*tan(f*x+e))^(1/2)-2*I/f*a^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+1/2*I/f*a^2/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c+1/2*I/f*a^2*d^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-1/2*I/f*a^2*d^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-1/2*I/f*a^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2-2*I/f*a^2*d^2/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+2*I/f*a^2*d^2/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-2/f*a^2*d/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-1/2*I/f*a^2/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-2*I/f*a^2/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+1/2*I/f*a^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2+2*I/f*a^2/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+2*I/f*a^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+4/f*a^2*d/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+2/f*a^2*d/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+4*I/f*a^2/(c^2+d^2)/(c+d*tan(f*x+e))^(1/2)*c-1/f*a^2*d/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c+1/f*a^2*d/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-4/f*a^2*d/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-2/f*a^2*d/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+1/2/f*a^2*d/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-1/2/f*a^2*d/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+2/f*a^2*d/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+2*I/f*a^2*d^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-2*I/f*a^2*d^2/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+2/f*a^2/d/(c^2+d^2)/(c+d*tan(f*x+e))^(1/2)*c^2","B"
1127,1,2446,64,0.238000," ","int((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x)","-\frac{2 a d}{f \left(c^{2}+d^{2}\right) \sqrt{c +d \tan \left(f x +e \right)}}-\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, d}{4 f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, d}{4 f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{4 f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c}{4 f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{2}}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{4 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c^{2}}{4 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, d^{2}}{4 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}-\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \sqrt{c^{2}+d^{2}}\, \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{2}}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, d^{2}}{4 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c d}{2 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{2 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c d}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c d}{f \left(c^{2}+d^{2}\right) \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, c d}{2 f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right)}+\frac{2 i a c}{f \left(c^{2}+d^{2}\right) \sqrt{c +d \tan \left(f x +e \right)}}-\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{3}{2}} \left(\sqrt{c^{2}+d^{2}}+c \right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"-2/f*a/(c^2+d^2)/(c+d*tan(f*x+e))^(1/2)*d-1/4/f*a/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*d+1/f*a/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d+1/4/f*a/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*d-1/f*a/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d-I/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+I/f*a/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-1/2/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c*d+2/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d+1/f*a/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d+I/f*a/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^2-2/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d-1/f*a/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d+1/4*I/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*d^2+I/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-1/4*I/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*d^2-1/4*I/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2+1/2/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c*d+1/4*I/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c^2-I/f*a/(c^2+d^2)^(1/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-I/f*a/(c^2+d^2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^2-1/4*I/f*a/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c+1/4*I/f*a/(c^2+d^2)/((c^2+d^2)^(1/2)+c)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*c-I/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^2+I/f*a/(c^2+d^2)^(3/2)/((c^2+d^2)^(1/2)+c)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^2+2*I/f*a/(c^2+d^2)/(c+d*tan(f*x+e))^(1/2)*c","B"
1128,1,580,170,0.409000," ","int(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x)","-\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{2 f a \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)}-\frac{d^{3} \sqrt{c +d \tan \left(f x +e \right)}}{2 f a \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)}+\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{2 f a \left(i d +c \right)^{3} \left(i d -c \right) \sqrt{-i d -c}}+\frac{i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{2 f a \left(i d +c \right)^{3} \left(i d -c \right) \sqrt{-i d -c}}-\frac{2 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{f a \left(i d +c \right)^{3} \left(i d -c \right) \sqrt{-i d -c}}-\frac{2 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{f a \left(i d +c \right)^{3} \left(i d -c \right) \sqrt{-i d -c}}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{2}}{2 f a \left(i d -c \right)^{\frac{3}{2}} \left(i d +c \right)^{2}}+\frac{i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{2 f a \left(i d -c \right)^{\frac{3}{2}} \left(i d +c \right)^{2}}+\frac{d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c}{f a \left(i d -c \right)^{\frac{3}{2}} \left(i d +c \right)^{2}}+\frac{2 i d^{2}}{f a \left(i d +c \right) \left(i c -d \right) \left(i c +d \right) \sqrt{c +d \tan \left(f x +e \right)}}"," ",0,"-1/2/f/a*d/(c+I*d)^3/(I*d-c)*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)*c^2-1/2/f/a*d^3/(c+I*d)^3/(I*d-c)*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)+1/2*I/f/a/(c+I*d)^3/(I*d-c)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3+1/2*I/f/a*d^2/(c+I*d)^3/(I*d-c)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c-2/f/a*d/(c+I*d)^3/(I*d-c)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2-2/f/a*d^3/(c+I*d)^3/(I*d-c)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))-1/2*I/f/a/(I*d-c)^(3/2)/(c+I*d)^2*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^2+1/2*I/f/a*d^2/(I*d-c)^(3/2)/(c+I*d)^2*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))+1/f/a*d/(I*d-c)^(3/2)/(c+I*d)^2*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c+2*I/f/a*d^2/(c+I*d)/(I*c-d)/(I*c+d)/(c+d*tan(f*x+e))^(1/2)","B"
1129,1,1568,238,0.450000," ","int(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x)","-\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{4}}{4 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{7 d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{2}}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{9 d^{5} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{3}}{4 f \,a^{2} \left(i d -c \right)^{\frac{3}{2}} \left(i d +c \right)^{3}}-\frac{11 i d^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{5}}{4 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{11 d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c^{3}}{4 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{3 d^{5} \sqrt{c +d \tan \left(f x +e \right)}\, c}{f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{11 i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{3}}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{5}}{4 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{15 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c^{4}}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{3 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{4}}{2 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{11 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{23 d^{5} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{i d^{4} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{2 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{11 i d^{6} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{33 i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{3 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{2}}{4 f \,a^{2} \left(i d -c \right)^{\frac{3}{2}} \left(i d +c \right)^{3}}-\frac{d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{4 f \,a^{2} \left(i d -c \right)^{\frac{3}{2}} \left(i d +c \right)^{3}}-\frac{31 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{8 f \,a^{2} \left(i d +c \right)^{3} \left(i d -c \right) \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{3 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c}{4 f \,a^{2} \left(i d -c \right)^{\frac{3}{2}} \left(i d +c \right)^{3}}-\frac{2 d^{3}}{f \,a^{2} \left(i c -d \right) \left(i c +d \right) \left(i d +c \right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}"," ",0,"-1/4/f/a^2*d/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^4+7/8/f/a^2*d^3/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^2+9/8/f/a^2*d^5/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)-1/4*I/f/a^2/(I*d-c)^(3/2)/(c+I*d)^3*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^3-11/8*I/f/a^2*d^4/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c+1/4/f/a^2*d/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^5-11/4/f/a^2*d^3/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^3-3/f/a^2*d^5/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c-11/8*I/f/a^2*d^2/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^3+1/4*I/f/a^2/(c+I*d)^3/(I*d-c)/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^5+15/8*I/f/a^2*d^2/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^4-3/2/f/a^2*d/(c+I*d)^3/(I*d-c)/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^4+11/8/f/a^2*d^3/(c+I*d)^3/(I*d-c)/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+23/8/f/a^2*d^5/(c+I*d)^3/(I*d-c)/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+1/2*I/f/a^2*d^4/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^2-11/8*I/f/a^2*d^6/(c+I*d)^3/(I*d-c)/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)-33/8*I/f/a^2*d^4/(c+I*d)^3/(I*d-c)/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+3/4/f/a^2*d/(I*d-c)^(3/2)/(c+I*d)^3*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^2-1/4/f/a^2*d^3/(I*d-c)^(3/2)/(c+I*d)^3*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))-31/8*I/f/a^2*d^2/(c+I*d)^3/(I*d-c)/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3+3/4*I/f/a^2*d^2/(I*d-c)^(3/2)/(c+I*d)^3*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c-2/f/a^2*d^3/(I*c-d)/(I*c+d)/(c+I*d)^2/(c+d*tan(f*x+e))^(1/2)","B"
1130,1,3053,317,0.457000," ","int(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"1/2/f/a^3*d/(I*d-c)^(3/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^3+3/4*I/f/a^3*d^2/(I*d-c)^(3/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^2+5/2/f/a^3*d^9/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)-7/4/f/a^3*d^7/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)-29/8/f/a^3*d^7/(c+I*d)^4/(I*d-c)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))-2*I/f/a^3*d^4/(I*c+d)/(I*c-d)/(c+I*d)^3/(c+d*tan(f*x+e))^(1/2)+49/12*I/f/a^3*d^8/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)+73/16*I/f/a^3*d^6/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^3-173/16*I/f/a^3*d^8/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c-59/4*I/f/a^3*d^4/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^4-155/12*I/f/a^3*d^6/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^2-1/2/f/a^3*d^3/(I*d-c)^(3/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c-1/8*I/f/a^3*d^4/(I*d-c)^(3/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))-1/8*I/f/a^3/(I*d-c)^(3/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^4+67/16*I/f/a^3*d^6/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c-109/12/f/a^3*d^3/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^5+45/8*I/f/a^3*d^4/(c+I*d)^4/(I*d-c)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3+149/16*I/f/a^3*d^6/(c+I*d)^4/(I*d-c)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+39/8/f/a^3*d^5/(c+I*d)^4/(I*d-c)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+53/12/f/a^3*d^5/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^3+55/4/f/a^3*d^7/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c-1/8/f/a^3*d/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^8+51/8/f/a^3*d^3/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^6-95/8/f/a^3*d^5/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^4-127/8/f/a^3*d^7/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^2-1/f/a^3*d/(c+I*d)^4/(I*d-c)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^6-1/8/f/a^3*d/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^6-15/16*I/f/a^3*d^2/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^5+13/4*I/f/a^3*d^4/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^3+9/4*I/f/a^3*d^2/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^6+1/8*I/f/a^3/(c+I*d)^4/(I*d-c)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^7-57/16*I/f/a^3*d^2/(c+I*d)^4/(I*d-c)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^5+15/2/f/a^3*d^3/(c+I*d)^4/(I*d-c)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^4+25/8/f/a^3*d^3/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^4+3/2/f/a^3*d^5/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^2+1/4/f/a^3*d/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^7-21/16*I/f/a^3*d^2/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^7+225/16*I/f/a^3*d^4/(c+I*d)^4/(I*d-c)/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^5","B"
1131,1,2772,135,0.296000," ","int((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x)","-\frac{2 a^{3} d}{3 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{12 i a^{3} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{12 i a^{3} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{6 i a^{3} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{6 i a^{3} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 i a^{3} c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{6 i a^{3} d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}-\frac{2 i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 i a^{3} c^{3}}{3 f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{2 i a^{3} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 i a^{3} c^{4}}{f \,d^{2} \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}+\frac{2 i a^{3} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{4 i a^{3} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{3} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{4 i a^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 i a^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 i a^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 i a^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{4 i a^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 i a^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 a^{3} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{6 a^{3} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{12 a^{3} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{8 a^{3} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{8 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{12 a^{3} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{6 a^{3} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{4 a^{3} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{12 i a^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}+\frac{2 a^{3} d^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{4 a^{3} d^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a^{3} c^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{2 a^{3} d^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{4 a^{3} d^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{16 a^{3} d c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}"," ",0,"-2/3/f*a^3*d/(c^2+d^2)/(c+d*tan(f*x+e))^(3/2)-6*I/f*a^3*d^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c+6*I/f*a^3*d^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c+12*I/f*a^3*d^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-12*I/f*a^3*d^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-4/f*a^3*d/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c+6/f*a^3*d/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2-12/f*a^3*d/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+8/f*a^3*d/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-8/f*a^3*d/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+4*I/f*a^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-4*I/f*a^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-2*I/f*a^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3-2/3*I/f*a^3/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^(3/2)*c^3-2*I/f*a^3*d^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+2*I/f*a^3/d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)*c^4+2*I/f*a^3*d^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-4*I/f*a^3*d^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+4*I/f*a^3*d^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+2*I/f*a^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3+12/f*a^3*d/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-6/f*a^3*d/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-4*I/f*a^3/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+4*I/f*a^3/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+4/f*a^3*d/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c-2*I/f*a^3/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2+2*I/f*a^3/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2+2*I/f*a^3/(c^2+d^2)/(c+d*tan(f*x+e))^(3/2)*c-6*I/f*a^3*d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)+2/f*a^3*d^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+4/f*a^3*d^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+2/f*a^3/d/(c^2+d^2)/(c+d*tan(f*x+e))^(3/2)*c^2-2/f*a^3*d^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-4/f*a^3*d^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-16/f*a^3*d/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)*c+12*I/f*a^3/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)*c^2","B"
1132,1,2699,108,0.296000," ","int((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x)","\frac{3 i a^{2} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{6 i a^{2} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{6 i a^{2} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 i a^{2} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{8 a^{2} d c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}+\frac{2 a^{2} c^{2}}{3 f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{2 i a^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 i a^{2} d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a^{2} d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a^{2} d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 i a^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{i a^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 i a^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{i a^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{3 a^{2} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{6 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{6 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a^{2} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{4 a^{2} d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 a^{2} d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 a^{2} d}{3 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{2 a^{2} d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{4 a^{2} d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a^{2} d^{3} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{a^{2} d^{3} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right)}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 a^{2} d^{3} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right)}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a^{2} d^{3} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right)}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{4 i a^{2} c}{3 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{4 i a^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}-\frac{4 i a^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}"," ",0,"-3*I/f*a^2*d^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c+6*I/f*a^2*d^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-6*I/f*a^2*d^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+3*I/f*a^2*d^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c+2*I/f*a^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+I/f*a^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3-8/f*a^2*d/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)*c+2/3/f*a^2/d/(c^2+d^2)/(c+d*tan(f*x+e))^(3/2)*c^2+4/3*I/f*a^2/(c^2+d^2)/(c+d*tan(f*x+e))^(3/2)*c+3/f*a^2*d/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2-6/f*a^2*d/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+6/f*a^2*d/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-2/f*a^2*d/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c+4/f*a^2*d/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c-3/f*a^2*d/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-2/3/f*a^2*d/(c^2+d^2)/(c+d*tan(f*x+e))^(3/2)-2*I/f*a^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-I/f*a^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2-I/f*a^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3+2*I/f*a^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+2*I/f*a^2*d^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-2*I/f*a^2*d^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-I/f*a^2*d^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))+2/f*a^2*d/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c+I/f*a^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-4/f*a^2*d/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c+I/f*a^2*d^2/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-2*I/f*a^2/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3+4*I/f*a^2/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)*c^2-4*I/f*a^2*d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)-2/f*a^2*d^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-1/f*a^2*d^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))+2/f*a^2*d^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+1/f*a^2*d^3/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))","B"
1133,1,2597,91,0.245000," ","int((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x)","\frac{3 i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{3 i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{3 i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{2 i a \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}-\frac{2 i a \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{3}}{2 f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{3}}{2 f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c d}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) c d}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{2 a d}{3 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c d}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{3 a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{3 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c d}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 i a c}{3 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{i a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}+\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{i a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{3}}{f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{4 a c d}{f \left(c^{2}+d^{2}\right)^{2} \sqrt{c +d \tan \left(f x +e \right)}}+\frac{a \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) d^{3}}{2 f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}-\frac{a \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) d^{3}}{2 f \left(c^{2}+d^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}"," ",0,"3/2*I/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c*d^2-3*I/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^2+3*I/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d^2-3/2*I/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c*d^2+1/2*I/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*d^2+I/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^2-I/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2-I/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^2-1/2*I/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*d^2-1/2*I/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2+2/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d-3/2/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2*d+I/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-1/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c*d-2/3/f*a/(c^2+d^2)/(c+d*tan(f*x+e))^(3/2)*d+1/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c*d+3/2/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^2*d+3/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d-I/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^3-2/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c*d+I/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2+1/2*I/f*a/(c^2+d^2)^2/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^2-1/2*I/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*c^3+1/2*I/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*c^3-3/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d+1/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^3-1/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^3-4/f*a/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)*c*d+2*I/f*a/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)*c^2-2*I/f*a/(c^2+d^2)^2/(c+d*tan(f*x+e))^(1/2)*d^2+2/3*I/f*a/(c^2+d^2)/(c+d*tan(f*x+e))^(3/2)*c+1/2/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*d^3-1/2/f*a/(c^2+d^2)^(5/2)/(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*d^3","B"
1134,1,1137,226,0.422000," ","int(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x)","\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{4}}{2 f a \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)}+\frac{d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)}+\frac{d^{5} \sqrt{c +d \tan \left(f x +e \right)}}{2 f a \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)}-\frac{2 i d^{2} c^{3}}{3 f a \left(i d -c \right)^{2} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{3 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{2}}{f a \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{4}}-\frac{i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{5} \sqrt{-i d -c}}+\frac{3 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{4}}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{5} \sqrt{-i d -c}}+\frac{6 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{5} \sqrt{-i d -c}}+\frac{3 d^{5} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{5} \sqrt{-i d -c}}-\frac{2 i d^{4}}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{4} \sqrt{c +d \tan \left(f x +e \right)}}+\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{4}}{2 f a \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{4}}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{5}}{2 f a \left(i d -c \right)^{2} \left(i d +c \right)^{5} \sqrt{-i d -c}}-\frac{2 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{3}}{f a \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{4}}+\frac{2 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c}{f a \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{4}}+\frac{i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{2 f a \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{4}}-\frac{6 i d^{2} c^{2}}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{4} \sqrt{c +d \tan \left(f x +e \right)}}+\frac{2 d^{3} c^{2}}{3 f a \left(i d -c \right)^{2} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}+\frac{2 d^{5}}{3 f a \left(i d -c \right)^{2} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{2 i d^{4} c}{3 f a \left(i d -c \right)^{2} \left(i d +c \right)^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{2 f a \left(i d -c \right)^{2} \left(i d +c \right)^{5} \sqrt{-i d -c}}+\frac{4 d^{3} c}{f a \left(i d -c \right)^{2} \left(i d +c \right)^{4} \sqrt{c +d \tan \left(f x +e \right)}}"," ",0,"1/2/f/a*d/(I*d-c)^2/(c+I*d)^5*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)*c^4+1/f/a*d^3/(I*d-c)^2/(c+I*d)^5*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)*c^2+1/2/f/a*d^5/(I*d-c)^2/(c+I*d)^5*(c+d*tan(f*x+e))^(1/2)/(d*tan(f*x+e)-I*d)-2/3*I/f/a*d^2/(I*d-c)^2/(c+I*d)^4/(c+d*tan(f*x+e))^(3/2)*c^3-3*I/f/a*d^2/(I*d-c)^(5/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^2-I/f/a*d^2/(I*d-c)^2/(c+I*d)^5/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3+3/f/a*d/(I*d-c)^2/(c+I*d)^5/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^4+6/f/a*d^3/(I*d-c)^2/(c+I*d)^5/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+3/f/a*d^5/(I*d-c)^2/(c+I*d)^5/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))-2*I/f/a*d^4/(I*d-c)^2/(c+I*d)^4/(c+d*tan(f*x+e))^(1/2)+1/2*I/f/a/(I*d-c)^(5/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^4-1/2*I/f/a/(I*d-c)^2/(c+I*d)^5/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^5-2/f/a*d/(I*d-c)^(5/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^3+2/f/a*d^3/(I*d-c)^(5/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c+1/2*I/f/a*d^4/(I*d-c)^(5/2)/(c+I*d)^4*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))-6*I/f/a*d^2/(I*d-c)^2/(c+I*d)^4/(c+d*tan(f*x+e))^(1/2)*c^2+2/3/f/a*d^3/(I*d-c)^2/(c+I*d)^4/(c+d*tan(f*x+e))^(3/2)*c^2+2/3/f/a*d^5/(I*d-c)^2/(c+I*d)^4/(c+d*tan(f*x+e))^(3/2)-2/3*I/f/a*d^4/(I*d-c)^2/(c+I*d)^4/(c+d*tan(f*x+e))^(3/2)*c-1/2*I/f/a*d^4/(I*d-c)^2/(c+I*d)^5/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+4/f/a*d^3/(I*d-c)^2/(c+I*d)^4/(c+d*tan(f*x+e))^(1/2)*c","B"
1135,1,2312,300,0.497000," ","int(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x)","-\frac{47 d^{7} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right)}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{2 d^{5}}{3 f \,a^{2} \left(i d +c \right)^{4} \left(i d -c \right)^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{d^{5} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right)}{4 f \,a^{2} \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{5}}+\frac{4 d^{5}}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \sqrt{c +d \tan \left(f x +e \right)}}+\frac{2 d^{3} c^{2}}{3 f \,a^{2} \left(i d +c \right)^{4} \left(i d -c \right)^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}-\frac{5 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{4}}{4 f \,a^{2} \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{5}}+\frac{8 d^{3} c^{2}}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \sqrt{c +d \tan \left(f x +e \right)}}+\frac{5 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{2}}{2 f \,a^{2} \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{5}}+\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{5}}{4 f \,a^{2} \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{5}}-\frac{13 d^{7} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{4 i d^{4} c}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \sqrt{c +d \tan \left(f x +e \right)}}-\frac{5 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c^{3}}{2 f \,a^{2} \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{5}}+\frac{5 i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{i d -c}}\right) c}{4 f \,a^{2} \left(i d -c \right)^{\frac{5}{2}} \left(i d +c \right)^{5}}-\frac{3 d^{5} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{2}}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{31 d^{5} \sqrt{c +d \tan \left(f x +e \right)}\, c^{3}}{4 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{4 d^{7} \sqrt{c +d \tan \left(f x +e \right)}\, c}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{2 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{6}}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}-\frac{i \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{7}}{4 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}-\frac{9 d^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{4}}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{7 d^{3} \sqrt{c +d \tan \left(f x +e \right)}\, c^{5}}{2 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{15 d^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{4}}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}-\frac{39 d^{5} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{2}}{4 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{d \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{6}}{4 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{15 i d^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{5}}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{15 i d^{4} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c^{3}}{4 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{19 i d^{2} \sqrt{c +d \tan \left(f x +e \right)}\, c^{6}}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{15 i d^{8} \sqrt{c +d \tan \left(f x +e \right)}}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}-\frac{d \sqrt{c +d \tan \left(f x +e \right)}\, c^{7}}{4 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{15 i d^{6} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} c}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{15 i d^{4} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{3}}{f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{11 i d^{6} \sqrt{c +d \tan \left(f x +e \right)}\, c^{2}}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}+\frac{61 i d^{6} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}+\frac{57 i d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{-i d -c}}\right) c^{5}}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(2 i c d +c^{2}-d^{2}\right) \sqrt{-i d -c}}-\frac{23 i d^{4} \sqrt{c +d \tan \left(f x +e \right)}\, c^{4}}{8 f \,a^{2} \left(i d -c \right)^{2} \left(i d +c \right)^{5} \left(d \tan \left(f x +e \right)-i d \right)^{2} \left(2 i c d +c^{2}-d^{2}\right)}"," ",0,"-13/8/f/a^2*d^7/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)+2/3/f/a^2*d^3/(c+I*d)^4/(I*d-c)^2/(c+d*tan(f*x+e))^(3/2)*c^2-5/4/f/a^2*d/(I*d-c)^(5/2)/(c+I*d)^5*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^4+8/f/a^2*d^3/(I*d-c)^2/(c+I*d)^5/(c+d*tan(f*x+e))^(1/2)*c^2+5/2/f/a^2*d^3/(I*d-c)^(5/2)/(c+I*d)^5*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^2+1/4*I/f/a^2/(I*d-c)^(5/2)/(c+I*d)^5*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^5+11/8*I/f/a^2*d^6/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^2+15/8*I/f/a^2*d^2/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^5+15/4*I/f/a^2*d^4/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^3-19/8*I/f/a^2*d^2/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^6+2/3/f/a^2*d^5/(c+I*d)^4/(I*d-c)^2/(c+d*tan(f*x+e))^(3/2)-1/4/f/a^2*d^5/(I*d-c)^(5/2)/(c+I*d)^5*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))+4*I/f/a^2*d^4/(I*d-c)^2/(c+I*d)^5/(c+d*tan(f*x+e))^(1/2)*c-5/2*I/f/a^2*d^2/(I*d-c)^(5/2)/(c+I*d)^5*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^3+5/4*I/f/a^2*d^4/(I*d-c)^(5/2)/(c+I*d)^5*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c-47/8/f/a^2*d^7/(I*d-c)^2/(c+I*d)^5/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))-9/8/f/a^2*d^3/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^4+4/f/a^2*d^5/(I*d-c)^2/(c+I*d)^5/(c+d*tan(f*x+e))^(1/2)+7/2/f/a^2*d^3/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^5-15/8/f/a^2*d^3/(I*d-c)^2/(c+I*d)^5/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^4-39/4/f/a^2*d^5/(I*d-c)^2/(c+I*d)^5/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2+1/4/f/a^2*d/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^6-3/f/a^2*d^5/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c^2+31/4/f/a^2*d^5/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^3+4/f/a^2*d^7/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c+2/f/a^2*d/(I*d-c)^2/(c+I*d)^5/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^6-1/4*I/f/a^2/(I*d-c)^2/(c+I*d)^5/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^7+15/8*I/f/a^2*d^8/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)-1/4/f/a^2*d/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^7+15/8*I/f/a^2*d^6/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(3/2)*c+15*I/f/a^2*d^4/(I*d-c)^2/(c+I*d)^5/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3+61/8*I/f/a^2*d^6/(I*d-c)^2/(c+I*d)^5/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c+57/8*I/f/a^2*d^2/(I*d-c)^2/(c+I*d)^5/(-d^2+2*I*c*d+c^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^5-23/8*I/f/a^2*d^4/(I*d-c)^2/(c+I*d)^5/(d*tan(f*x+e)-I*d)^2/(-d^2+2*I*c*d+c^2)*(c+d*tan(f*x+e))^(1/2)*c^4","B"
1136,1,4108,387,0.454000," ","int(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"2/3*I/f/a^3*d^6/(I*d-c)^2/(c+I*d)^6/(c+d*tan(f*x+e))^(3/2)*c+15/8*I/f/a^3*d^4/(I*d-c)^(5/2)/(c+I*d)^6*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^2-15/8*I/f/a^3*d^2/(I*d-c)^(5/2)/(c+I*d)^6*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^4+10*I/f/a^3*d^4/(I*d-c)^2/(c+I*d)^6/(c+d*tan(f*x+e))^(1/2)*c^2+19/2/f/a^3*d^9/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))+2/3*I/f/a^3*d^4/(I*d-c)^2/(c+I*d)^6/(c+d*tan(f*x+e))^(3/2)*c^3-3/4/f/a^3*d^5/(I*d-c)^(5/2)/(c+I*d)^6*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c-3/4/f/a^3*d/(I*d-c)^(5/2)/(c+I*d)^6*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^5+5/2/f/a^3*d^3/(I*d-c)^(5/2)/(c+I*d)^6*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^3-4/f/a^3*d^5/(I*d-c)^2/(c+I*d)^6/(c+d*tan(f*x+e))^(1/2)*c-2/3/f/a^3*d^5/(I*d-c)^2/(c+I*d)^6/(c+d*tan(f*x+e))^(3/2)*c^2+1/8*I/f/a^3/(I*d-c)^(5/2)/(c+I*d)^6*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))*c^6-1/8*I/f/a^3*d^6/(I*d-c)^(5/2)/(c+I*d)^6*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))+6*I/f/a^3*d^6/(I*d-c)^2/(c+I*d)^6/(c+d*tan(f*x+e))^(1/2)-35/8/f/a^3*d^11/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)+27/8/f/a^3*d^9/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)-99/4/f/a^3*d^9/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c-85/4*I/f/a^3*d^4/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^7-229/8*I/f/a^3*d^6/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^5-2/3/f/a^3*d^7/(I*d-c)^2/(c+I*d)^6/(c+d*tan(f*x+e))^(3/2)+1/8/f/a^3*d/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^10-73/8/f/a^3*d^3/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^8+12/f/a^3*d^5/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^6+95/2/f/a^3*d^7/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^4+175/8/f/a^3*d^9/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^2+1/8/f/a^3*d/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^8-227/16*I/f/a^3*d^6/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^3+51/4*I/f/a^3*d^8/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^3+297/16*I/f/a^3*d^10/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c-85/16*I/f/a^3*d^4/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^5+91/16*I/f/a^3*d^2/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^7-365/16*I/f/a^3*d^8/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c-41/8/f/a^3*d^3/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^6+11/8/f/a^3*d^7/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^2-1/4/f/a^3*d/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^9+83/6/f/a^3*d^3/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^7+11/3/f/a^3*d^5/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^5+7/8/f/a^3*d^7/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^2-125/8/f/a^3*d^3/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^6-51/2/f/a^3*d^5/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^4-1/8*I/f/a^3/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^9-91/12*I/f/a^3*d^10/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)-211/6/f/a^3*d^7/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^3-29/4/f/a^3*d^5/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^4+5/4/f/a^3*d/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^8+25/16*I/f/a^3*d^2/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2)*c^9+83/6*I/f/a^3*d^8/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^2+19/16*I/f/a^3*d^2/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c^7-177/16*I/f/a^3*d^4/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^5-635/16*I/f/a^3*d^6/(c+I*d)^6/(I*d-c)^2/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))*c^3-123/16*I/f/a^3*d^8/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)*c-11/4*I/f/a^3*d^2/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^8+47/2*I/f/a^3*d^4/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^6+143/3*I/f/a^3*d^6/(c+I*d)^6/(I*d-c)^2/(d*tan(f*x+e)-I*d)^3/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)*c^4","B"
1137,1,1079,208,0.523000," ","int((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(5/2),x)","\frac{\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, a^{2} \left(i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,c^{2}+32 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d +23 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}+16 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d +16 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{2}+18 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{i d a}\, d -4 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{i d a}\, \tan \left(f x +e \right) d -10 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d +32 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}-16 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d +16 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{2}-2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{i d a}\, c \right) \sqrt{2}}{16 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/16/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*a^2*(I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c^2+32*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d+23*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*d^2+16*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d+16*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^2+18*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(I*d*a)^(1/2)*d-4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(I*d*a)^(1/2)*tan(f*x+e)*d-10*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d+32*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*d^2-16*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d+16*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^2-2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(I*d*a)^(1/2)*c)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/d/(I*d*a)^(1/2)*2^(1/2)/(-a*(I*d-c))^(1/2)","B"
1138,1,866,201,0.367000," ","int((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(3/2),x)","\frac{\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, a \left(-\ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c +3 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a d +2 i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+4 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a d +4 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c +2 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c +2 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a d -2 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c +2 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d a \sqrt{i d a}\right) \sqrt{2}}{4 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/4/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*a*(-ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c+3*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d+2*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+4*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d+4*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c+2*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c+2*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d-2*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c+2*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d*a*(I*d*a)^(1/2))/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d*a)^(1/2)*2^(1/2)/(-a*(I*d-c))^(1/2)","B"
1139,1,866,114,0.475000," ","int((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, a \left(i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) d^{2}-i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) c d +i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \sqrt{i d a}\, c^{2}+i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \sqrt{i d a}\, d^{2}+\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) c d -\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \sqrt{i d a}\, \tan \left(f x +e \right) c^{2}-\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \sqrt{i d a}\, \tan \left(f x +e \right) d^{2}+\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) d^{2}\right) \sqrt{2}}{2 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}\, \left(i c -d \right) \left(-\tan \left(f x +e \right)+i\right)}"," ",0,"1/2/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)*a*(I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*d^2-I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*c*d+I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*(I*d*a)^(1/2)*c^2+I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*(I*d*a)^(1/2)*d^2+2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*c*d-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*(I*d*a)^(1/2)*tan(f*x+e)*c^2-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*(I*d*a)^(1/2)*tan(f*x+e)*d^2+2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*d^2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d*a)^(1/2)*2^(1/2)/(-a*(I*d-c))^(1/2)/(I*c-d)/(-tan(f*x+e)+I)","B"
1140,1,877,95,0.445000," ","int((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(1/2),x)","\frac{\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) d -2 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c +\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c -i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) d +4 i \tan \left(f x +e \right) c \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c +4 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d -4 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) d +4 c \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\right)}{4 f a \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(i c -d \right) \left(-\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"1/4/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a*(I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d-2*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c+2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c-I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d+4*I*tan(f*x+e)*c*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c+4*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d-4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d+4*c*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*c-d)/(-tan(f*x+e)+I)^2","B"
1141,1,1180,139,0.434000," ","int((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x)","-\frac{\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(3 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) d -9 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c +3 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) c -9 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) d +9 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) d +3 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c +12 i \left(\tan^{2}\left(f x +e \right)\right) c \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-9 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c +16 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) d -3 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d -4 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{2}\left(f x +e \right)\right) d -20 i c \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+32 \tan \left(f x +e \right) c \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+12 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d \right)}{24 f \,a^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(i c -d \right) \left(-\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"-1/24/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*(3*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d-9*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c+3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c-9*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d+9*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d+3*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c+12*I*tan(f*x+e)^2*c*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-9*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c+16*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d-3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d-4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d-20*I*c*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+32*tan(f*x+e)*c*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+12*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d)/a^2/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*c-d)/(-tan(f*x+e)+I)^3","B"
1142,1,2226,206,0.380000," ","int((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x)","\frac{\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(15 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c^{2}+90 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) d^{2}+180 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c d +60 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) c^{2}-15 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d^{2}-120 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c d -304 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{2}\left(f x +e \right)\right) c d +220 i \left(\tan^{2}\left(f x +e \right)\right) c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+12 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{2}\left(f x +e \right)\right) d^{2}-60 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) d^{2}-60 \left(\tan^{3}\left(f x +e \right)\right) c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-15 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{4}\left(f x +e \right)\right) d^{2}-30 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{4}\left(f x +e \right)\right) c d -80 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{3}\left(f x +e \right)\right) c d +120 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) c d -12 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{3}\left(f x +e \right)\right) d^{2}+464 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) c d -60 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c^{2}+60 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) d^{2}-30 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c d +308 \tan \left(f x +e \right) c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-148 i c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+60 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d^{2}-60 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) d^{2}+240 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c d -90 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c^{2}+15 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{4}\left(f x +e \right)\right) c^{2}\right)}{240 f \,a^{3} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(i c -d \right)^{2} \left(-\tan \left(f x +e \right)+i\right)^{4}}"," ",0,"1/240/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a^3*(-90*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2-304*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d+220*I*tan(f*x+e)^2*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+12*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^2-80*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c*d+15*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2-15*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d^2+464*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d+60*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^2-60*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d^2+308*tan(f*x+e)*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-60*tan(f*x+e)^3*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-148*I*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+60*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^2-12*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*d^2-60*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^2+240*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d-60*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2+60*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^2-30*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c*d+120*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c*d-120*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c*d+90*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^2+180*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c*d+15*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^2-15*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*d^2-30*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c*d)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*c-d)^2/(-tan(f*x+e)+I)^4","B"
1143,1,1518,265,0.395000," ","int((a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, a^{2} \left(-16 \sqrt{2}\, \left(\tan^{2}\left(f x +e \right)\right) d^{2} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}-28 \sqrt{2}\, \tan \left(f x +e \right) c d \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+207 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c \,d^{2}+3 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{3}-96 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}+96 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{2}+96 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d +52 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) d^{2}-45 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2} d +135 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,d^{3}-96 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d +136 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c d +96 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d -96 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}-6 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{2}+114 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, d^{2}-96 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d +96 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{2}\right) \sqrt{2}}{96 f d \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/96/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)*a^2*(-16*2^(1/2)*tan(f*x+e)^2*d^2*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-28*2^(1/2)*tan(f*x+e)*c*d*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+207*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d^2+3*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^3-96*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d^2+96*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^2+96*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d+52*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*d^2-45*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2*d+135*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d^3-96*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d+136*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c*d+96*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d-96*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*d^2-6*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^2+114*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*d^2-96*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d+96*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^2)*2^(1/2)/d/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d*a)^(1/2)/(-a*(I*d-c))^(1/2)","B"
1144,1,1234,251,0.470000," ","int((a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, a \left(-3 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2}+4 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) d -8 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c +18 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d +11 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}+10 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, d +8 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c -8 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a d -8 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a d +8 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c +8 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a d +10 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c -8 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c +8 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d a \sqrt{i d a}\right) \sqrt{2}}{16 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/16/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)*a*(-3*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2+4*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*d-8*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c+18*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d+11*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*d^2+10*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*d+8*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c-8*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d-8*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*d*a*2^(1/2)*(-a*(I*d-c))^(1/2)+8*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c+8*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d+10*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c-8*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c+8*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d*a*(I*d*a)^(1/2))/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d*a)^(1/2)*2^(1/2)/(-a*(I*d-c))^(1/2)","B"
1145,1,1701,153,0.453000," ","int((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, \left(2 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{2} d -2 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, d^{2}-i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,d^{3}+3 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a \,c^{2} d +\ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a \,d^{3}-3 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2} d +2 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,d^{3}+2 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{3}+2 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c \,d^{2}+2 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a c \,d^{2}+2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) d^{2}+2 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c \,d^{2}-2 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) c d -2 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{3}-2 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c \,d^{2}-2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c d +2 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{2} d +2 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{3}\right) \sqrt{2}}{4 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}\, \left(i c -d \right) \left(-\tan \left(f x +e \right)+i\right)}"," ",0,"1/4/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)*(2*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^2*d-2*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*d^2-I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d^3+3*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*a*c^2*d+ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*a*d^3-3*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2*d+2*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*d^3+2*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^3+2*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d^2+2*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*a*c*d^2+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*d^2+2*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d^2-2*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*c*d-2*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^3-2*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d^2-2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c*d+2*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^2*d+2*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^3)*2^(1/2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d*a)^(1/2)/(-a*(I*d-c))^(1/2)/(I*c-d)/(-tan(f*x+e)+I)","B"
1146,1,1169,152,0.448000," ","int((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(1/2),x)","-\frac{\left(i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c -2 i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) d +\sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) d -i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c +2 \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c +8 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a \,d^{2}-4 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2}-4 \tan \left(f x +e \right) c \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}-\sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d -4 i \sqrt{i d a}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) d +4 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}+4 i c \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}-4 \sqrt{i d a}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d \right) \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}}{4 f a \sqrt{i d a}\, \left(-\tan \left(f x +e \right)+i\right)^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}"," ",0,"-1/4/f/a*(I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c-2*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d+(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d-I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c+2*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c+8*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*d^2-4*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*d^2-4*tan(f*x+e)*c*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d-4*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d+4*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*d^2+4*I*c*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-4*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d)*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)/(I*d*a)^(1/2)/(-tan(f*x+e)+I)^2/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)","B"
1147,1,1275,135,0.381000," ","int((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x)","\frac{\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(-12 i \left(\tan^{2}\left(f x +e \right)\right) c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+12 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d^{2}-3 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) c^{2}-3 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) d^{2}-8 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{2}\left(f x +e \right)\right) c d -32 \tan \left(f x +e \right) c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+20 i c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-20 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{2}\left(f x +e \right)\right) d^{2}+9 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c^{2}+9 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) d^{2}+9 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c^{2}+9 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) d^{2}-3 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c^{2}-3 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d^{2}-32 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) d^{2}-8 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c d \right)}{24 f \,a^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(i c -d \right) \left(-\tan \left(f x +e \right)+i\right)^{3}}"," ",0,"1/24/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a^2*(-12*I*tan(f*x+e)^2*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+12*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^2-3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^2-3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d^2-8*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d-32*tan(f*x+e)*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+20*I*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-20*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^2+9*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2+9*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^2+9*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2+9*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^2-3*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2-3*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d^2-32*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^2-8*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*c-d)/(-tan(f*x+e)+I)^3","B"
1148,1,1657,179,0.351000," ","int((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x)","-\frac{\left(-60 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) d^{2}+90 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c^{2}+90 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) d^{2}-15 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{4}\left(f x +e \right)\right) c^{2}-15 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{4}\left(f x +e \right)\right) d^{2}+56 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) c d -40 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{3}\left(f x +e \right)\right) c d -15 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c^{2}-15 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d^{2}+60 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) d^{2}+220 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) d^{2}+40 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c d -212 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{2}\left(f x +e \right)\right) d^{2}+60 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) c^{2}-60 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c^{2}+60 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d^{2}-220 \left(\tan^{2}\left(f x +e \right)\right) c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+148 c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-60 i \left(\tan^{3}\left(f x +e \right)\right) c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-52 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{3}\left(f x +e \right)\right) d^{2}+308 i \tan \left(f x +e \right) c^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+136 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{2}\left(f x +e \right)\right) c d \right) \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}}{240 f \,a^{3} \left(-\tan \left(f x +e \right)+i\right)^{4} \left(i c -d \right) \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}"," ",0,"-1/240/f/a^3*(-60*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^2+90*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2+90*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^2-15*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^2-15*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*d^2+56*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d-40*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c*d-15*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2-15*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d^2+60*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d^2+220*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^2+40*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d-212*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^2+60*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^2-60*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2+60*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^2-220*tan(f*x+e)^2*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+148*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-60*I*tan(f*x+e)^3*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-52*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*d^2+308*I*tan(f*x+e)*c^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+136*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d)*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)/(-tan(f*x+e)+I)^4/(I*c-d)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)","B"
1149,1,1851,342,0.380000," ","int((a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(5/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, a^{2} \left(-96 \sqrt{2}\, \left(\tan^{3}\left(f x +e \right)\right) d^{3} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}-272 \sqrt{2}\, \left(\tan^{2}\left(f x +e \right)\right) c \,d^{2} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}-236 \sqrt{2}\, \tan \left(f x +e \right) c^{2} d \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}-894 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, d^{3}-768 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}+272 i \sqrt{2}\, \left(\tan^{2}\left(f x +e \right)\right) d^{3} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+1202 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{2} d +768 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{2}+768 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d -1089 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,d^{4}-300 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{3} d +2700 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c \,d^{3}+428 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) d^{3}-768 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d +15 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{4}-30 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{3}+2066 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c \,d^{2}+2070 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2} d^{2}+904 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) c \,d^{2}+768 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d -768 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}-768 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d +768 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{2}\right) \sqrt{2}}{768 f d \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/768/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)*a^2*(-96*2^(1/2)*tan(f*x+e)^3*d^3*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-272*2^(1/2)*tan(f*x+e)^2*c*d^2*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-236*2^(1/2)*tan(f*x+e)*c^2*d*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-894*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*d^3-768*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d^2+272*I*2^(1/2)*tan(f*x+e)^2*d^3*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+1202*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^2*d+768*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^2+768*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d-1089*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d^4-300*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^3*d+2700*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d^3+428*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*d^3-768*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d+15*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^4-30*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^3+2066*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c*d^2+2070*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2*d^2+904*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*c*d^2+768*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d-768*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*d^2-768*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d+768*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^2)*2^(1/2)/d/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d*a)^(1/2)/(-a*(I*d-c))^(1/2)","B"
1150,1,1503,305,0.381000," ","int((a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, a \left(48 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a d -54 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, d^{2}-69 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,d^{3}+48 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c -48 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a d +135 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2} d -15 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{3}+165 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c \,d^{2}+28 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) d^{2}+16 i \sqrt{2}\, \left(\tan^{2}\left(f x +e \right)\right) d^{2} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+66 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{2}+136 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c d +52 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) c d -48 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c +48 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c -48 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a d -48 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c +48 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d a \sqrt{i d a}\right) \sqrt{2}}{96 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/96/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)*a*(48*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d-54*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*d^2-69*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d^3+48*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c-48*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d+135*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2*d-15*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^3+165*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d^2+28*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*d^2+16*I*2^(1/2)*tan(f*x+e)^2*d^2*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+66*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^2+136*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c*d+52*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*c*d-48*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c+48*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c-48*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d-48*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c+48*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d*a*(I*d*a)^(1/2))*2^(1/2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d*a)^(1/2)/(-a*(I*d-c))^(1/2)","B"
1151,1,2130,202,0.418000," ","int((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, \left(5 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a \,c^{2} d^{2}-7 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a \,d^{4}-4 i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{2}\left(f x +e \right)\right) c \,d^{2}+16 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c \,d^{3}-3 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c \,d^{3}-18 i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) c^{2} d -16 i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c \,d^{2}-6 i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) d^{3}-15 i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{3} d +15 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a \,c^{3} d +3 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a c \,d^{3}+4 \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(\tan^{2}\left(f x +e \right)\right) d^{3}+16 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{3} d -8 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{4}+8 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{4}+5 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2} d^{2}-7 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,d^{4}+12 \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) c \,d^{2}-8 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{4}+8 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,d^{4}-18 \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c^{2} d -2 \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d^{3}+16 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{3} d +16 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c \,d^{3}\right) \sqrt{2}}{16 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}\, \left(i c -d \right) \left(-\tan \left(f x +e \right)+i\right)}"," ",0,"1/16/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)*(5*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*a*c^2*d^2-7*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*a*d^4-4*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d^2+16*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d^3-3*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d^3-18*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^2*d-16*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d^2-6*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^3-15*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^3*d+15*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*a*c^3*d+3*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*a*c*d^3+4*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^3+16*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^3*d-8*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^4+8*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^4+5*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2*d^2-7*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d^4+12*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d^2-8*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^4+8*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*d^4-18*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d-2*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^3+16*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^3*d+16*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d^3)*2^(1/2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d*a)^(1/2)/(-a*(I*d-c))^(1/2)/(I*c-d)/(-tan(f*x+e)+I)","B"
1152,1,2647,200,0.423000," ","int((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/4/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a*(I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2*d-(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^3+12*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^2*d-4*I*tan(f*x+e)*c^3*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-12*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d+10*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c^2*d^2-4*c^3*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+8*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^3-12*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^3+16*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d^2+4*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*d^4-12*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d^3-2*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*d^4+I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^3-(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c*d^2+2*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2*d+2*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^3-I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2*d+2*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c*d^2+2*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*d^4-4*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^3+12*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*c*d^3-20*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c^2*d^2+(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^3-4*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d^2+(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c*d^2-24*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c*d^3+2*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^3+20*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d^2-10*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*c^2*d^2-I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d^3)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*c-d)/(-tan(f*x+e)+I)^2/(I*d*a)^(1/2)","B"
1153,1,3161,201,0.303000," ","int((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"1/24*I/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a^2*(-9*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c*d^2+9*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^3+3*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d^3+20*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^2*d+128*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d^2+3*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d^3+24*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^3*a*c*d^3-72*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c*d^3+16*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^2*d+20*c^3*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-44*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^3-24*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^3*a*d^4-24*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*d^4+36*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^3-12*tan(f*x+e)^2*c^3*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+3*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c*d^2-9*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2*d-80*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^3+52*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d^2+72*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*d^4-24*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d^3+9*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c*d^2-9*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2*d+72*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*c*d^3+4*I*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d-3*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^3-76*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d^2-3*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c*d^2+32*I*tan(f*x+e)*c^3*(I*d*a)^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+72*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*d^4-9*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^3+3*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2*d+3*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^2*d+3*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^3-9*I*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^3-9*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^3)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d*a)^(1/2)/(I*c-d)/(-tan(f*x+e)+I)^3","B"
1154,1,2559,178,0.340000," ","int((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x)","\text{Expression too large to display}"," ",0,"1/240/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a^3*(120*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^2*d^2+624*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^2*d^2+40*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d^3-112*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c^2*d^2+136*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^3*d+220*I*tan(f*x+e)^2*c^4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+308*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^4-112*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d^2-60*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^4+220*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^4+136*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^3*d+40*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d^3-148*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*d^4+308*tan(f*x+e)*c^4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-60*tan(f*x+e)^3*c^4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-148*I*c^4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+40*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^3*d+30*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^2*d^2-180*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2*d^2+60*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d^4-60*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^4-60*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^4+136*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d^3+40*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c^3*d+136*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c*d^3+624*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^2*d^2+15*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^4+15*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d^4+60*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^4-120*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2*d^2+15*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^4+15*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*d^4-90*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^4-90*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^4+30*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2*d^2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*c-d)^2/(-tan(f*x+e)+I)^4","B"
1155,1,1295,157,0.501000," ","int((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(1/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, a^{2} \left(-5 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2} d +i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{3}-5 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,d^{3}-2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, d^{2}+4 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d +4 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}+4 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{2}-4 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d +4 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d -4 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,d^{2}+i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c \,d^{2}-2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{2}-4 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d -4 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,d^{2}\right) \sqrt{2}}{4 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(c^{2}+d^{2}\right) d \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/4/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)*a^2*(-5*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2*d+I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^3-5*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*d^3-2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*d^2+4*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d+4*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*d^2+4*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^2-4*I*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d+4*I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d-4*I*d^2*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*2^(1/2)*(-a*(I*d-c))^(1/2)+I*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c*d^2-2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^2-4*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d-4*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*d^2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c^2+d^2)/d/(I*d*a)^(1/2)*2^(1/2)/(-a*(I*d-c))^(1/2)","B"
1156,1,986,114,0.392000," ","int((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(1/2),x)","\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, a^{2} \left(i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) c -i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) d -i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \sqrt{i d a}\, c +i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \sqrt{i d a}\, d -\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) c^{2}-\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) d^{2}+\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) c +\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) d -\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \sqrt{i d a}\, c -\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \sqrt{i d a}\, d \right) \sqrt{2}}{2 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(c^{2}+d^{2}\right) \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/2/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)*a^2*(I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*c-I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*d-I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*(I*d*a)^(1/2)*c+I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*(I*d*a)^(1/2)*d-2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*c^2-2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*d^2+2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*c+2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*d-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*(I*d*a)^(1/2)*c-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*(I*d*a)^(1/2)*d)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c^2+d^2)/(I*d*a)^(1/2)*2^(1/2)/(-a*(I*d-c))^(1/2)","B"
1157,1,209,62,0.417000," ","int((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x)","-\frac{\left(i d \tan \left(f x +e \right)-i c +c \tan \left(f x +e \right)+d \right) a \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{2}}{2 f \left(-\tan \left(f x +e \right)+i\right) \left(i c -d \right) \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}"," ",0,"-1/2/f*(I*d*tan(f*x+e)-I*c+c*tan(f*x+e)+d)*a*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/(-tan(f*x+e)+I)/(I*c-d)*2^(1/2)/(-a*(I*d-c))^(1/2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)","B"
1158,1,1738,143,0.374000," ","int(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x)","-\frac{\sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, \left(-2 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c^{3}+4 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c^{2} d +i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) d^{3}-i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) d^{3}+\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c^{3}-3 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c \,d^{2}+4 i \tan \left(f x +e \right) c \,d^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-3 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c^{2} d +6 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c^{2} d -2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) d^{3}-\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c^{3}+3 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) c \,d^{2}+4 i \tan \left(f x +e \right) c^{3} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+3 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) c^{2} d +4 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d^{3}+6 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) c \,d^{2}-4 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) c^{2} d -4 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) d^{3}+4 c^{3} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+4 c \,d^{2} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\right)}{4 f a \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(i d -c \right) \left(i d +c \right)^{2} \left(i c -d \right) \left(-\tan \left(f x +e \right)+i\right)^{2}}"," ",0,"-1/4/f*(a*(1+I*tan(f*x+e)))^(1/2)*(c+d*tan(f*x+e))^(1/2)/a*(-2*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^3+4*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d+I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d^3-I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^3+2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^3-3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c*d^2+4*I*tan(f*x+e)*c*d^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-3*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2*d+6*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2*d-2*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^3-2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^3+3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c*d^2+4*I*tan(f*x+e)*c^3*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+3*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2*d+4*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^3+6*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c*d^2-4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^2*d-4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^3+4*c^3*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+4*c*d^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d-c)/(c+I*d)^2/(I*c-d)/(-tan(f*x+e)+I)^2","B"
1159,1,2946,154,0.383000," ","int(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"1/24/f*(c+d*tan(f*x+e))^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)/a^2*(-18*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^2*d^2+54*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2*d^2-36*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^3*d+36*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c*d^3+12*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^3*d-12*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c*d^3-32*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^2*d^2-40*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d^3-40*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^3*d-64*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^4+56*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^3*d+56*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d^3+32*tan(f*x+e)*c^4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-20*I*c^4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+36*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^4+12*I*tan(f*x+e)^2*c^4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-28*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^4+16*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d^2-9*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^4-18*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2*d^2+36*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^3*d-36*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c*d^3-9*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^4+96*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^3*d+96*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d^3-12*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^3*d+12*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c*d^3+3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d^4-9*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^4-9*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^4+3*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^4+3*I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*d^4-16*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^2*d^2+3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^4+54*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2*d^2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(I*d-c)/(c+I*d)^3/(I*c-d)/(-tan(f*x+e)+I)^3","B"
1160,1,5218,214,0.428000," ","int(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1161,1,1813,165,0.432000," ","int((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x)","\frac{\sqrt{2}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(-2 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,d^{2} \sqrt{i d a}+i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a c \,d^{3}-2 i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d +i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a \,c^{2} d^{2}+\ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a \,c^{3} d +\ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) a c \,d^{3}-6 i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c \,d^{2}+2 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d +i \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a \,d^{4} \sqrt{-a \left(i d -c \right)}+\sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,c^{4} \sqrt{-a \left(i d -c \right)}+\ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2} d^{2}+2 i \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a \,d^{2} \sqrt{-a \left(i d -c \right)}+i \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{3} d -2 \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a \,d^{2} \sqrt{-a \left(i d -c \right)}-6 \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c^{2} d +2 \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d^{3}+2 i \sqrt{2}\, c^{3} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}-2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d +2 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,d^{2} \sqrt{i d a}+2 \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d \right) a^{2}}{2 f \sqrt{c +d \tan \left(f x +e \right)}\, d \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(c^{2}+d^{2}\right) \left(i c -d \right) \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/2/f*2^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*(-2*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*d^2*(I*d*a)^(1/2)+I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d^3*(-a*(I*d-c))^(1/2)-2*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d*(I*d*a)^(1/2)+I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c^2*d^2*(-a*(I*d-c))^(1/2)+ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*a*c^3*d+ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*a*c*d^3-6*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c*d^2+2*I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d*(-a*(I*d-c))^(1/2)+I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*d^4*(-a*(I*d-c))^(1/2)+2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c^4*(-a*(I*d-c))^(1/2)+ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2*d^2+2*I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*d^2*(-a*(I*d-c))^(1/2)+I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c^3*d*(-a*(I*d-c))^(1/2)-2*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*d^2*(-a*(I*d-c))^(1/2)-6*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d+2*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^3+2*I*2^(1/2)*c^3*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*(-a*(I*d-c))^(1/2)-2*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d+2*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*d^2*(I*d*a)^(1/2)+2*(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d)*a^2/(c+d*tan(f*x+e))^(1/2)/d/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c^2+d^2)/(I*c-d)/(I*d*a)^(1/2)/(-a*(I*d-c))^(1/2)","B"
1162,1,1840,103,0.383000," ","int((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x)","\frac{\sqrt{2}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(-i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c d \sqrt{i d a}+i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,d^{2} \sqrt{i d a}+i \sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d +2 i \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c \,d^{2}-i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{2} \sqrt{i d a}+i \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a c d \sqrt{-a \left(i d -c \right)}-i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d +i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,c^{2}+\sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a c d \sqrt{-a \left(i d -c \right)}+\sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a \,d^{2} \sqrt{-a \left(i d -c \right)}-2 \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c^{2} d -2 \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d^{3}-i \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a \,d^{2} \sqrt{-a \left(i d -c \right)}+2 i \sqrt{2}\, c^{3} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}+\ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2}+\sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a c d -\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c d \sqrt{i d a}-\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,d^{2} \sqrt{i d a}-\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{2} \sqrt{i d a}-\sqrt{i d a}\, \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c d \right) a}{2 f \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(c^{2}+d^{2}\right)^{2} \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{c +d \tan \left(f x +e \right)}}"," ",0,"1/2/f*2^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*(-I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d*(I*d*a)^(1/2)+I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*d^2*(I*d*a)^(1/2)+I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d*(I*d*a)^(1/2)+2*I*2^(1/2)*c*d^2*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^2*(I*d*a)^(1/2)+I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c*d*(-a*(I*d-c))^(1/2)-I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d*(-a*(I*d-c))^(1/2)+I*2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c^2+2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c*d*(-a*(I*d-c))^(1/2)+2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*d^2*(-a*(I*d-c))^(1/2)-2*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d-2*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^3-I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*d^2*(-a*(I*d-c))^(1/2)+2*I*2^(1/2)*c^3*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*(-a*(I*d-c))^(1/2)+ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2+2^(1/2)*(-a*(I*d-c))^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c*d-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d*(I*d*a)^(1/2)-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*d^2*(I*d*a)^(1/2)-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^2*(I*d*a)^(1/2)-(I*d*a)^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d)*a/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c^2+d^2)^2/(I*d*a)^(1/2)/(-a*(I*d-c))^(1/2)/(c+d*tan(f*x+e))^(1/2)","B"
1163,1,1291,104,0.385000," ","int((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x)","\frac{\sqrt{2}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(-2 \sqrt{2}\, \tan \left(f x +e \right) d^{2} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-2 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a c \,d^{2}+2 i \sqrt{2}\, \tan \left(f x +e \right) c d \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{2} d -i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,d^{3}-\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,c^{2} d +\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{3}+2 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d^{2}+i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{3}-i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a c \,d^{2}-\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{3}-\ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c \,d^{2}+2 \sqrt{2}\, c d \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-2 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{2} d \right)}{2 f \sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(c^{2}+d^{2}\right) \left(i c -d \right) \sqrt{-a \left(i d -c \right)}\, \left(-\tan \left(f x +e \right)+i\right)}"," ",0,"1/2/f*2^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*(-2*2^(1/2)*tan(f*x+e)*d^2*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-2*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*c*d^2+2*I*2^(1/2)*tan(f*x+e)*c*d*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^2*d-I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*d^3-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*c^2*d+ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*d^3+2*I*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^2+I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^3-I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c*d^2-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^3-ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d^2+2*2^(1/2)*c*d*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-2*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^2*d)/(c+d*tan(f*x+e))^(1/2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c^2+d^2)/(I*c-d)/(-a*(I*d-c))^(1/2)/(-tan(f*x+e)+I)","B"
1164,1,3196,160,0.373000," ","int(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"1/4/f*(2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^4*d*(-a*(I*d-c))^(1/2)-2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c*d^4*(-a*(I*d-c))^(1/2)+4*I*tan(f*x+e)^2*c^4*d*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+16*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^2*d^3-8*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^3*d^2-12*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d^4-2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^5*(-a*(I*d-c))^(1/2)+6*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^3*d^2*(-a*(I*d-c))^(1/2)+2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d^5*(-a*(I*d-c))^(1/2)+2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^5*(-a*(I*d-c))^(1/2)+4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^5+4*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^3*d^2*(-a*(I*d-c))^(1/2)-4*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c*d^4*(-a*(I*d-c))^(1/2)+2*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^4*d*(-a*(I*d-c))^(1/2)+8*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2*d^3*(-a*(I*d-c))^(1/2)+8*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^3*d^2*(-a*(I*d-c))^(1/2)+2*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c*d^4*(-a*(I*d-c))^(1/2)-2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^5*(-a*(I*d-c))^(1/2)+12*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^5+4*I*tan(f*x+e)*c^5*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-8*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d^3+8*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^3*d^2+8*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d^4+4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^4*d+24*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^2*d^3+20*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^5-4*c*d^4*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-8*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^5-2*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^5*(-a*(I*d-c))^(1/2)-2*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^5*(-a*(I*d-c))^(1/2)-4*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^4*d*(-a*(I*d-c))^(1/2)+4*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2*d^3*(-a*(I*d-c))^(1/2)-6*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^2*d^3*(-a*(I*d-c))^(1/2)+2*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^3*d^2*(-a*(I*d-c))^(1/2)-7*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c*d^4*(-a*(I*d-c))^(1/2)+7*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^4*d*(-a*(I*d-c))^(1/2)-2*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2*d^3*(-a*(I*d-c))^(1/2))/a*(a*(1+I*tan(f*x+e)))^(1/2)/(-tan(f*x+e)+I)^2/(I*c-d)/(c+I*d)^3/(I*d-c)^2/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c+d*tan(f*x+e))^(1/2)","B"
1165,1,4835,219,0.316000," ","int(1/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"-1/24/f*(75*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^4*d^2-15*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2*d^4+3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^5*d-30*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^3*d^3+15*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c*d^5+15*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^4*d^2-75*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^2*d^4+36*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^5*d-36*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c*d^5+12*I*tan(f*x+e)^2*c^6*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+256*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^6-40*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^4*d^2-68*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d^4+30*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^3*d^3-3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c*d^5-20*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^5*d+104*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^3*d^3+124*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d^5+296*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^2*d^4-52*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c^4*d^2-152*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c^2*d^4+124*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^4*d^2+15*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^4*c^4*d^2*(-a*(I*d-c))^(1/2)-30*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^4*c^2*d^4*(-a*(I*d-c))^(1/2)+6*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^3*c^5*d*(-a*(I*d-c))^(1/2)+60*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^3*c^3*d^3*(-a*(I*d-c))^(1/2)-42*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^3*c*d^5*(-a*(I*d-c))^(1/2)+45*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^2*c^4*d^2*(-a*(I*d-c))^(1/2)+45*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^2*c^2*d^4*(-a*(I*d-c))^(1/2)-42*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)*c^5*d*(-a*(I*d-c))^(1/2)+60*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)*c^3*d^3*(-a*(I*d-c))^(1/2)+6*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)*c*d^5*(-a*(I*d-c))^(1/2)+3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*c^6*(-a*(I*d-c))^(1/2)+136*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^4*d^2+380*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^2*d^4+92*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^5*d+40*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^3*d^3-52*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d^5+12*I*tan(f*x+e)^3*c^5*d*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+72*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c^3*d^3-100*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*d^6+204*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*d^6+60*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^5*d+72*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^3*d^3+12*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d^5+32*tan(f*x+e)*c^6*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^4*d^6*(-a*(I*d-c))^(1/2)-9*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^2*c^6*(-a*(I*d-c))^(1/2)-9*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*tan(f*x+e)^2*d^6*(-a*(I*d-c))^(1/2)-30*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*c^4*d^2*(-a*(I*d-c))^(1/2)+15*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*2^(1/2)*c^2*d^4*(-a*(I*d-c))^(1/2)-20*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^6-48*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^6+3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^6+9*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d^6-9*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^6-3*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*d^6-15*2^(1/2)*(-a*(I*d-c))^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^5*d+60*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c*d^5)/a^2*(a*(1+I*tan(f*x+e)))^(1/2)/(-tan(f*x+e)+I)^3/(I*c-d)/(c+I*d)^4/(I*d-c)^2/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c+d*tan(f*x+e))^(1/2)","B"
1166,1,7870,290,0.358000," ","int(1/(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1167,1,1852,146,0.339000," ","int((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x)","\frac{\sqrt{2}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(-18 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) c^{2} d^{2}-3 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2} \sqrt{i d a}+7 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) d^{4}-6 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c d \sqrt{i d a}+3 i \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2} \sqrt{-a \left(i d -c \right)}-20 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{3} d -4 \sqrt{2}\, \tan \left(f x +e \right) c^{3} d \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+20 \sqrt{2}\, \tan \left(f x +e \right) c \,d^{3} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}-3 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{2} \sqrt{i d a}+6 i \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a c d \sqrt{-a \left(i d -c \right)}-3 \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2} \sqrt{-a \left(i d -c \right)}-7 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{4}+18 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{2} d^{2}+\sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, d^{4}+3 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,c^{2}-i \sqrt{2}\, \tan \left(f x +e \right) c^{4} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}-6 \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a c d \sqrt{-a \left(i d -c \right)}+3 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2} \sqrt{i d a}+4 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c \,d^{3}-3 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2}+6 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c d \sqrt{i d a}+3 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{2} \sqrt{i d a}\right) a^{2}}{3 f \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(c^{2}+d^{2}\right)^{2} \left(i c -d \right) \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/3/f*2^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*(-18*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*c^2*d^2-3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*d^2*(I*d*a)^(1/2)+7*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*d^4-6*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d*(I*d*a)^(1/2)+3*I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*d^2*(-a*(I*d-c))^(1/2)-20*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^3*d-4*2^(1/2)*tan(f*x+e)*c^3*d*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+20*2^(1/2)*tan(f*x+e)*c*d^3*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^2*(I*d*a)^(1/2)+6*I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c*d*(-a*(I*d-c))^(1/2)-3*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*d^2*(-a*(I*d-c))^(1/2)-7*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^4+18*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^2*d^2+(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*d^4+3*I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c^2*(-a*(I*d-c))^(1/2)-I*2^(1/2)*tan(f*x+e)*c^4*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-6*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c*d*(-a*(I*d-c))^(1/2)+3*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*d^2*(I*d*a)^(1/2)+4*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c*d^3-3*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2+6*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d*(I*d*a)^(1/2)+3*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^2*(I*d*a)^(1/2))*a^2/(c+d*tan(f*x+e))^(3/2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c^2+d^2)^2/(I*c-d)/(I*d*a)^(1/2)/(-a*(I*d-c))^(1/2)","B"
1168,1,1791,145,0.332000," ","int((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x)","\frac{\sqrt{2}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(-3 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2} \sqrt{i d a}+4 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c \,d^{3}-6 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c d \sqrt{i d a}+3 i \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2} \sqrt{-a \left(i d -c \right)}-20 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{3} d -4 \sqrt{2}\, \tan \left(f x +e \right) c^{3} d \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+20 \sqrt{2}\, \tan \left(f x +e \right) c \,d^{3} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}-3 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{2} \sqrt{i d a}+6 i \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a c d \sqrt{-a \left(i d -c \right)}-3 \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2} \sqrt{-a \left(i d -c \right)}-6 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{4}+20 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, c^{2} d^{2}+2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, d^{4}+3 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) a \,c^{2}+8 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) d^{4}-6 \sqrt{2}\, \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \tan \left(f x +e \right) a c d \sqrt{-a \left(i d -c \right)}+3 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{2} \sqrt{i d a}-16 i \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}\, \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \tan \left(f x +e \right) c^{2} d^{2}-3 \ln \left(\frac{2 i a \tan \left(f x +e \right) d +i a c +2 \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \sqrt{i d a}+d a}{2 \sqrt{i d a}}\right) \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, a \,c^{2}+6 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c d \sqrt{i d a}+3 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{2} \sqrt{i d a}\right) a}{6 f \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(c^{2}+d^{2}\right)^{2} \left(i c -d \right) \sqrt{i d a}\, \sqrt{-a \left(i d -c \right)}}"," ",0,"1/6/f*2^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*(-3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*d^2*(I*d*a)^(1/2)+4*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c*d^3-6*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d*(I*d*a)^(1/2)+3*I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*d^2*(-a*(I*d-c))^(1/2)-20*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^3*d-4*2^(1/2)*tan(f*x+e)*c^3*d*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+20*2^(1/2)*tan(f*x+e)*c*d^3*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)-3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^2*(I*d*a)^(1/2)+6*I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c*d*(-a*(I*d-c))^(1/2)-3*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)^2*a*d^2*(-a*(I*d-c))^(1/2)-6*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^4+20*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*c^2*d^2+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*d^4+3*I*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*a*c^2*(-a*(I*d-c))^(1/2)+8*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*d^4-6*2^(1/2)*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*tan(f*x+e)*a*c*d*(-a*(I*d-c))^(1/2)+3*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*d^2*(I*d*a)^(1/2)-16*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)*2^(1/2)*(-a*(I*d-c))^(1/2)*tan(f*x+e)*c^2*d^2-3*ln(1/2*(2*I*a*tan(f*x+e)*d+I*a*c+2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*(I*d*a)^(1/2)+d*a)/(I*d*a)^(1/2))*2^(1/2)*(-a*(I*d-c))^(1/2)*a*c^2+6*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d*(I*d*a)^(1/2)+3*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^2*(I*d*a)^(1/2))*a/(c+d*tan(f*x+e))^(3/2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c^2+d^2)^2/(I*c-d)/(I*d*a)^(1/2)/(-a*(I*d-c))^(1/2)","B"
1169,1,2448,153,0.401000," ","int((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x)","\frac{\sqrt{2}\, \sqrt{a \left(1+i \tan \left(f x +e \right)\right)}\, \left(-9 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{3} d^{2}+12 \sqrt{2}\, c^{3} d \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-3 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{4} d -15 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{2} d^{3}+14 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, c^{2} d^{2}-4 \sqrt{2}\, \tan \left(f x +e \right) c^{2} d^{2} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+10 i \sqrt{2}\, \left(\tan^{2}\left(f x +e \right)\right) c^{2} d^{2} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+3 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,d^{5}+12 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \tan \left(f x +e \right) c \,d^{3}-3 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{5}-9 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{4} d +3 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{2} d^{3}+3 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) a \,c^{5}+3 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) a \,d^{5}+12 i \sqrt{2}\, \tan \left(f x +e \right) c^{3} d \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}+2 i \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, d^{4}-4 \sqrt{2}\, \tan \left(f x +e \right) d^{4} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-9 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a \,c^{3} d^{2}+6 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \tan \left(f x +e \right) a c \,d^{4}-3 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) a \,c^{3} d^{2}+9 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) a c \,d^{4}-6 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,c^{4} d +9 \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,c^{2} d^{3}-2 i \sqrt{2}\, \left(\tan^{2}\left(f x +e \right)\right) d^{4} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-15 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a \,c^{3} d^{2}-3 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{2}\left(f x +e \right)\right) a c \,d^{4}-12 \sqrt{2}\, \left(\tan^{2}\left(f x +e \right)\right) c \,d^{3} \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}-9 i \ln \left(\frac{3 c a +i a \tan \left(f x +e \right) c -i d a +3 a \tan \left(f x +e \right) d +2 \sqrt{2}\, \sqrt{-a \left(i d -c \right)}\, \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}}{\tan \left(f x +e \right)+i}\right) \left(\tan^{3}\left(f x +e \right)\right) a \,c^{2} d^{3}\right)}{6 f \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \tan \left(f x +e \right)\right) \left(1+i \tan \left(f x +e \right)\right)}\, \left(c^{2}+d^{2}\right)^{2} \left(i c -d \right) \sqrt{-a \left(i d -c \right)}\, \left(-\tan \left(f x +e \right)+i\right)}"," ",0,"1/6/f*2^(1/2)*(a*(1+I*tan(f*x+e)))^(1/2)*(-2*I*2^(1/2)*tan(f*x+e)^2*d^4*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+3*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*d^5+12*I*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d^3+10*I*2^(1/2)*tan(f*x+e)^2*c^2*d^2*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+12*I*2^(1/2)*tan(f*x+e)*c^3*d*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-3*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^5-9*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^4*d+3*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^2*d^3+3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^5-3*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*a*c^3*d^2+9*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*a*c*d^4-6*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*c^4*d+9*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*c^2*d^3+2*I*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^4-4*2^(1/2)*tan(f*x+e)*d^4*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-9*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^3*d^2+6*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c*d^4-9*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*a*c^3*d^2+12*2^(1/2)*c^3*d*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*a*d^5-15*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*c^3*d^2-3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*a*c*d^4-3*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^4*d-15*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*a*c^2*d^3+14*I*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d^2-12*2^(1/2)*tan(f*x+e)^2*c*d^3*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-4*2^(1/2)*tan(f*x+e)*c^2*d^2*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-9*I*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*a*c^2*d^3)/(c+d*tan(f*x+e))^(3/2)/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c^2+d^2)^2/(I*c-d)/(-a*(I*d-c))^(1/2)/(-tan(f*x+e)+I)","B"
1170,1,4889,231,0.370000," ","int(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"-1/12/f*(-30*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^2*d^5*(-a*(I*d-c))^(1/2)-48*c^5*d^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-8*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*d^7+28*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*d^7-84*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^3*d^4-24*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c*d^6+76*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c^4*d^3+104*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c^2*d^5+108*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^5*d^2-3*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^7*(-a*(I*d-c))^(1/2)-36*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*d^7+12*I*tan(f*x+e)*c^7*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-12*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^6*d-80*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^4*d^3-76*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^2*d^5+264*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^3*d^4+156*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c*d^6+36*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^6*d+120*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^4*d^3+84*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^2*d^5-30*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^3*d^4*(-a*(I*d-c))^(1/2)+15*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c*d^6*(-a*(I*d-c))^(1/2)+6*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^6*d*(-a*(I*d-c))^(1/2)-30*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^4*d^3*(-a*(I*d-c))^(1/2)+27*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^5*d^2*(-a*(I*d-c))^(1/2)-75*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^3*d^4*(-a*(I*d-c))^(1/2)-3*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c*d^6*(-a*(I*d-c))^(1/2)+24*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^6*d*(-a*(I*d-c))^(1/2)-24*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^2*d^5*(-a*(I*d-c))^(1/2)+3*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*d^7*(-a*(I*d-c))^(1/2)-3*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*d^7*(-a*(I*d-c))^(1/2)-6*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^7*(-a*(I*d-c))^(1/2)-15*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^6*d*(-a*(I*d-c))^(1/2)+30*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^4*d^3*(-a*(I*d-c))^(1/2)-3*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^2*d^5*(-a*(I*d-c))^(1/2)+3*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^5*d^2*(-a*(I*d-c))^(1/2)+12*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*c^7+30*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^5*d^2*(-a*(I*d-c))^(1/2)-15*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*c^3*d^4*(-a*(I*d-c))^(1/2)+12*I*tan(f*x+e)^3*c^5*d^2*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)+72*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c^3*d^4+60*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^3*c*d^6+24*I*tan(f*x+e)^2*c^6*d*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)-24*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c*d^6*(-a*(I*d-c))^(1/2)+3*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^6*d*(-a*(I*d-c))^(1/2)+75*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^4*d^3*(-a*(I*d-c))^(1/2)-27*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^2*d^5*(-a*(I*d-c))^(1/2)+30*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^5*d^2*(-a*(I*d-c))^(1/2)+30*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c^3*d^4*(-a*(I*d-c))^(1/2)-6*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)*c*d^6*(-a*(I*d-c))^(1/2)+15*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^4*d^3*(-a*(I*d-c))^(1/2)-30*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^4*c^2*d^5*(-a*(I*d-c))^(1/2)+24*I*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*c^5*d^2*(-a*(I*d-c))^(1/2)-36*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^4*d^3-96*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)^2*c^2*d^5-144*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^5*d^2-276*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c^3*d^4-120*I*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)*tan(f*x+e)*c*d^6+6*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^3*d^7*(-a*(I*d-c))^(1/2)+3*2^(1/2)*ln((3*c*a+I*a*tan(f*x+e)*c-I*d*a+3*a*tan(f*x+e)*d+2*2^(1/2)*(-a*(I*d-c))^(1/2)*(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2))/(tan(f*x+e)+I))*tan(f*x+e)^2*c^7*(-a*(I*d-c))^(1/2))/a*(a*(1+I*tan(f*x+e)))^(1/2)/(-tan(f*x+e)+I)^2/(I*c-d)/(c+I*d)^4/(I*d-c)^3/(a*(c+d*tan(f*x+e))*(1+I*tan(f*x+e)))^(1/2)/(c+d*tan(f*x+e))^(3/2)","B"
1171,1,7061,294,0.346000," ","int(1/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1172,1,10145,374,0.368000," ","int(1/(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1173,0,0,102,2.638000," ","int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x)","F"
1174,0,0,155,1.482000," ","int((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^n,x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{3} \left(c +d \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^n,x)","F"
1175,0,0,95,1.240000," ","int((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^n,x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{2} \left(c +d \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^n,x)","F"
1176,0,0,61,1.308000," ","int((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^n,x)","\int \left(a +i a \tan \left(f x +e \right)\right) \left(c +d \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^n,x)","F"
1177,0,0,184,1.492000," ","int((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{n}}{a +i a \tan \left(f x +e \right)}\, dx"," ",0,"int((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x)","F"
1178,0,0,259,1.251000," ","int((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x)","F"
1179,0,0,360,1.267000," ","int((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x)","F"
1180,0,0,180,4.482000," ","int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x)","F"
1181,0,0,108,2.248000," ","int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x)","F"
1182,0,0,70,4.386000," ","int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e)),x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e)),x)","F"
1183,0,0,114,3.820000," ","int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e)),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{c +d \tan \left(f x +e \right)}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e)),x)","F"
1184,0,0,169,4.243000," ","int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\left(c +d \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x)","F"
1185,0,0,246,4.976000," ","int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\left(c +d \tan \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x)","F"
1186,0,0,105,1.546000," ","int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x)","F"
1187,0,0,98,1.342000," ","int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(1/2),x)","\int \left(a +i a \tan \left(f x +e \right)\right)^{m} \sqrt{c +d \tan \left(f x +e \right)}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(1/2),x)","F"
1188,0,0,98,1.934000," ","int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x)","F"
1189,0,0,107,1.347000," ","int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x)","F"
1190,0,0,106,1.297000," ","int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{m}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x)","F"
1191,1,247,136,0.023000," ","int((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e)),x)","\frac{b^{3} d \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{3 \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} d}{2 f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) b^{3} c}{2 f}+\frac{3 a^{2} b d \tan \left(f x +e \right)}{f}+\frac{3 a \,b^{2} c \tan \left(f x +e \right)}{f}-\frac{b^{3} d \tan \left(f x +e \right)}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} d}{2 f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b c}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} d}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,b^{3}}{2 f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f}"," ",0,"1/3/f*b^3*d*tan(f*x+e)^3+3/2/f*tan(f*x+e)^2*a*b^2*d+1/2/f*tan(f*x+e)^2*b^3*c+3/f*a^2*b*d*tan(f*x+e)+3/f*a*b^2*c*tan(f*x+e)-1/f*b^3*d*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*a^3*d+3/2/f*ln(1+tan(f*x+e)^2)*a^2*b*c-3/2/f*ln(1+tan(f*x+e)^2)*a*b^2*d-1/2/f*ln(1+tan(f*x+e)^2)*c*b^3+1/f*arctan(tan(f*x+e))*a^3*c-3/f*arctan(tan(f*x+e))*a^2*b*d-3/f*arctan(tan(f*x+e))*a*b^2*c+1/f*arctan(tan(f*x+e))*b^3*d","A"
1192,1,151,85,0.026000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e)),x)","\frac{b^{2} d \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{2 a b d \tan \left(f x +e \right)}{f}+\frac{c \,b^{2} \tan \left(f x +e \right)}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b c}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} d}{2 f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b d}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f}"," ",0,"1/2/f*b^2*d*tan(f*x+e)^2+2/f*a*b*d*tan(f*x+e)+1/f*c*b^2*tan(f*x+e)+1/2/f*ln(1+tan(f*x+e)^2)*a^2*d+1/f*ln(1+tan(f*x+e)^2)*a*b*c-1/2/f*ln(1+tan(f*x+e)^2)*b^2*d+1/f*arctan(tan(f*x+e))*a^2*c-2/f*arctan(tan(f*x+e))*a*b*d-1/f*arctan(tan(f*x+e))*b^2*c","A"
1193,1,77,42,0.022000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e)),x)","\frac{b d \tan \left(f x +e \right)}{f}+\frac{a \ln \left(1+\tan^{2}\left(f x +e \right)\right) d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c b}{2 f}+\frac{a \arctan \left(\tan \left(f x +e \right)\right) c}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b d}{f}"," ",0,"b*d*tan(f*x+e)/f+1/2/f*a*ln(1+tan(f*x+e)^2)*d+1/2/f*ln(1+tan(f*x+e)^2)*c*b+1/f*a*arctan(tan(f*x+e))*c-1/f*arctan(tan(f*x+e))*b*d","A"
1194,1,153,58,0.236000," ","int((c+d*tan(f*x+e))/(a+b*tan(f*x+e)),x)","-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) d a}{f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) c b}{f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) d a}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c b}{2 f \left(a^{2}+b^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a c}{f \left(a^{2}+b^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b d}{f \left(a^{2}+b^{2}\right)}"," ",0,"-1/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*d*a+1/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*c*b+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*d*a-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*c*b+1/f/(a^2+b^2)*arctan(tan(f*x+e))*a*c+1/f/(a^2+b^2)*arctan(tan(f*x+e))*b*d","B"
1195,1,301,110,0.244000," ","int((c+d*tan(f*x+e))/(a+b*tan(f*x+e))^2,x)","\frac{d a}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{c b}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) a b c}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) b^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b c}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/f/(a^2+b^2)/(a+b*tan(f*x+e))*d*a-1/f/(a^2+b^2)/(a+b*tan(f*x+e))*c*b-1/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^2*d+2/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a*b*c+1/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*b^2*d+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*a^2*d-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*a*b*c-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*b^2*d+1/f/(a^2+b^2)^2*arctan(tan(f*x+e))*a^2*c+2/f/(a^2+b^2)^2*arctan(tan(f*x+e))*a*b*d-1/f/(a^2+b^2)^2*arctan(tan(f*x+e))*b^2*c","B"
1196,1,483,172,0.315000," ","int((c+d*tan(f*x+e))/(a+b*tan(f*x+e))^3,x)","-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{3} d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} b c}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a \,b^{2} d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) c \,b^{3}}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{d a}{2 f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}-\frac{c b}{2 f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{a^{2} d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{2 a b c}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{b^{2} d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} d}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b c}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,b^{3}}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^3*d+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^2*b*c+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a*b^2*d-1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*c*b^3+1/2/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*d*a-1/2/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*c*b+1/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^2*d-2/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*a*b*c-1/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*b^2*d+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^3*d-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^2*b*c-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a*b^2*d+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*c*b^3+1/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a^3*c+3/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a^2*b*d-3/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a*b^2*c-1/f/(a^2+b^2)^3*arctan(tan(f*x+e))*b^3*d","B"
1197,1,460,209,0.025000," ","int((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x)","\frac{b^{3} d^{2} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{\left(\tan^{3}\left(f x +e \right)\right) a \,b^{2} d^{2}}{f}+\frac{2 \left(\tan^{3}\left(f x +e \right)\right) b^{3} c d}{3 f}+\frac{3 \left(\tan^{2}\left(f x +e \right)\right) a^{2} b \,d^{2}}{2 f}+\frac{3 \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} c d}{f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) b^{3} c^{2}}{2 f}-\frac{\left(\tan^{2}\left(f x +e \right)\right) b^{3} d^{2}}{2 f}+\frac{a^{3} d^{2} \tan \left(f x +e \right)}{f}+\frac{6 a^{2} b c d \tan \left(f x +e \right)}{f}+\frac{3 a \,b^{2} c^{2} \tan \left(f x +e \right)}{f}-\frac{3 a \,b^{2} d^{2} \tan \left(f x +e \right)}{f}-\frac{2 b^{3} c d \tan \left(f x +e \right)}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} c d}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,c^{2}}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,d^{2}}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} c d}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c^{2}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} d^{2}}{2 f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{2}}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} d^{2}}{f}-\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c d}{f}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{2}}{f}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d^{2}}{f}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b^{3} c d}{f}"," ",0,"1/4/f*b^3*d^2*tan(f*x+e)^4+1/f*tan(f*x+e)^3*a*b^2*d^2+2/3/f*tan(f*x+e)^3*b^3*c*d+3/2/f*tan(f*x+e)^2*a^2*b*d^2+3/f*tan(f*x+e)^2*a*b^2*c*d+1/2/f*tan(f*x+e)^2*b^3*c^2-1/2/f*tan(f*x+e)^2*b^3*d^2+1/f*a^3*d^2*tan(f*x+e)+6/f*a^2*b*c*d*tan(f*x+e)+3/f*a*b^2*c^2*tan(f*x+e)-3/f*a*b^2*d^2*tan(f*x+e)-2/f*b^3*c*d*tan(f*x+e)+1/f*ln(1+tan(f*x+e)^2)*a^3*c*d+3/2/f*ln(1+tan(f*x+e)^2)*a^2*b*c^2-3/2/f*ln(1+tan(f*x+e)^2)*a^2*b*d^2-3/f*ln(1+tan(f*x+e)^2)*a*b^2*c*d-1/2/f*ln(1+tan(f*x+e)^2)*b^3*c^2+1/2/f*ln(1+tan(f*x+e)^2)*b^3*d^2+1/f*arctan(tan(f*x+e))*a^3*c^2-1/f*arctan(tan(f*x+e))*a^3*d^2-6/f*arctan(tan(f*x+e))*a^2*b*c*d-3/f*arctan(tan(f*x+e))*a*b^2*c^2+3/f*arctan(tan(f*x+e))*a*b^2*d^2+2/f*arctan(tan(f*x+e))*b^3*c*d","B"
1198,1,287,129,0.025000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x)","\frac{b^{2} d^{2} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) a b \,d^{2}}{f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) b^{2} c d}{f}+\frac{a^{2} \tan \left(f x +e \right) d^{2}}{f}+\frac{4 a b c d \tan \left(f x +e \right)}{f}+\frac{b^{2} c^{2} \tan \left(f x +e \right)}{f}-\frac{b^{2} d^{2} \tan \left(f x +e \right)}{f}+\frac{a^{2} \ln \left(1+\tan^{2}\left(f x +e \right)\right) c d}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,c^{2}}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,d^{2}}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} c d}{f}+\frac{a^{2} \arctan \left(\tan \left(f x +e \right)\right) c^{2}}{f}-\frac{a^{2} \arctan \left(\tan \left(f x +e \right)\right) d^{2}}{f}-\frac{4 \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f}"," ",0,"1/3/f*b^2*d^2*tan(f*x+e)^3+1/f*tan(f*x+e)^2*a*b*d^2+1/f*tan(f*x+e)^2*b^2*c*d+1/f*a^2*tan(f*x+e)*d^2+4/f*a*b*c*d*tan(f*x+e)+1/f*b^2*c^2*tan(f*x+e)-1/f*b^2*d^2*tan(f*x+e)+1/f*a^2*ln(1+tan(f*x+e)^2)*c*d+1/f*ln(1+tan(f*x+e)^2)*a*b*c^2-1/f*ln(1+tan(f*x+e)^2)*a*b*d^2-1/f*ln(1+tan(f*x+e)^2)*b^2*c*d+1/f*a^2*arctan(tan(f*x+e))*c^2-1/f*a^2*arctan(tan(f*x+e))*d^2-4/f*arctan(tan(f*x+e))*a*b*c*d-1/f*arctan(tan(f*x+e))*b^2*c^2+1/f*arctan(tan(f*x+e))*b^2*d^2","B"
1199,1,151,87,0.022000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^2,x)","\frac{b \,d^{2} \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{a \,d^{2} \tan \left(f x +e \right)}{f}+\frac{2 b c d \tan \left(f x +e \right)}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a c d}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} b}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b \,d^{2}}{2 f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b c d}{f}"," ",0,"1/2/f*b*d^2*tan(f*x+e)^2+1/f*a*d^2*tan(f*x+e)+2/f*b*c*d*tan(f*x+e)+1/f*ln(1+tan(f*x+e)^2)*a*c*d+1/2/f*ln(1+tan(f*x+e)^2)*c^2*b-1/2/f*ln(1+tan(f*x+e)^2)*b*d^2+1/f*arctan(tan(f*x+e))*a*c^2-1/f*arctan(tan(f*x+e))*a*d^2-2/f*arctan(tan(f*x+e))*b*c*d","A"
1200,1,249,103,0.198000," ","int((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e)),x)","\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(a^{2}+b^{2}\right) b}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) a c d}{f \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(a +b \tan \left(f x +e \right)\right) c^{2}}{f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a c d}{f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} b}{2 f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b \,d^{2}}{2 f \left(a^{2}+b^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f \left(a^{2}+b^{2}\right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f \left(a^{2}+b^{2}\right)}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b c d}{f \left(a^{2}+b^{2}\right)}"," ",0,"1/f/(a^2+b^2)/b*ln(a+b*tan(f*x+e))*a^2*d^2-2/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*a*c*d+1/f/(a^2+b^2)*b*ln(a+b*tan(f*x+e))*c^2+1/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*a*c*d-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*c^2*b+1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*b*d^2+1/f/(a^2+b^2)*arctan(tan(f*x+e))*a*c^2-1/f/(a^2+b^2)*arctan(tan(f*x+e))*a*d^2+2/f/(a^2+b^2)*arctan(tan(f*x+e))*b*c*d","B"
1201,1,465,126,0.235000," ","int((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^2,x)","-\frac{a^{2} d^{2}}{f \left(a^{2}+b^{2}\right) b \left(a +b \tan \left(f x +e \right)\right)}+\frac{2 a c d}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{b \,c^{2}}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{4 \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-1/f/(a^2+b^2)/b/(a+b*tan(f*x+e))*a^2*d^2+2/f/(a^2+b^2)/(a+b*tan(f*x+e))*a*c*d-1/f/(a^2+b^2)*b/(a+b*tan(f*x+e))*c^2-2/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^2*c*d+2/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a*b*c^2-2/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a*b*d^2+2/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*b^2*c*d+1/f/(a^2+b^2)^2*arctan(tan(f*x+e))*a^2*c^2-1/f/(a^2+b^2)^2*arctan(tan(f*x+e))*a^2*d^2+4/f/(a^2+b^2)^2*arctan(tan(f*x+e))*a*b*c*d-1/f/(a^2+b^2)^2*arctan(tan(f*x+e))*b^2*c^2+1/f/(a^2+b^2)^2*arctan(tan(f*x+e))*b^2*d^2+1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*a^2*c*d-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*a*b*c^2+1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*a*b*d^2-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*b^2*c*d","B"
1202,1,753,212,0.244000," ","int((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^3,x)","-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b^{3} c d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{a^{2} d^{2}}{2 f \left(a^{2}+b^{2}\right) b \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{2 a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{2 a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{2 a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{2 b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{2 \ln \left(a +b \tan \left(f x +e \right)\right) a^{3} c d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,d^{2}}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{6 \ln \left(a +b \tan \left(f x +e \right)\right) a \,b^{2} c d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{2}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} d^{2}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} c d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c^{2}}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} d^{2}}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) b^{3} d^{2}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{b \,c^{2}}{2 f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{a c d}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) b^{3} c^{2}}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} c d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,c^{2}}{2 f \left(a^{2}+b^{2}\right)^{3}}"," ",0,"3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^2*b*d^2-3/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a*b^2*c^2+3/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a*b^2*d^2-3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^2*b*d^2-2/f/(a^2+b^2)^3*arctan(tan(f*x+e))*b^3*c*d-1/2/f/(a^2+b^2)/b/(a+b*tan(f*x+e))^2*a^2*d^2+2/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^2*c*d-2/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*a*b*c^2+2/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*a*b*d^2-2/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*b^2*c*d-2/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^3*c*d+6/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a^2*b*c*d+6/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a*b^2*c*d-3/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a*b^2*c*d+1/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a^3*c^2-1/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a^3*d^2+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*b^3*c^2-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*b^3*d^2+1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*b^3*d^2-1/2/f/(a^2+b^2)*b/(a+b*tan(f*x+e))^2*c^2+1/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*a*c*d+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^2*b*c^2+1/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^3*c*d-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^2*b*c^2-1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*b^3*c^2","B"
1203,1,720,294,0.026000," ","int((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x)","\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{3}}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3} d^{3}}{f}+\frac{b^{3} d^{3} \tan \left(f x +e \right)}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c \,d^{2}}{2 f}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{3} c^{2} d}{f}+\frac{3 a \,b^{2} c^{3} \tan \left(f x +e \right)}{f}+\frac{\left(\tan^{3}\left(f x +e \right)\right) b^{3} c^{2} d}{f}-\frac{3 \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} d^{3}}{2 f}+\frac{3 a^{3} c \,d^{2} \tan \left(f x +e \right)}{f}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{3} c \,d^{2}}{f}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,d^{3}}{f}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{3}}{f}-\frac{3 b^{3} c^{2} d \tan \left(f x +e \right)}{f}-\frac{3 a^{2} b \,d^{3} \tan \left(f x +e \right)}{f}+\frac{\left(\tan^{3}\left(f x +e \right)\right) a^{2} b \,d^{3}}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} c^{2} d}{2 f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,c^{3}}{2 f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} d^{3}}{2 f}+\frac{b^{3} d^{3} \left(\tan^{5}\left(f x +e \right)\right)}{5 f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) b^{3} c^{3}}{2 f}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b^{3} d^{3}}{3 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} d^{3}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c^{3}}{2 f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) a^{3} d^{3}}{2 f}+\frac{3 \left(\tan^{4}\left(f x +e \right)\right) a \,b^{2} d^{3}}{4 f}+\frac{9 \left(\tan^{2}\left(f x +e \right)\right) a \,b^{2} c^{2} d}{2 f}+\frac{3 \left(\tan^{4}\left(f x +e \right)\right) b^{3} c \,d^{2}}{4 f}-\frac{3 \left(\tan^{2}\left(f x +e \right)\right) b^{3} c \,d^{2}}{2 f}-\frac{9 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b c \,d^{2}}{2 f}+\frac{9 \left(\tan^{2}\left(f x +e \right)\right) a^{2} b c \,d^{2}}{2 f}-\frac{9 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} c^{2} d}{2 f}+\frac{3 \left(\tan^{3}\left(f x +e \right)\right) a \,b^{2} c \,d^{2}}{f}-\frac{9 a \,b^{2} c \,d^{2} \tan \left(f x +e \right)}{f}-\frac{9 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,c^{2} d}{f}+\frac{9 a^{2} b \,c^{2} d \tan \left(f x +e \right)}{f}+\frac{9 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c \,d^{2}}{f}"," ",0,"1/f*arctan(tan(f*x+e))*a^3*c^3-1/f*arctan(tan(f*x+e))*b^3*d^3-1/2/f*ln(1+tan(f*x+e)^2)*a^3*d^3-1/2/f*ln(1+tan(f*x+e)^2)*b^3*c^3+1/f*b^3*d^3*tan(f*x+e)+1/2/f*tan(f*x+e)^2*a^3*d^3-1/3/f*tan(f*x+e)^3*b^3*d^3+1/5/f*b^3*d^3*tan(f*x+e)^5+1/2/f*tan(f*x+e)^2*b^3*c^3+9/2/f*tan(f*x+e)^2*a*b^2*c^2*d+3/f*arctan(tan(f*x+e))*b^3*c^2*d+3/f*a*b^2*c^3*tan(f*x+e)+1/f*tan(f*x+e)^3*b^3*c^2*d-3/2/f*tan(f*x+e)^2*a*b^2*d^3+1/f*tan(f*x+e)^3*a^2*b*d^3+3/2/f*ln(1+tan(f*x+e)^2)*a^3*c^2*d+3/2/f*ln(1+tan(f*x+e)^2)*a^2*b*c^3+3/2/f*ln(1+tan(f*x+e)^2)*a*b^2*d^3+3/2/f*ln(1+tan(f*x+e)^2)*b^3*c*d^2+3/f*a^3*c*d^2*tan(f*x+e)+3/4/f*tan(f*x+e)^4*b^3*c*d^2-3/f*arctan(tan(f*x+e))*a^3*c*d^2+3/f*arctan(tan(f*x+e))*a^2*b*d^3-3/f*arctan(tan(f*x+e))*a*b^2*c^3-3/f*b^3*c^2*d*tan(f*x+e)-3/f*a^2*b*d^3*tan(f*x+e)-3/2/f*tan(f*x+e)^2*b^3*c*d^2+3/4/f*tan(f*x+e)^4*a*b^2*d^3+3/f*tan(f*x+e)^3*a*b^2*c*d^2-9/f*a*b^2*c*d^2*tan(f*x+e)-9/2/f*ln(1+tan(f*x+e)^2)*a^2*b*c*d^2-9/f*arctan(tan(f*x+e))*a^2*b*c^2*d+9/2/f*tan(f*x+e)^2*a^2*b*c*d^2-9/2/f*ln(1+tan(f*x+e)^2)*a*b^2*c^2*d+9/f*a^2*b*c^2*d*tan(f*x+e)+9/f*arctan(tan(f*x+e))*a*b^2*c*d^2","B"
1204,1,460,213,0.028000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x)","\frac{b^{2} d^{3} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{2 \left(\tan^{3}\left(f x +e \right)\right) a b \,d^{3}}{3 f}+\frac{\left(\tan^{3}\left(f x +e \right)\right) b^{2} c \,d^{2}}{f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) a^{2} d^{3}}{2 f}+\frac{3 \left(\tan^{2}\left(f x +e \right)\right) a b c \,d^{2}}{f}+\frac{3 \left(\tan^{2}\left(f x +e \right)\right) b^{2} c^{2} d}{2 f}-\frac{\left(\tan^{2}\left(f x +e \right)\right) b^{2} d^{3}}{2 f}+\frac{3 a^{2} c \,d^{2} \tan \left(f x +e \right)}{f}+\frac{6 a b \,c^{2} d \tan \left(f x +e \right)}{f}-\frac{2 a b \,d^{3} \tan \left(f x +e \right)}{f}+\frac{b^{2} c^{3} \tan \left(f x +e \right)}{f}-\frac{3 b^{2} c \,d^{2} \tan \left(f x +e \right)}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} c^{2} d}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} d^{3}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,c^{3}}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a b c \,d^{2}}{f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} c^{2} d}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} d^{3}}{2 f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{3}}{f}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} c \,d^{2}}{f}-\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2} d}{f}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{3}}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{3}}{f}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{2} c \,d^{2}}{f}"," ",0,"1/4/f*b^2*d^3*tan(f*x+e)^4+2/3/f*tan(f*x+e)^3*a*b*d^3+1/f*tan(f*x+e)^3*b^2*c*d^2+1/2/f*tan(f*x+e)^2*a^2*d^3+3/f*tan(f*x+e)^2*a*b*c*d^2+3/2/f*tan(f*x+e)^2*b^2*c^2*d-1/2/f*tan(f*x+e)^2*b^2*d^3+3/f*a^2*c*d^2*tan(f*x+e)+6/f*a*b*c^2*d*tan(f*x+e)-2/f*a*b*d^3*tan(f*x+e)+1/f*b^2*c^3*tan(f*x+e)-3/f*b^2*c*d^2*tan(f*x+e)+3/2/f*ln(1+tan(f*x+e)^2)*a^2*c^2*d-1/2/f*ln(1+tan(f*x+e)^2)*a^2*d^3+1/f*ln(1+tan(f*x+e)^2)*a*b*c^3-3/f*ln(1+tan(f*x+e)^2)*a*b*c*d^2-3/2/f*ln(1+tan(f*x+e)^2)*b^2*c^2*d+1/2/f*ln(1+tan(f*x+e)^2)*b^2*d^3+1/f*arctan(tan(f*x+e))*a^2*c^3-3/f*arctan(tan(f*x+e))*a^2*c*d^2-6/f*arctan(tan(f*x+e))*a*b*c^2*d+2/f*arctan(tan(f*x+e))*a*b*d^3-1/f*arctan(tan(f*x+e))*b^2*c^3+3/f*arctan(tan(f*x+e))*b^2*c*d^2","B"
1205,1,247,140,0.028000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^3,x)","\frac{b \,d^{3} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) a \,d^{3}}{2 f}+\frac{3 \left(\tan^{2}\left(f x +e \right)\right) b c \,d^{2}}{2 f}+\frac{3 a c \,d^{2} \tan \left(f x +e \right)}{f}+\frac{3 b \,c^{2} d \tan \left(f x +e \right)}{f}-\frac{b \,d^{3} \tan \left(f x +e \right)}{f}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,c^{2} d}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,d^{3}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3} b}{2 f}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b c \,d^{2}}{2 f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f}"," ",0,"1/3/f*b*d^3*tan(f*x+e)^3+1/2/f*tan(f*x+e)^2*a*d^3+3/2/f*tan(f*x+e)^2*b*c*d^2+3/f*a*c*d^2*tan(f*x+e)+3/f*b*c^2*d*tan(f*x+e)-1/f*b*d^3*tan(f*x+e)+3/2/f*ln(1+tan(f*x+e)^2)*a*c^2*d-1/2/f*ln(1+tan(f*x+e)^2)*a*d^3+1/2/f*ln(1+tan(f*x+e)^2)*c^3*b-3/2/f*ln(1+tan(f*x+e)^2)*b*c*d^2+1/f*arctan(tan(f*x+e))*a*c^3-3/f*arctan(tan(f*x+e))*a*c*d^2-3/f*arctan(tan(f*x+e))*b*c^2*d+1/f*arctan(tan(f*x+e))*b*d^3","A"
1206,1,364,140,0.211000," ","int((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e)),x)","\frac{d^{3} \tan \left(f x +e \right)}{f b}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{3} d^{3}}{f \,b^{2} \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} c \,d^{2}}{f b \left(a^{2}+b^{2}\right)}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a \,c^{2} d}{f \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(a +b \tan \left(f x +e \right)\right) c^{3}}{f \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,c^{2} d}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,d^{3}}{2 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3} b}{2 f \left(a^{2}+b^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b c \,d^{2}}{2 f \left(a^{2}+b^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f \left(a^{2}+b^{2}\right)}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(a^{2}+b^{2}\right)}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f \left(a^{2}+b^{2}\right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f \left(a^{2}+b^{2}\right)}"," ",0,"1/f*d^3/b*tan(f*x+e)-1/f/b^2/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^3*d^3+3/f/b/(a^2+b^2)*ln(a+b*tan(f*x+e))*a^2*c*d^2-3/f/(a^2+b^2)*ln(a+b*tan(f*x+e))*a*c^2*d+1/f*b/(a^2+b^2)*ln(a+b*tan(f*x+e))*c^3+3/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*a*c^2*d-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*a*d^3-1/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*c^3*b+3/2/f/(a^2+b^2)*ln(1+tan(f*x+e)^2)*b*c*d^2+1/f/(a^2+b^2)*arctan(tan(f*x+e))*a*c^3-3/f/(a^2+b^2)*arctan(tan(f*x+e))*a*c*d^2+3/f/(a^2+b^2)*arctan(tan(f*x+e))*b*c^2*d-1/f/(a^2+b^2)*arctan(tan(f*x+e))*b*d^3","B"
1207,1,671,230,0.256000," ","int((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^2,x)","\frac{a^{3} d^{3}}{f \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 a^{2} c \,d^{2}}{f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{3 a \,c^{2} d}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{b \,c^{3}}{f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{4} d^{3}}{f \left(a^{2}+b^{2}\right)^{2} b^{2}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} d^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b \ln \left(a +b \tan \left(f x +e \right)\right) a \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{6 b \ln \left(a +b \tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a b c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2} d}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{3}}{f \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))*a^3*d^3-3/f/b/(a^2+b^2)/(a+b*tan(f*x+e))*a^2*c*d^2+3/f/(a^2+b^2)/(a+b*tan(f*x+e))*a*c^2*d-1/f*b/(a^2+b^2)/(a+b*tan(f*x+e))*c^3+1/f/(a^2+b^2)^2/b^2*ln(a+b*tan(f*x+e))*a^4*d^3-3/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^2*c^2*d+3/f/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^2*d^3+2/f/(a^2+b^2)^2*b*ln(a+b*tan(f*x+e))*a*c^3-6/f/(a^2+b^2)^2*b*ln(a+b*tan(f*x+e))*a*c*d^2+3/f/(a^2+b^2)^2*b^2*ln(a+b*tan(f*x+e))*c^2*d+3/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*a^2*c^2*d-1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*a^2*d^3-1/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*a*b*c^3+3/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*a*b*c*d^2-3/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*b^2*c^2*d+1/2/f/(a^2+b^2)^2*ln(1+tan(f*x+e)^2)*b^2*d^3+1/f/(a^2+b^2)^2*arctan(tan(f*x+e))*a^2*c^3-3/f/(a^2+b^2)^2*arctan(tan(f*x+e))*a^2*c*d^2+6/f/(a^2+b^2)^2*arctan(tan(f*x+e))*a*b*c^2*d-2/f/(a^2+b^2)^2*arctan(tan(f*x+e))*a*b*d^3-1/f/(a^2+b^2)^2*arctan(tan(f*x+e))*b^2*c^3+3/f/(a^2+b^2)^2*arctan(tan(f*x+e))*b^2*c*d^2","B"
1208,1,1063,235,0.258000," ","int((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^3,x)","\frac{9 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,c^{2} d}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{9 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{9 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} b c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a^{2} d^{3}}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3} d^{3}}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{9 \ln \left(a +b \tan \left(f x +e \right)\right) a \,b^{2} c^{2} d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 a^{2} c \,d^{2}}{2 f b \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{6 b a c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{a^{3} d^{3}}{2 f \,b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{\ln \left(a +b \tan \left(f x +e \right)\right) a^{3} d^{3}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(a +b \tan \left(f x +e \right)\right) b^{3} c^{3}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{b \,c^{3}}{2 f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{3}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,d^{3}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c^{3}}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{3} c^{2} d}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{2 b a \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 b^{2} c^{2} d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{a^{4} d^{3}}{f \left(a^{2}+b^{2}\right)^{2} b^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{9 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b c \,d^{2}}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{9 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} b \,c^{3}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a \,b^{2} d^{3}}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) b^{3} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 a \,c^{2} d}{2 f \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{3 a^{2} c^{2} d}{f \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,c^{3}}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c \,d^{2}}{2 f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{3} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \tan \left(f x +e \right)\right) a^{3} c^{2} d}{f \left(a^{2}+b^{2}\right)^{3}}"," ",0,"9/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a^2*b*c^2*d+9/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a*b^2*c*d^2+9/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^2*b*c*d^2-9/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^2*b*c*d^2-3/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^2*d^3+1/f/(a^2+b^2)^3*arctan(tan(f*x+e))*b^3*d^3-1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^3*d^3+9/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a*b^2*c^2*d-3/2/f/b/(a^2+b^2)/(a+b*tan(f*x+e))^2*a^2*c*d^2+6/f/(a^2+b^2)^2*b/(a+b*tan(f*x+e))*a*c*d^2-9/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a*b^2*c^2*d+1/2/f/b^2/(a^2+b^2)/(a+b*tan(f*x+e))^2*a^3*d^3+1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^3*d^3-1/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*b^3*c^3-1/2/f*b/(a^2+b^2)/(a+b*tan(f*x+e))^2*c^3+1/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a^3*c^3+1/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*b^3*c^3-3/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a^2*b*d^3-3/f/(a^2+b^2)^3*arctan(tan(f*x+e))*b^3*c^2*d-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^2*b*c^3-2/f/(a^2+b^2)^2*b/(a+b*tan(f*x+e))*a*c^3-3/f/(a^2+b^2)^2*b^2/(a+b*tan(f*x+e))*c^2*d-1/f/(a^2+b^2)^2/b^2/(a+b*tan(f*x+e))*a^4*d^3+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a*b^2*d^3+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^2*b*c^3-3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a*b^2*d^3+3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*b^3*c*d^2+3/2/f/(a^2+b^2)/(a+b*tan(f*x+e))^2*a*c^2*d+3/f/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^2*c^2*d-3/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a*b^2*c^3-3/f/(a^2+b^2)^3*arctan(tan(f*x+e))*a^3*c*d^2+3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*a^3*c^2*d-3/2/f/(a^2+b^2)^3*ln(1+tan(f*x+e)^2)*b^3*c*d^2-3/f/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^3*c^2*d","B"
1209,1,498,188,0.214000," ","int((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e)),x)","\frac{b^{4} \left(\tan^{2}\left(f x +e \right)\right)}{2 f d}+\frac{4 b^{3} a \tan \left(f x +e \right)}{f d}-\frac{b^{4} c \tan \left(f x +e \right)}{f \,d^{2}}+\frac{d \ln \left(c +d \tan \left(f x +e \right)\right) a^{4}}{f \left(c^{2}+d^{2}\right)}-\frac{4 \ln \left(c +d \tan \left(f x +e \right)\right) a^{3} b c}{f \left(c^{2}+d^{2}\right)}+\frac{6 \ln \left(c +d \tan \left(f x +e \right)\right) c^{2} a^{2} b^{2}}{f d \left(c^{2}+d^{2}\right)}-\frac{4 \ln \left(c +d \tan \left(f x +e \right)\right) c^{3} a \,b^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) c^{4} b^{4}}{f \,d^{3} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{4} d}{2 f \left(c^{2}+d^{2}\right)}+\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} b c}{f \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b^{2} d}{f \left(c^{2}+d^{2}\right)}-\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{3} c}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{4} d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{4} c}{f \left(c^{2}+d^{2}\right)}+\frac{4 \arctan \left(\tan \left(f x +e \right)\right) a^{3} b d}{f \left(c^{2}+d^{2}\right)}-\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b^{2} c}{f \left(c^{2}+d^{2}\right)}-\frac{4 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{3} d}{f \left(c^{2}+d^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{4} c}{f \left(c^{2}+d^{2}\right)}"," ",0,"1/2/f*b^4/d*tan(f*x+e)^2+4/f*b^3/d*a*tan(f*x+e)-1/f*b^4/d^2*c*tan(f*x+e)+1/f*d/(c^2+d^2)*ln(c+d*tan(f*x+e))*a^4-4/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*a^3*b*c+6/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*c^2*a^2*b^2-4/f/d^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*c^3*a*b^3+1/f/d^3/(c^2+d^2)*ln(c+d*tan(f*x+e))*c^4*b^4-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^4*d+2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^3*b*c+3/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^2*b^2*d-2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a*b^3*c-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*b^4*d+1/f/(c^2+d^2)*arctan(tan(f*x+e))*a^4*c+4/f/(c^2+d^2)*arctan(tan(f*x+e))*a^3*b*d-6/f/(c^2+d^2)*arctan(tan(f*x+e))*a^2*b^2*c-4/f/(c^2+d^2)*arctan(tan(f*x+e))*a*b^3*d+1/f/(c^2+d^2)*arctan(tan(f*x+e))*b^4*c","B"
1210,1,364,144,0.295000," ","int((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x)","\frac{b^{3} \tan \left(f x +e \right)}{f d}+\frac{a^{3} d \ln \left(c +d \tan \left(f x +e \right)\right)}{f \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} b c}{f \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) a \,b^{2} c^{2}}{f d \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) b^{3} c^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right)}-\frac{a^{3} \ln \left(1+\tan^{2}\left(f x +e \right)\right) d}{2 f \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b c}{2 f \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} d}{2 f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,b^{3}}{2 f \left(c^{2}+d^{2}\right)}+\frac{a^{3} \arctan \left(\tan \left(f x +e \right)\right) c}{f \left(c^{2}+d^{2}\right)}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f \left(c^{2}+d^{2}\right)}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(c^{2}+d^{2}\right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f \left(c^{2}+d^{2}\right)}"," ",0,"1/f*b^3/d*tan(f*x+e)+1/f*a^3*d/(c^2+d^2)*ln(c+d*tan(f*x+e))-3/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*a^2*b*c+3/f/d/(c^2+d^2)*ln(c+d*tan(f*x+e))*a*b^2*c^2-1/f/d^2/(c^2+d^2)*ln(c+d*tan(f*x+e))*b^3*c^3-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^3*d+3/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^2*b*c+3/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a*b^2*d-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*c*b^3+1/f*a^3/(c^2+d^2)*arctan(tan(f*x+e))*c+3/f/(c^2+d^2)*arctan(tan(f*x+e))*a^2*b*d-3/f/(c^2+d^2)*arctan(tan(f*x+e))*a*b^2*c-1/f/(c^2+d^2)*arctan(tan(f*x+e))*b^3*d","B"
1211,1,249,103,0.249000," ","int((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x)","\frac{d \ln \left(c +d \tan \left(f x +e \right)\right) a^{2}}{f \left(c^{2}+d^{2}\right)}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) a b c}{f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(c^{2}+d^{2}\right) d}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b c}{f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} d}{2 f \left(c^{2}+d^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f \left(c^{2}+d^{2}\right)}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b d}{f \left(c^{2}+d^{2}\right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f \left(c^{2}+d^{2}\right)}"," ",0,"1/f/(c^2+d^2)*d*ln(c+d*tan(f*x+e))*a^2-2/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*a*b*c+1/f/(c^2+d^2)/d*ln(c+d*tan(f*x+e))*b^2*c^2-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^2*d+1/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a*b*c+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*b^2*d+1/f/(c^2+d^2)*arctan(tan(f*x+e))*a^2*c+2/f/(c^2+d^2)*arctan(tan(f*x+e))*a*b*d-1/f/(c^2+d^2)*arctan(tan(f*x+e))*b^2*c","B"
1212,1,153,59,0.231000," ","int((a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x)","\frac{\ln \left(c +d \tan \left(f x +e \right)\right) d a}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) c b}{f \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) d a}{2 f \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c b}{2 f \left(c^{2}+d^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a c}{f \left(c^{2}+d^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b d}{f \left(c^{2}+d^{2}\right)}"," ",0,"1/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*d*a-1/f/(c^2+d^2)*ln(c+d*tan(f*x+e))*c*b-1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*d*a+1/2/f/(c^2+d^2)*ln(1+tan(f*x+e)^2)*c*b+1/f/(c^2+d^2)*arctan(tan(f*x+e))*a*c+1/f/(c^2+d^2)*arctan(tan(f*x+e))*b*d","B"
1213,1,212,118,0.323000," ","int(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x)","-\frac{b^{2} \ln \left(a +b \tan \left(f x +e \right)\right)}{f \left(d a -c b \right) \left(a^{2}+b^{2}\right)}+\frac{d^{2} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \left(d a -c b \right) \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) d a}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c b}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a c}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)}"," ",0,"-1/f*b^2/(a*d-b*c)/(a^2+b^2)*ln(a+b*tan(f*x+e))+1/f*d^2/(a*d-b*c)/(c^2+d^2)*ln(c+d*tan(f*x+e))-1/2/f/(a^2+b^2)/(c^2+d^2)*ln(1+tan(f*x+e)^2)*d*a-1/2/f/(a^2+b^2)/(c^2+d^2)*ln(1+tan(f*x+e)^2)*c*b+1/f/(a^2+b^2)/(c^2+d^2)*arctan(tan(f*x+e))*a*c-1/f/(a^2+b^2)/(c^2+d^2)*arctan(tan(f*x+e))*b*d","A"
1214,1,411,183,0.344000," ","int(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x)","\frac{b^{2}}{f \left(d a -c b \right) \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{3 b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b^{3} \ln \left(a +b \tan \left(f x +e \right)\right) a c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{d^{3} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)}"," ",0,"1/f*b^2/(a*d-b*c)/(a^2+b^2)/(a+b*tan(f*x+e))-3/f*b^2/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^2*d+2/f*b^3/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a*c-1/f*b^4/(a*d-b*c)^2/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*d+1/f*d^3/(a*d-b*c)^2/(c^2+d^2)*ln(c+d*tan(f*x+e))-1/2/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^2*d-1/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a*b*c+1/2/f/(a^2+b^2)^2/(c^2+d^2)*ln(1+tan(f*x+e)^2)*b^2*d+1/f/(a^2+b^2)^2/(c^2+d^2)*arctan(tan(f*x+e))*a^2*c-2/f/(a^2+b^2)^2/(c^2+d^2)*arctan(tan(f*x+e))*a*b*d-1/f/(a^2+b^2)^2/(c^2+d^2)*arctan(tan(f*x+e))*b^2*c","B"
1215,1,747,277,0.394000," ","int(1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x)","\frac{b^{2}}{2 f \left(d a -c b \right) \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}+\frac{3 b^{2} a^{2} d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{2 b^{3} a c}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{b^{4} d}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{6 b^{2} \ln \left(a +b \tan \left(f x +e \right)\right) a^{4} d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{8 b^{3} \ln \left(a +b \tan \left(f x +e \right)\right) a^{3} c d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{3 b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{3 b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{b^{6} \ln \left(a +b \tan \left(f x +e \right)\right) c^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}-\frac{b^{6} \ln \left(a +b \tan \left(f x +e \right)\right) d^{2}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{3}}+\frac{d^{4} \ln \left(c +d \tan \left(f x +e \right)\right)}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} d}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b c}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} d}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c \,b^{3}}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3} d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)}"," ",0,"1/2/f*b^2/(a*d-b*c)/(a^2+b^2)/(a+b*tan(f*x+e))^2+3/f*b^2/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^2*d-2/f*b^3/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*a*c+1/f*b^4/(a*d-b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))*d-6/f*b^2/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^4*d^2+8/f*b^3/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^3*c*d-3/f*b^4/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^2*c^2-3/f*b^4/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^2*d^2+1/f*b^6/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*c^2-1/f*b^6/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*d^2+1/f*d^4/(a*d-b*c)^3/(c^2+d^2)*ln(c+d*tan(f*x+e))-1/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^3*d-3/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a^2*b*c+3/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*a*b^2*d+1/2/f/(a^2+b^2)^3/(c^2+d^2)*ln(1+tan(f*x+e)^2)*c*b^3+1/f/(a^2+b^2)^3/(c^2+d^2)*arctan(tan(f*x+e))*a^3*c-3/f/(a^2+b^2)^3/(c^2+d^2)*arctan(tan(f*x+e))*a^2*b*d-3/f/(a^2+b^2)^3/(c^2+d^2)*arctan(tan(f*x+e))*a*b^2*c+1/f/(a^2+b^2)^3/(c^2+d^2)*arctan(tan(f*x+e))*b^3*d","B"
1216,1,891,285,0.219000," ","int((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^2,x)","-\frac{8 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{3} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{6 a^{2} b^{2} c^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{4 c^{3} a \,b^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{8 \arctan \left(\tan \left(f x +e \right)\right) a^{3} b c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{4} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{4} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{4} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{d \,a^{4}}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{b^{4} \tan \left(f x +e \right)}{f \,d^{2}}+\frac{6 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{4} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{12 d \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} b^{2} c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{4 \ln \left(c +d \tan \left(f x +e \right)\right) a \,b^{3} c^{4}}{f \,d^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{4 a^{3} b c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) a^{4} c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{4 d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) a^{3} b}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{4 \ln \left(c +d \tan \left(f x +e \right)\right) b^{4} c^{3}}{f d \left(c^{2}+d^{2}\right)^{2}}-\frac{4 \ln \left(c +d \tan \left(f x +e \right)\right) a^{3} b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{12 \ln \left(c +d \tan \left(f x +e \right)\right) a \,b^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{c^{4} b^{4}}{f \,d^{3} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) b^{4} c^{5}}{f \,d^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{3} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{4} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{4} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"-8/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a*b^3*c*d-6/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*a^2*b^2*c^2+4/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))*c^3*a*b^3+6/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^2*b^2*c*d+8/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^3*b*c*d-1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^4*d^2+1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*b^4*c^2-1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*b^4*d^2-1/f*d/(c^2+d^2)/(c+d*tan(f*x+e))*a^4+1/f*b^4/d^2*tan(f*x+e)+1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^4*c^2-12/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a^2*b^2*c+4/f/d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a*b^3*c^4+2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*b^3*d^2-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*b^4*c*d-6/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^2*b^2*c^2+4/f/(c^2+d^2)/(c+d*tan(f*x+e))*a^3*b*c-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^4*c*d+2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^3*b*c^2+2/f*d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a^4*c+4/f*d^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a^3*b-2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^3*b*d^2-2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*b^3*c^2-4/f/d/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*b^4*c^3-4/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a^3*b*c^2+12/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a*b^3*c^2-1/f/d^3/(c^2+d^2)/(c+d*tan(f*x+e))*c^4*b^4-2/f/d^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*b^4*c^5+6/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^2*b^2*d^2","B"
1217,1,671,223,0.255000," ","int((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x)","-\frac{d \,a^{3}}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 a^{2} b c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{3 a \,b^{2} c^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{b^{3} c^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 d \ln \left(c +d \tan \left(f x +e \right)\right) a^{3} c}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} b}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{6 d \ln \left(c +d \tan \left(f x +e \right)\right) a \,b^{2} c}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) b^{3} c^{4}}{f \left(c^{2}+d^{2}\right)^{2} d^{2}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) b^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b^{3} c d}{f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"-1/f*d/(c^2+d^2)/(c+d*tan(f*x+e))*a^3+3/f/(c^2+d^2)/(c+d*tan(f*x+e))*a^2*b*c-3/f/d/(c^2+d^2)/(c+d*tan(f*x+e))*a*b^2*c^2+1/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))*b^3*c^3+2/f/(c^2+d^2)^2*d*ln(c+d*tan(f*x+e))*a^3*c-3/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a^2*b*c^2+3/f/(c^2+d^2)^2*d^2*ln(c+d*tan(f*x+e))*a^2*b-6/f/(c^2+d^2)^2*d*ln(c+d*tan(f*x+e))*a*b^2*c+1/f/(c^2+d^2)^2/d^2*ln(c+d*tan(f*x+e))*b^3*c^4+3/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*b^3*c^2-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^3*c*d+3/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^2*b*c^2-3/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^2*b*d^2+3/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*b^2*c*d-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*b^3*c^2+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*b^3*d^2+1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^3*c^2-1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^3*d^2+6/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^2*b*c*d-3/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a*b^2*c^2+3/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a*b^2*d^2-2/f/(c^2+d^2)^2*arctan(tan(f*x+e))*b^3*c*d","B"
1218,1,465,126,0.258000," ","int((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x)","-\frac{d \,a^{2}}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 a b c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}-\frac{b^{2} c^{2}}{f \left(c^{2}+d^{2}\right) d \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) a b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) a b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{4 \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"-1/f/(c^2+d^2)*d/(c+d*tan(f*x+e))*a^2+2/f/(c^2+d^2)/(c+d*tan(f*x+e))*a*b*c-1/f/(c^2+d^2)/d/(c+d*tan(f*x+e))*b^2*c^2+2/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a^2*c*d-2/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a*b*c^2+2/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a*b*d^2-2/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*b^2*c*d+1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^2*c^2-1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a^2*d^2+4/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a*b*c*d-1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*b^2*c^2+1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*b^2*d^2-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^2*c*d+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*b*c^2-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*b*d^2+1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*b^2*c*d","B"
1219,1,301,111,0.242000," ","int((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x)","-\frac{d a}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{c b}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) a c d}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) c^{2} b}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a c d}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} b}{2 f \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2}}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b c d}{f \left(c^{2}+d^{2}\right)^{2}}"," ",0,"-1/f/(c^2+d^2)/(c+d*tan(f*x+e))*d*a+1/f/(c^2+d^2)/(c+d*tan(f*x+e))*c*b+2/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a*c*d-1/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c^2*b+1/f/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*b*d^2-1/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*c*d+1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*c^2*b-1/2/f/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*b*d^2+1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a*c^2-1/f/(c^2+d^2)^2*arctan(tan(f*x+e))*a*d^2+2/f/(c^2+d^2)^2*arctan(tan(f*x+e))*b*c*d","B"
1220,1,412,184,0.371000," ","int(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x)","\frac{b^{3} \ln \left(a +b \tan \left(f x +e \right)\right)}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right)}-\frac{d^{2}}{f \left(d a -c b \right) \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) a c}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{3 d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2} b}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) b}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a c d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{2} b}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b \,d^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,c^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,d^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b c d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{2}}"," ",0,"1/f*b^3/(a*d-b*c)^2/(a^2+b^2)*ln(a+b*tan(f*x+e))-1/f*d^2/(a*d-b*c)/(c^2+d^2)/(c+d*tan(f*x+e))+2/f*d^3/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a*c-3/f*d^2/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c^2*b-1/f*d^4/(a*d-b*c)^2/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*b-1/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*c*d-1/2/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*c^2*b+1/2/f/(a^2+b^2)/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*b*d^2+1/f/(a^2+b^2)/(c^2+d^2)^2*arctan(tan(f*x+e))*a*c^2-1/f/(a^2+b^2)/(c^2+d^2)^2*arctan(tan(f*x+e))*a*d^2-2/f/(a^2+b^2)/(c^2+d^2)^2*arctan(tan(f*x+e))*b*c*d","B"
1221,1,652,290,0.408000," ","int(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x)","-\frac{b^{3}}{f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}+\frac{4 b^{3} \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}-\frac{2 b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) a c}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b^{5} \ln \left(a +b \tan \left(f x +e \right)\right) d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2}}-\frac{d^{3}}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) a c}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{4 d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2} b}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 d^{5} \ln \left(c +d \tan \left(f x +e \right)\right) b}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{4 \arctan \left(\tan \left(f x +e \right)\right) a b c d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{2}}"," ",0,"-1/f*b^3/(a*d-b*c)^2/(a^2+b^2)/(a+b*tan(f*x+e))+4/f*b^3/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^2*d-2/f*b^4/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a*c+2/f*b^5/(a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*d-1/f*d^3/(a*d-b*c)^2/(c^2+d^2)/(c+d*tan(f*x+e))+2/f*d^4/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a*c-4/f*d^3/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c^2*b-2/f*d^5/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*b-1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^2*c*d-1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*b*c^2+1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*b*d^2+1/f/(a^2+b^2)^2/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*b^2*c*d+1/f/(a^2+b^2)^2/(c^2+d^2)^2*arctan(tan(f*x+e))*a^2*c^2-1/f/(a^2+b^2)^2/(c^2+d^2)^2*arctan(tan(f*x+e))*a^2*d^2-4/f/(a^2+b^2)^2/(c^2+d^2)^2*arctan(tan(f*x+e))*a*b*c*d-1/f/(a^2+b^2)^2/(c^2+d^2)^2*arctan(tan(f*x+e))*b^2*c^2+1/f/(a^2+b^2)^2/(c^2+d^2)^2*arctan(tan(f*x+e))*b^2*d^2","B"
1222,1,1080,453,0.424000," ","int(1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x)","\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c^{2}}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} c d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} d^{2}}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 b^{4} a c}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{9 b^{5} \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} d^{2}}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{3}}-\frac{2 b^{6} \ln \left(a +b \tan \left(f x +e \right)\right) a c d}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{3}}-\frac{10 b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) a^{3} c d}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{3}}-\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b c d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{2}}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} d^{2}}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b^{3} c d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{3 b^{5} \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{3}}-\frac{5 d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) c^{2} b}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{2}}+\frac{2 d^{5} \ln \left(c +d \tan \left(f x +e \right)\right) a c}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{2}}-\frac{4 b^{3} a^{2} d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}+\frac{10 b^{3} \ln \left(a +b \tan \left(f x +e \right)\right) a^{4} d^{2}}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{3}}+\frac{3 b^{7} \ln \left(a +b \tan \left(f x +e \right)\right) d^{2}}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{3}}-\frac{b^{7} \ln \left(a +b \tan \left(f x +e \right)\right) c^{2}}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} c d}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,c^{2}}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,d^{2}}{2 f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{2}}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} d^{2}}{f \left(a^{2}+b^{2}\right)^{3} \left(c^{2}+d^{2}\right)^{2}}-\frac{3 d^{6} \ln \left(c +d \tan \left(f x +e \right)\right) b}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{2}}-\frac{2 b^{5} d}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(f x +e \right)\right)}-\frac{b^{3}}{2 f \left(d a -c b \right)^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)^{2}}-\frac{d^{4}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)}"," ",0,"2/f*b^4/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*a*c+9/f*b^5/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^2*d^2-2/f*b^6/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a*c*d-10/f*b^4/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^3*c*d-6/f/(a^2+b^2)^3/(c^2+d^2)^2*arctan(tan(f*x+e))*a^2*b*c*d+3/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a*b^2*c*d-3/f/(a^2+b^2)^3/(c^2+d^2)^2*arctan(tan(f*x+e))*a*b^2*c^2+3/f/(a^2+b^2)^3/(c^2+d^2)^2*arctan(tan(f*x+e))*a*b^2*d^2+2/f/(a^2+b^2)^3/(c^2+d^2)^2*arctan(tan(f*x+e))*b^3*c*d+3/f*b^5/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^2*c^2-5/f*d^4/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*c^2*b+2/f*d^5/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*a*c-4/f*b^3/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*a^2*d+10/f*b^3/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*a^4*d^2+1/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*b^3*c^2+3/f*b^7/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*d^2-1/f*b^7/(a*d-b*c)^4/(a^2+b^2)^3*ln(a+b*tan(f*x+e))*c^2-1/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*b^3*d^2+1/f/(a^2+b^2)^3/(c^2+d^2)^2*arctan(tan(f*x+e))*a^3*c^2-1/f/(a^2+b^2)^3/(c^2+d^2)^2*arctan(tan(f*x+e))*a^3*d^2-3/f*d^6/(a*d-b*c)^4/(c^2+d^2)^2*ln(c+d*tan(f*x+e))*b-2/f*b^5/(a*d-b*c)^3/(a^2+b^2)^2/(a+b*tan(f*x+e))*d-1/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^3*c*d-3/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^2*b*c^2+3/2/f/(a^2+b^2)^3/(c^2+d^2)^2*ln(1+tan(f*x+e)^2)*a^2*b*d^2-1/2/f*b^3/(a*d-b*c)^2/(a^2+b^2)/(a+b*tan(f*x+e))^2-1/f*d^4/(a*d-b*c)^3/(c^2+d^2)/(c+d*tan(f*x+e))","B"
1223,1,1411,404,0.292000," ","int((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^3,x)","-\frac{6 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} b c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{9 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b^{2} c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{6 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{3} c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{4 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{3} d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) b^{4} c^{4}}{f \left(c^{2}+d^{2}\right)^{3} d}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{4} c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} b \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b^{2} d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{3} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{4} c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{4} d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{4} d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b^{2} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{4 \ln \left(c +d \tan \left(f x +e \right)\right) a^{3} b \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{2 a^{3} b c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{3 d \ln \left(c +d \tan \left(f x +e \right)\right) a^{4} c^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{4 \ln \left(c +d \tan \left(f x +e \right)\right) a \,b^{3} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) b^{4} c^{6}}{f \left(c^{2}+d^{2}\right)^{3} d^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{4} c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{c^{4} b^{4}}{2 f \,d^{3} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{4 b^{4} c^{3}}{f d \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{4 \arctan \left(\tan \left(f x +e \right)\right) a^{3} b \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{2 d \,a^{4} c}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{4 d^{2} a^{3} b}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 b^{4} c^{5}}{f \,d^{3} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{3 c^{2} a^{2} b^{2}}{f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{12 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{3} c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{12 d \,a^{2} b^{2} c}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{4 a \,b^{3} c^{4}}{f \,d^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{18 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b^{2} c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{12 d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) a \,b^{3} c}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{12 d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) a^{3} b c}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{18 d \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} b^{2} c^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) a^{4}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{d \,a^{4}}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{4} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{4} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{2 a \,b^{3} c^{3}}{f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{12 \arctan \left(\tan \left(f x +e \right)\right) a^{3} b \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{6 d \ln \left(c +d \tan \left(f x +e \right)\right) b^{4} c^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{6 d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} b^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{4 a^{3} b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{12 a \,b^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{4} c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}"," ",0,"4/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a*b^3*d^3+3/f/(c^2+d^2)^3/d*ln(c+d*tan(f*x+e))*b^4*c^4+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^4*d^3-6/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^3*b*c*d^2-6/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^2*b^2*c^3-4/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^3*b*c^3+2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*a^3*b*c+3/f/(c^2+d^2)^3*d*ln(c+d*tan(f*x+e))*a^4*c^2+4/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*b^3*c^3+1/f/(c^2+d^2)^3/d^3*ln(c+d*tan(f*x+e))*b^4*c^6-3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^4*c*d^2-1/2/f/d^3/(c^2+d^2)/(c+d*tan(f*x+e))^2*c^4*b^4+4/f/d/(c^2+d^2)^2/(c+d*tan(f*x+e))*b^4*c^3-4/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^3*b*d^3-2/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*a^4*c-4/f*d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*a^3*b+2/f/d^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*b^4*c^5+9/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^2*b^2*c^2*d+6/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*b^3*c*d^2-3/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*c^2*a^2*b^2-12/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a*b^3*c^2*d+12/f*d/(c^2+d^2)^2/(c+d*tan(f*x+e))*a^2*b^2*c-4/f/d^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*a*b^3*c^4+18/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^2*b^2*c*d^2-12/f/(c^2+d^2)^3*d^2*ln(c+d*tan(f*x+e))*a*b^3*c+12/f/(c^2+d^2)^3*d^2*ln(c+d*tan(f*x+e))*a^3*b*c-18/f/(c^2+d^2)^3*d*ln(c+d*tan(f*x+e))*a^2*b^2*c^2-1/f/(c^2+d^2)^3*d^3*ln(c+d*tan(f*x+e))*a^4-1/2/f*d/(c^2+d^2)/(c+d*tan(f*x+e))^2*a^4+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b^4*d^3+1/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^4*c^3+1/f/(c^2+d^2)^3*arctan(tan(f*x+e))*b^4*c^3+2/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*a*b^3*c^3+12/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^3*b*c^2*d+6/f/(c^2+d^2)^3*d*ln(c+d*tan(f*x+e))*b^4*c^2-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^4*c^2*d+2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^3*b*c^3+6/f/(c^2+d^2)^3*d^3*ln(c+d*tan(f*x+e))*a^2*b^2-3/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^2*b^2*d^3-2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*b^3*c^3-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b^4*c^2*d+4/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*a^3*b*c^2-12/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*a*b^3*c^2-3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*b^4*c*d^2","B"
1224,1,1063,236,0.279000," ","int((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x)","-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{9 \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} b c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{6 d a \,b^{2} c}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{3} d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{d \,a^{3}}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{3} c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) b^{3} c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{b^{3} c^{3}}{2 f \,d^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{3 d^{2} a^{2} b}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{9 \ln \left(c +d \tan \left(f x +e \right)\right) a \,b^{2} c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{3} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3} d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 b^{3} c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) a^{3} d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) b^{3} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{9 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{9 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 a \,b^{2} c^{2}}{2 f d \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{9 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{9 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,b^{2} c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{2 d \,a^{3} c}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) a^{3} c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} b \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a \,b^{2} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{3} c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 a^{2} b c}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{3 a^{2} b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) a \,b^{2} d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{3} c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} b \,c^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{b^{3} c^{4}}{f \left(c^{2}+d^{2}\right)^{2} d^{2} \left(c +d \tan \left(f x +e \right)\right)}"," ",0,"9/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^2*b*c*d^2+6/f/(c^2+d^2)^2*d/(c+d*tan(f*x+e))*a*b^2*c-9/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^2*b*c*d^2+9/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*b^2*c^2*d-1/2/f*d/(c^2+d^2)/(c+d*tan(f*x+e))^2*a^3-3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^3*c*d^2-3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^3*c*d^2+1/2/f/d^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*b^3*c^3-3/f/(c^2+d^2)^2*d^2/(c+d*tan(f*x+e))*a^2*b-9/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*b^2*c^2*d+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^3*d^3+1/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^3*c^3+1/f/(c^2+d^2)^3*arctan(tan(f*x+e))*b^3*d^3-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b^3*c^3-3/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*b^3*c^2-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^3*d^3+1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^3*c^3+9/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^2*b*c^2*d+9/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a*b^2*c*d^2-3/2/f/d/(c^2+d^2)/(c+d*tan(f*x+e))^2*a*b^2*c^2-3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^2*b*d^3-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*b^2*d^3-2/f/(c^2+d^2)^2*d/(c+d*tan(f*x+e))*a^3*c+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^3*c^2*d-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^3*c^2*d-3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^2*b*c^3-3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a*b^2*c^3-3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*b^3*c^2*d+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b^3*c*d^2+3/2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*a^2*b*c+3/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*a^2*b*c^2+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^2*b*c^3+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*b^2*d^3-1/f/(c^2+d^2)^2/d^2/(c+d*tan(f*x+e))*b^3*c^4","B"
1225,1,753,219,0.223000," ","int((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x)","-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) a^{2} d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(c +d \tan \left(f x +e \right)\right) b^{2} d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{6 \ln \left(c +d \tan \left(f x +e \right)\right) a b c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a b c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{d \,a^{2}}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{2 b^{2} c d}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{2 \ln \left(c +d \tan \left(f x +e \right)\right) a b \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) b^{2} c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{a b c}{f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{2 a b \,c^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{2 a b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{b^{2} c^{2}}{2 f \left(c^{2}+d^{2}\right) d \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{2} c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{2 a^{2} c d}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}"," ",0,"-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^2*d^3+1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^2*d^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^2*d^3-3/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*b*c*d^2+6/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a*b*c^2*d+6/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*b*c*d^2-1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b^2*d^3+1/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^2*c^3-1/f/(c^2+d^2)^3*arctan(tan(f*x+e))*b^2*c^3-1/2/f/(c^2+d^2)*d/(c+d*tan(f*x+e))^2*a^2-3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a^2*c*d^2-2/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a*b*d^3+2/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*b^2*c*d+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^2*c^2*d-2/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*b*c^3-3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^2*c^2*d+1/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*a*b*c+2/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*a*b*c^2-2/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*a*b*d^2-1/2/f/(c^2+d^2)/d/(c+d*tan(f*x+e))^2*b^2*c^2-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^2*c^2*d+1/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*b*c^3+3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b^2*c^2*d+3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*b^2*c*d^2-2/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*a^2*c*d","B"
1226,1,483,173,0.252000," ","int((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x)","\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) a \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) a \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(c +d \tan \left(f x +e \right)\right) c^{3} b}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(c +d \tan \left(f x +e \right)\right) b c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{d a}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}+\frac{c b}{2 f \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{2 a c d}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{c^{2} b}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{b \,d^{2}}{f \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,c^{2} d}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,d^{3}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3} b}{2 f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b c \,d^{2}}{2 f \left(c^{2}+d^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f \left(c^{2}+d^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f \left(c^{2}+d^{2}\right)^{3}}"," ",0,"3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*c^2*d-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*d^3-1/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*c^3*b+3/f/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b*c*d^2-1/2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*d*a+1/2/f/(c^2+d^2)/(c+d*tan(f*x+e))^2*c*b-2/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*a*c*d+1/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*c^2*b-1/f/(c^2+d^2)^2/(c+d*tan(f*x+e))*b*d^2-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*c^2*d+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*d^3+1/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c^3*b-3/2/f/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b*c*d^2+1/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a*c^3-3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*a*c*d^2+3/f/(c^2+d^2)^3*arctan(tan(f*x+e))*b*c^2*d-1/f/(c^2+d^2)^3*arctan(tan(f*x+e))*b*d^3","B"
1227,1,748,284,0.361000," ","int(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x)","-\frac{b^{4} \ln \left(a +b \tan \left(f x +e \right)\right)}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right)}-\frac{d^{2}}{2 f \left(d a -c b \right) \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{2 d^{3} a c}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 d^{2} c^{2} b}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{d^{4} b}{f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{3 d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{d^{6} \ln \left(c +d \tan \left(f x +e \right)\right) a^{2}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{8 d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) a b \,c^{3}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{6 d^{2} \ln \left(c +d \tan \left(f x +e \right)\right) b^{2} c^{4}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{3 d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}+\frac{d^{6} \ln \left(c +d \tan \left(f x +e \right)\right) b^{2}}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,c^{2} d}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a \,d^{3}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) c^{3} b}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b c \,d^{2}}{2 f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a \,c^{3}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a c \,d^{2}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b \,c^{2} d}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b \,d^{3}}{f \left(a^{2}+b^{2}\right) \left(c^{2}+d^{2}\right)^{3}}"," ",0,"-1/f*b^4/(a*d-b*c)^3/(a^2+b^2)*ln(a+b*tan(f*x+e))-1/2/f*d^2/(a*d-b*c)/(c^2+d^2)/(c+d*tan(f*x+e))^2-2/f*d^3/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*a*c+3/f*d^2/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*c^2*b+1/f*d^4/(a*d-b*c)^2/(c^2+d^2)^2/(c+d*tan(f*x+e))*b+3/f*d^4/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^2*c^2-1/f*d^6/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^2-8/f*d^3/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*b*c^3+6/f*d^2/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^2*c^4+3/f*d^4/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^2*c^2+1/f*d^6/(a*d-b*c)^3/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^2-3/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*c^2*d+1/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*d^3-1/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*c^3*b+3/2/f/(a^2+b^2)/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b*c*d^2+1/f/(a^2+b^2)/(c^2+d^2)^3*arctan(tan(f*x+e))*a*c^3-3/f/(a^2+b^2)/(c^2+d^2)^3*arctan(tan(f*x+e))*a*c*d^2-3/f/(a^2+b^2)/(c^2+d^2)^3*arctan(tan(f*x+e))*b*c^2*d+1/f/(a^2+b^2)/(c^2+d^2)^3*arctan(tan(f*x+e))*b*d^3","B"
1228,1,1079,455,0.395000," ","int(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x)","\frac{2 d^{5} b}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{b^{4}}{f \left(d a -c b \right)^{3} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(f x +e \right)\right)}-\frac{5 b^{4} \ln \left(a +b \tan \left(f x +e \right)\right) a^{2} d}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a b c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}-\frac{10 d^{4} \ln \left(c +d \tan \left(f x +e \right)\right) a b \,c^{3}}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{3}}-\frac{2 d^{6} \ln \left(c +d \tan \left(f x +e \right)\right) a b c}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{3}}-\frac{6 \arctan \left(\tan \left(f x +e \right)\right) a b \,c^{2} d}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} c^{2} d}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b \,c^{3}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}+\frac{2 b^{5} \ln \left(a +b \tan \left(f x +e \right)\right) a c}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{2}}+\frac{3 d^{5} \ln \left(c +d \tan \left(f x +e \right)\right) a^{2} c^{2}}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}-\frac{2 d^{4} a c}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{4 d^{3} c^{2} b}{f \left(d a -c b \right)^{3} \left(c^{2}+d^{2}\right)^{2} \left(c +d \tan \left(f x +e \right)\right)}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b \,d^{3}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{2} c \,d^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}+\frac{10 d^{3} \ln \left(c +d \tan \left(f x +e \right)\right) b^{2} c^{4}}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{3}}+\frac{9 d^{5} \ln \left(c +d \tan \left(f x +e \right)\right) b^{2} c^{2}}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2} d^{3}}{2 f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}-\frac{d^{3}}{2 f \left(d a -c b \right)^{2} \left(c^{2}+d^{2}\right) \left(c +d \tan \left(f x +e \right)\right)^{2}}-\frac{d^{7} \ln \left(c +d \tan \left(f x +e \right)\right) a^{2}}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{3}}+\frac{3 d^{7} \ln \left(c +d \tan \left(f x +e \right)\right) b^{2}}{f \left(d a -c b \right)^{4} \left(c^{2}+d^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2} c^{3}}{f \left(a^{2}+b^{2}\right)^{2} \left(c^{2}+d^{2}\right)^{3}}-\frac{3 b^{6} \ln \left(a +b \tan \left(f x +e \right)\right) d}{f \left(d a -c b \right)^{4} \left(a^{2}+b^{2}\right)^{2}}"," ",0,"2/f*d^5/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*b+1/f*b^4/(a*d-b*c)^3/(a^2+b^2)/(a+b*tan(f*x+e))-5/f*b^4/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^2*d-10/f*d^4/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*b*c^3-2/f*d^6/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a*b*c+3/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*b*c*d^2-6/f/(a^2+b^2)^2/(c^2+d^2)^3*arctan(tan(f*x+e))*a*b*c^2*d+2/f*b^5/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a*c+3/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^2*c^2-3/f/(a^2+b^2)^2/(c^2+d^2)^3*arctan(tan(f*x+e))*a^2*c*d^2-2/f*d^4/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*a*c+4/f*d^3/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*c^2*b+2/f/(a^2+b^2)^2/(c^2+d^2)^3*arctan(tan(f*x+e))*a*b*d^3+3/f/(a^2+b^2)^2/(c^2+d^2)^3*arctan(tan(f*x+e))*b^2*c*d^2+10/f*d^3/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^2*c^4+9/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^2*c^2-3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^2*c^2*d-1/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a*b*c^3+3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b^2*c^2*d-1/2/f*d^3/(a*d-b*c)^2/(c^2+d^2)/(c+d*tan(f*x+e))^2-1/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*a^2+3/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*b^2+1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*a^2*d^3-1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*b^2*d^3+1/f/(a^2+b^2)^2/(c^2+d^2)^3*arctan(tan(f*x+e))*a^2*c^3-1/f/(a^2+b^2)^2/(c^2+d^2)^3*arctan(tan(f*x+e))*b^2*c^3-3/f*b^6/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*d","B"
1229,1,2073,181,0.419000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3,x)","-\frac{3 \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a \,b^{2}}{4 f d}+\frac{3 \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a \,b^{2} c}{4 f d}+\frac{3 \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a \,b^{2}}{4 f d}+\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{3 \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2} b}{4 f}-\frac{3 \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2} b}{4 f}+\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b^{3} c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b^{3} c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} b^{3} c}{3 f \,d^{2}}+\frac{2 \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} a \,b^{2}}{f d}-\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{3}}{4 f}+\frac{6 \sqrt{c +d \tan \left(f x +e \right)}\, a^{2} b}{f}+\frac{2 b^{3} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f \,d^{2}}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{3}}{4 f}-\frac{3 \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a \,b^{2} c}{4 f d}-\frac{3 \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{2} b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a^{2} b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{3} c}{4 f d}-\frac{3 d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a \,b^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a^{3}}{4 f d}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{3} c}{4 f d}+\frac{3 \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a^{2} b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 b^{3} \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{3 \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{2} b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{3 d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a \,b^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a^{3}}{4 f d}"," ",0,"-3/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b^2+3/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c+3/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b^2+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^3+3/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b-3/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^3-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3*c-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^3+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3*c-2/3/f/d^2*(c+d*tan(f*x+e))^(3/2)*b^3*c+2/f/d*(c+d*tan(f*x+e))^(3/2)*a*b^2-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^3-1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3+6/f*(c+d*tan(f*x+e))^(1/2)*a^2*b+2/5/f/d^2*b^3*(c+d*tan(f*x+e))^(5/2)+1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3-3/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c-3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b*c-3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*b-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c-3/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b^2-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^3+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c+3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*b-2/f*b^3*(c+d*tan(f*x+e))^(1/2)+3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b*c+3/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b^2+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^3","B"
1230,1,1507,131,0.245000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2,x)","\frac{2 b^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 d f}+\frac{4 a b \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{2 \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a^{2}}{4 d f}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b^{2}}{4 d f}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2} c}{4 d f}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a b}{2 f}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{2} c}{4 d f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a^{2}}{4 d f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b^{2}}{4 d f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2} c}{4 d f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a b}{2 f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{2} c}{4 d f}+\frac{2 \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"2/3*b^2*(c+d*tan(f*x+e))^(3/2)/d/f+4*a*b*(c+d*tan(f*x+e))^(1/2)/f-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c+d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2-d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2-d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2+d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c-1/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c+1/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c","B"
1231,1,968,102,0.240000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e)),x)","\frac{2 b \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a}{4 f d}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a c}{4 f d}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b}{4 f}+\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a}{4 f d}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a c}{4 f d}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b}{4 f}-\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}"," ",0,"2*b*(c+d*tan(f*x+e))^(1/2)/f-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c","B"
1232,1,1171,142,0.458000," ","int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x)","-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a}{4 f d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a c}{4 f d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b}{4 f \left(a^{2}+b^{2}\right)}+\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b c}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a}{4 f d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a c}{4 f d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b}{4 f \left(a^{2}+b^{2}\right)}-\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b c}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 d b \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}\, b}{\sqrt{\left(d a -c b \right) b}}\right) a}{f \left(a^{2}+b^{2}\right) \sqrt{\left(d a -c b \right) b}}+\frac{2 b^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}\, b}{\sqrt{\left(d a -c b \right) b}}\right) c}{f \left(a^{2}+b^{2}\right) \sqrt{\left(d a -c b \right) b}}"," ",0,"-1/4/f/d/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a+1/4/f/d/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+1/4/f/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+1/4/f/d/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/d/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/4/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c-2/f*d*b/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a+2/f*b^2/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*c","B"
1233,1,1890,199,0.541000," ","int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x)","\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b^{2}}{4 f d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2} c}{4 f d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a b}{2 f \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{2} c}{4 f d \left(a^{2}+b^{2}\right)^{2}}+\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{2}}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b^{2}}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{2}}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b^{2}}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a^{2}}{4 f d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a^{2}}{4 f d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b^{2}}{4 f d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2} c}{4 f d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a b}{2 f \left(a^{2}+b^{2}\right)^{2}}+\frac{2 \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a b}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a b c}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{2} c}{4 f d \left(a^{2}+b^{2}\right)^{2}}-\frac{2 \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a b}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a b c}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d b \sqrt{c +d \tan \left(f x +e \right)}\, a^{2}}{f \left(a^{2}+b^{2}\right)^{2} \left(\tan \left(f x +e \right) b d +d a \right)}-\frac{d \,b^{3} \sqrt{c +d \tan \left(f x +e \right)}}{f \left(a^{2}+b^{2}\right)^{2} \left(\tan \left(f x +e \right) b d +d a \right)}-\frac{3 d b \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}\, b}{\sqrt{\left(d a -c b \right) b}}\right) a^{2}}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{\left(d a -c b \right) b}}+\frac{4 b^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}\, b}{\sqrt{\left(d a -c b \right) b}}\right) a c}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{\left(d a -c b \right) b}}+\frac{d \,b^{3} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}\, b}{\sqrt{\left(d a -c b \right) b}}\right)}{f \left(a^{2}+b^{2}\right)^{2} \sqrt{\left(d a -c b \right) b}}"," ",0,"1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2+1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c+1/2/f/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c+1/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2-1/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2-1/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2+1/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2+1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2-1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2-1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c-1/2/f/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b+2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b-2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c+1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c-2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b+2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c-1/f*d*b/(a^2+b^2)^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*a^2-1/f*d*b^3/(a^2+b^2)^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)-3/f*d*b/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2+4/f*b^2/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a*c+1/f*d*b^3/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))","B"
1234,1,3203,304,0.497000," ","int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"-1/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3*c-3/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*b+2/f*b^5/(a^2+b^2)^3/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*c^2+3/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*b-3/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b*c-1/4/f/d/(a^2+b^2)^3*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c-9/4/f*d^2*b/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a^4-1/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^3+1/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c+1/4/f/d/(a^2+b^2)^3*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^3+3/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b^2+1/4/f*d^2*b^6/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2/(a*d-b*c)*(c+d*tan(f*x+e))^(3/2)-5/2/f*d^2*b^3/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a^2+1/4/f*d^2*b^5/(a^2+b^2)^3/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))-3/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b^2+3/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b*c-6/f*d*b^4/(a^2+b^2)^3/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a*c+10/f*d*b^2/(a^2+b^2)^3/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^3*c-3/2/f*d^2*b^4/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2/(a*d-b*c)*(c+d*tan(f*x+e))^(3/2)*a^2+2/f*d*b^2/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a^3*c+3/4/f/d/(a^2+b^2)^3*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c-7/4/f*d^2*b^2/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2/(a*d-b*c)*(c+d*tan(f*x+e))^(3/2)*a^4-15/4/f*d^2*b/(a^2+b^2)^3/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^4+9/2/f*d^2*b^3/(a^2+b^2)^3/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2-3/4/f/d/(a^2+b^2)^3*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b^2+3/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b^2-3/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c-6/f*b^3/(a^2+b^2)^3/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2*c^2+2/f*d*b^4/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a*c+2/f*d*b^5/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2/(a*d-b*c)*(c+d*tan(f*x+e))^(3/2)*a*c+2/f*d*b^3/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2/(a*d-b*c)*(c+d*tan(f*x+e))^(3/2)*a^3*c+3/4/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b+1/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3*c-1/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^3-3/4/f/(a^2+b^2)^3*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b+1/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^3-1/4/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3+1/4/f/(a^2+b^2)^3*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3-1/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^3-1/4/f*d^2*b^5/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)+1/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^3","B"
1235,1,3518,224,0.383000," ","int((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"-3/4/f*d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c^2-3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b*c^2-3/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*b+3/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b*c+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^3*c-3/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b*c-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^3*c+3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b*c^2+3/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b^2*c-3/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b^2*c+2/7/f/d^2*(c+d*tan(f*x+e))^(7/2)*b^3+2/f*d*a^3*(c+d*tan(f*x+e))^(1/2)+2/f*(c+d*tan(f*x+e))^(3/2)*a^2*b-2/f*b^3*c*(c+d*tan(f*x+e))^(1/2)+3/f*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b-3/f*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^3-2/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^3*c-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^3+3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*b*c+6/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b^2*c+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^3*c-3/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c^2+3/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b^2-6/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b^2*c-3/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b^2+3/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c^2-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^3*c-3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*b*c-1/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3*c+1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^3+2/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^3*c-1/f*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3-1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^3+1/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3*c-2/3/f*(c+d*tan(f*x+e))^(3/2)*b^3-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3*c^2+6/f*a^2*b*c*(c+d*tan(f*x+e))^(1/2)-1/4/f*d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3+6/5/f/d*(c+d*tan(f*x+e))^(5/2)*a*b^2+1/4/f*d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3*c^2-6/f*d*a*b^2*(c+d*tan(f*x+e))^(1/2)+1/f*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3-2/5/f/d^2*(c+d*tan(f*x+e))^(5/2)*b^3*c+3/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*b+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c^2+3/4/f*d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2","B"
1236,1,2577,165,0.286000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x)","\frac{2 d \,a^{2} \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{2 d \,b^{2} \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{2 d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b^{2} c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{2} c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2}}{4 f}-\frac{d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2}}{4 f}+\frac{d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{2}}{4 f}-\frac{d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{2}}{4 f}+\frac{2 \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 a b c \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b^{2} c}{4 d f}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a^{2} c}{4 d f}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b^{2} c}{4 d f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a^{2} c}{4 d f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a b}{2 f}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a b c}{f}-\frac{2 d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a^{2} c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b^{2} c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{2} c^{2}}{4 d f}-\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a b}{2 f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b^{2} c^{2}}{4 d f}+\frac{2 \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a b \,c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a b \,c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2} c^{2}}{4 d f}+\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a b c}{f}+\frac{2 d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a^{2} c^{2}}{4 d f}+\frac{4 a b \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{2 b^{2} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d f}"," ",0,"2*d/f*a^2*(c+d*tan(f*x+e))^(1/2)-2*d/f*b^2*(c+d*tan(f*x+e))^(1/2)-2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2*c+2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*c-2*d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b+1/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2-1/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2+1/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2-1/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b*c-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b*c+4/f*a*b*c*(c+d*tan(f*x+e))^(1/2)-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*c+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*c-1/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b-1/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c-2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*c+2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2*c-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^2-d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2+1/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^2+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c^2-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c^2+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c^2+d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2-d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2+1/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c+2*d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b+d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c^2+4/3*a*b*(c+d*tan(f*x+e))^(3/2)/f+2/5*b^2*(c+d*tan(f*x+e))^(5/2)/d/f","B"
1237,1,1665,126,0.245000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x)","-\frac{d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a}{4 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b}{4 f}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a \,c^{2}}{4 f d}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b c}{2 f}-\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b \,c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b}{4 f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a \,c^{2}}{4 f d}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b c}{2 f}+\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b \,c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b \,d^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b \,d^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a}{4 f}+\frac{2 a \sqrt{c +d \tan \left(f x +e \right)}\, d}{f}+\frac{2 c b \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a c}{4 f d}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a c}{4 f d}+\frac{2 b \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}"," ",0,"-1/4/f*d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b*c+1/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^2-1/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a+2/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2-1/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^2+1/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c+1/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a-2/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*d^2-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*d^2+1/4/f*d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+2/f*a*(c+d*tan(f*x+e))^(1/2)*d+2/f*c*b*(c+d*tan(f*x+e))^(1/2)-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b*c-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*c+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*c+2/3*b*(c+d*tan(f*x+e))^(3/2)/f","B"
1238,1,1964,142,0.424000," ","int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x)","\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a c}{4 f d \left(a^{2}+b^{2}\right)}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b c}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a c}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b \,c^{2}}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b}{4 f \left(a^{2}+b^{2}\right)}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a \,c^{2}}{4 f d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b c}{2 f \left(a^{2}+b^{2}\right)}-\frac{d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) a c}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b \,c^{2}}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a}{4 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b c}{2 f \left(a^{2}+b^{2}\right)}+\frac{d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b}{4 f \left(a^{2}+b^{2}\right)}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a \,c^{2}}{4 f d \left(a^{2}+b^{2}\right)}+\frac{d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a}{4 f \left(a^{2}+b^{2}\right)}+\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b c}{f \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a c}{4 f d \left(a^{2}+b^{2}\right)}+\frac{2 d^{2} \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}\, b}{\sqrt{\left(d a -c b \right) b}}\right) a^{2}}{f \left(a^{2}+b^{2}\right) \sqrt{\left(d a -c b \right) b}}-\frac{4 d \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}\, b}{\sqrt{\left(d a -c b \right) b}}\right) a b c}{f \left(a^{2}+b^{2}\right) \sqrt{\left(d a -c b \right) b}}+\frac{2 \arctan \left(\frac{\sqrt{c +d \tan \left(f x +e \right)}\, b}{\sqrt{\left(d a -c b \right) b}}\right) b^{2} c^{2}}{f \left(a^{2}+b^{2}\right) \sqrt{\left(d a -c b \right) b}}"," ",0,"1/4/f/d/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*c-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b*c-2/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2-1/4/f/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b+1/4/f/d/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^2+1/2/f/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-1/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a+2/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2-1/4/f*d/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a-1/2/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c+1/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a+1/4/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b-1/4/f/d/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^2+1/f*d^2/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b-1/f*d^2/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b+1/4/f*d/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b*c-1/4/f/d/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*c+2/f*d^2/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2-4/f*d/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a*b*c+2/f/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*b^2*c^2","B"
1239,1,3224,207,0.442000," ","int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"-2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b*c+1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*c-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*c+1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c-1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c-5/f*d/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2*c*b+2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b*c-1/f*d/(a^2+b^2)^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*a^2*c*b+1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c^2-1/f/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c+2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c^2-2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c^2+2/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b+3/f*d/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*b^3*c-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^2-2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2*c-2/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b+1/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2-1/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2-2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*c-1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c^2+1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^2+2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2*c+1/f*d^2/(a^2+b^2)^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*b^2*a-1/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2+1/f/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c-1/2/f/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b+1/2/f/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b+4/f/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a*b^2*c^2-1/f*d/(a^2+b^2)^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*b^3*c+1/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2+2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*c-3/f*d^2/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*b^2*a+1/4/f*d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2-1/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2+1/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2-1/4/f*d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2+1/f*d^2/(a^2+b^2)^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*a^3+1/f*d^2/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^3","B"
1240,1,4715,303,0.491000," ","int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"-3/2/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b*c-1/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^3*c+3/4/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(c^2+d^2)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b-3/4/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(c^2+d^2)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b-3/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b*c^2+3/2/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*b*c-1/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^3*c+6/f/(a^2+b^2)^3/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2*b^2*c^2-3/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b*c^2-3/4/f*d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2+3/f*d^2/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b+3/f*d^2/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*b+1/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c^2-1/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^3-1/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c^2-1/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^3+2/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^3*c+3/4/f*d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2+3/4/f*d^2/(a^2+b^2)^3/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*b^4-5/4/f*d^2/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(3/2)*b^5-2/f/(a^2+b^2)^3/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*b^4*c^2+1/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3*c^2+3/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(c^2+d^2)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c-3/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(c^2+d^2)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c+1/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(c^2+d^2)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c-6/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b^2*c+3/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c^2-6/f*d/(a^2+b^2)^3/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^3*b*c+10/f*d/(a^2+b^2)^3/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a*b^3*c-2/f*d/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(3/2)*a^3*c*b^2-2/f*d/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(3/2)*a*c*b^4-5/2/f*d^2/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a^2*b^3*c+2/f*d/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a*b^4*c^2-13/4/f*d^2/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a^4*b*c-6/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b^2*c+3/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b^2+3/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*b*c+3/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*b*c-3/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b^2*c^2+3/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b^2-1/4/f/d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(c^2+d^2)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3*c+2/f*d/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a^3*b^2*c^2+3/4/f*d^2/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(3/2)*a^4*b-1/2/f*d^2/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(3/2)*a^2*b^3+1/2/f*d^3/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a^3*b^2-3/4/f*d^3/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a*b^4+3/4/f*d^2/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*b^5*c-13/2/f*d^2/(a^2+b^2)^3/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2*b^2+2/f*d/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^3*c-1/4/f*d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3-1/2/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3*c-1/4/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(c^2+d^2)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3+1/2/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3*c+1/4/f/(a^2+b^2)^3*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(c^2+d^2)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^3+1/f/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3*c^2+5/4/f*d^3/(a^2+b^2)^3/(tan(f*x+e)*b*d+d*a)^2*(c+d*tan(f*x+e))^(1/2)*a^5+3/4/f*d^2/(a^2+b^2)^3/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^4+1/4/f*d/(a^2+b^2)^3*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^3-1/f*d^2/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3-1/f*d^2/(a^2+b^2)^3/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^3","B"
1241,1,5053,286,0.401000," ","int((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1242,1,3700,197,0.257000," ","int((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"1/2*d^2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b+3/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c+3/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c^2-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c^3+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c^3-3/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c^2-1/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c^3+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^3-3*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*c^2+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c^3-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^3+1/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2+2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2*c+2/3*d/f*(c+d*tan(f*x+e))^(3/2)*a^2-2/3*d/f*b^2*(c+d*tan(f*x+e))^(3/2)-2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b*c^2-1/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b*c+2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b*c^2+2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*c+1/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b*c+6*d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c-6*d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c-2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*c-1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c^2-2*d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b-2*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2*c-3*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2*c^2-1/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2+1/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2+3/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c-1/2*d^2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b-3/4*d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c-3/4*d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c+4/3/f*(c+d*tan(f*x+e))^(3/2)*a*b*c+4*d/f*a^2*c*(c+d*tan(f*x+e))^(1/2)-4*d^2/f*a*b*(c+d*tan(f*x+e))^(1/2)+d^3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2-d^3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2+4/f*a*b*c^2*(c+d*tan(f*x+e))^(1/2)-4*d/f*b^2*c*(c+d*tan(f*x+e))^(1/2)-d^3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2+d^3/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2+1/4/d/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*c^2-1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*c^2+1/4/d/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c^2+2*d^2/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b+3*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2*c^2+3*d/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*c^2+4/5*a*b*(c+d*tan(f*x+e))^(5/2)/f+2/7*b^2*(c+d*tan(f*x+e))^(7/2)/d/f","B"
1243,1,2405,160,0.252000," ","int((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x)","\frac{2 a \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} d}{3 f}+\frac{a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{4 a c d \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) d^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{2 \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}} b c}{3 f}+\frac{2 c^{2} b \sqrt{c +d \tan \left(f x +e \right)}}{f}-\frac{2 b \,d^{2} \sqrt{c +d \tan \left(f x +e \right)}}{f}+\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a \,c^{2}}{4 f d}+\frac{2 d \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{2 d \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, a c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a \,c^{2}}{4 f d}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b \,c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b \,c^{3}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b \,c^{2}}{4 f}-\frac{d^{2} \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b}{4 f}+\frac{d^{2} \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b}{4 f}+\frac{3 \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, b \,c^{2}}{4 f}+\frac{2 b \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f}-\frac{d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{3 d^{2} \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 a \arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{3 a \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) c^{2} d}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{3 d^{2} \arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) b c}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b c}{2 f}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-2 \sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b \,c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{\arctan \left(\frac{2 \sqrt{c +d \tan \left(f x +e \right)}+\sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}}{\sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}\right) \sqrt{c^{2}+d^{2}}\, b \,c^{2}}{f \sqrt{2 \sqrt{c^{2}+d^{2}}-2 c}}-\frac{d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a}{4 f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a \,c^{3}}{4 f d}+\frac{d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, a}{4 f}+\frac{\ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a \,c^{3}}{4 f d}-\frac{3 d \ln \left(d \tan \left(f x +e \right)+c +\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}+\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a c}{4 f}-\frac{\ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, \sqrt{c^{2}+d^{2}}\, b c}{2 f}+\frac{3 d \ln \left(\sqrt{c +d \tan \left(f x +e \right)}\, \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}-d \tan \left(f x +e \right)-c -\sqrt{c^{2}+d^{2}}\right) \sqrt{2 \sqrt{c^{2}+d^{2}}+2 c}\, a c}{4 f}"," ",0,"2/3/f*a*(c+d*tan(f*x+e))^(3/2)*d+1/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^3+4/f*a*c*d*(c+d*tan(f*x+e))^(1/2)-1/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*d^3+2/3/f*(c+d*tan(f*x+e))^(3/2)*b*c+2/f*c^2*b*(c+d*tan(f*x+e))^(1/2)-2/f*b*d^2*(c+d*tan(f*x+e))^(1/2)+1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*c^2+2/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*c-2/f*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*c-1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*c^2-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3-3/4/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^2-1/4/f*d^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/4/f*d^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+3/4/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^2+2/5*b*(c+d*tan(f*x+e))^(5/2)/f-1/f*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b+3/f*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c-3/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d+3/f*a/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*c^2*d+1/f*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b-3/f*d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+1/2/f*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b*c+1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b*c^2-1/f/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b*c^2-1/4/f*d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^3+1/4/f*d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a+1/4/f/d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^3-3/4/f*d*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/2/f*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b*c+3/4/f*d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c","B"
1244,1,2802,165,0.435000," ","int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"2*d^2*(c+d*tan(f*x+e))^(1/2)/b/f-6/f*d*b/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a*c^2-2/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*c-1/4/f/d/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*c^2+1/4/f/d/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*c^2+2/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*c+1/4/f/d/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^3-3/4/f*d/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/4/f*d/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a+1/4/f*d^2/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/4/f*d^2/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-3/4/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^2-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b*c^2+1/2/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b*c+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b*c^2-1/2/f/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b*c-3/f*d^2/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c-1/4/f/d/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^3+3/4/f*d/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+6/f*d^2/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2*c+1/f*d^2/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b-2/f*d^3/b/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^3-3/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2+1/4/f*d/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/f*d^2/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b+3/f*d^2/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+3/f*d/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2-1/f*d^3/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3+1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3+2/f*b^2/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*c^3+3/4/f/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^2+1/f*d^3/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a","B"
1245,1,4601,211,0.476000," ","int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"-3/4/f*d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^3-1/2/f*d^2/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b+3/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c+3/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*c^2-3/2/f/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c^2+3/2/f/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c^2-2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c^3+2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c^3+4/f/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a*c^3*b^2+3/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2*c^2-1/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2-3/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c+2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*c+2/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b+2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2*c-1/f/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b*c+2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b*c^2-2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b*c^2+1/f/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b*c+1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*c^2-1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c^2-10/f*d^2/(a^2+b^2)^2*b^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a*c-1/f*d/(a^2+b^2)^2*b*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*a^2*c^2+2/f*d^2/(a^2+b^2)^2*b^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*a*c-7/f*d/(a^2+b^2)^2*b/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2*c^2-2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2*c-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*c^2-2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*c-2/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a*b-6/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c+1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c^2+6/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c+1/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2+1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c^3+1/f*d^3/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2-1/f*d^3/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2+1/f*d^3/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2-1/f*d^3/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2-1/f*d/(a^2+b^2)^2*b^3*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*c^2+1/f*d^3/(a^2+b^2)^2/b/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^4+2/f*d^2/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^3*c+3/4/f*d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c+1/2/f*d^2/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b-3/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2*c^2-1/f*d^3/(a^2+b^2)^2/b*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*a^4+2/f*d^2/(a^2+b^2)^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*a^3*c-1/f*d^3/(a^2+b^2)^2*b*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+d*a)*a^2-3/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*c^2-1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c^3+1/4/f/d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^3-1/4/f*d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2+1/4/f*d/(a^2+b^2)^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2+5/f*d^3/(a^2+b^2)^2*b/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^2+5/f*d/(a^2+b^2)^2*b^3/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*c^2","B"
1246,1,6771,317,0.489000," ","int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
1247,1,10033,216,0.328000," ","int((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1248,1,8262,152,0.300000," ","int((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1249,1,5680,112,0.270000," ","int((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1250,1,3976,84,0.255000," ","int((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"-2/f*d^3/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a+1/f*d^2/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b-1/f/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+1/4/f*d^2/(c^2+d^2)^(3/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/4/f/(c^2+d^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-1/f/d^2*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c-1/f/d/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^4+1/4/f*d/(c^2+d^2)^(3/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+1/f/d^2/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^4-1/4/f/d^2/(c^2+d^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^3+1/f/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3-1/f/d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2+1/4/f/(c^2+d^2)^(3/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^2-1/f/d^2/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^4+1/f/d^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3+1/4/f/d/(c^2+d^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^2+1/4/f/d^2/(c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^3-1/4/f/d/(c^2+d^2)^(3/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^3-1/4/f*d/(c^2+d^2)^(3/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/4/f/d/(c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^2+1/f/d/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^4-1/f*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a-1/4/f*d^2/(c^2+d^2)^(3/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/4/f*d/(c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a-1/f*d^2/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b+1/4/f*d/(c^2+d^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/f/d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2+1/4/f/d/(c^2+d^2)^(3/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^3+3/f*d/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2-3/f*d/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2-1/f*d^2/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c-1/f/d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2-1/f/d^2/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3+1/f/d^2*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+1/f*d^2/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+1/f/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+1/f*d/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a-1/f/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3-1/4/f/d^2*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c+1/f/d^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2-2/f/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2+2/f/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2+1/4/f/d^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-1/4/f/(c^2+d^2)^(3/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^2+2/f*d^3/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a+1/4/f/(c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c","B"
1251,1,4446,142,0.401000," ","int(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"-1/4/f*d^2/(a^2+b^2)/(c^2+d^2)^(3/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b-1/f/d^2/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2-1/f*d/(a^2+b^2)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a+1/4/f*d^2/(a^2+b^2)/(c^2+d^2)^(3/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+2/f*d^3/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a+1/f*d/(a^2+b^2)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a-1/4/f/d/(a^2+b^2)/(c^2+d^2)^(3/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^3+3/f*d/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2+1/4/f/d^2/(a^2+b^2)/(c^2+d^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^3-1/f/d/(a^2+b^2)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2+1/f/d^2/(a^2+b^2)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3-1/f/d/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^4-3/f*d/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2+1/f/d/(a^2+b^2)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^2-1/f*d^2/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+1/f/d^2/(a^2+b^2)/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^4-1/4/f*d/(a^2+b^2)/(c^2+d^2)^(3/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/f/d^2/(a^2+b^2)/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^4+1/4/f/d/(a^2+b^2)/(c^2+d^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^2+1/f/d^2/(a^2+b^2)*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c-1/4/f/d^2/(a^2+b^2)/(c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^3+1/f/d/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*c^4-1/4/f/d/(a^2+b^2)/(c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^2-1/f/d^2/(a^2+b^2)*(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c+1/f*d^2/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c-1/f/d^2/(a^2+b^2)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3+1/4/f/d/(a^2+b^2)/(c^2+d^2)^(3/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c^3+1/4/f*d/(a^2+b^2)/(c^2+d^2)^(3/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+1/f/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3+2/f/(a^2+b^2)/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2-1/4/f/(a^2+b^2)/(c^2+d^2)^(3/2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^2+1/f/d^2/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2+1/f*d^2/(a^2+b^2)/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b-1/f*d^2/(a^2+b^2)/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b+1/4/f*d/(a^2+b^2)/(c^2+d^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a-1/4/f*d/(a^2+b^2)/(c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a-1/4/f/d^2/(a^2+b^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-1/f/(a^2+b^2)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c-1/f/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^3-2/f/(a^2+b^2)/(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c^2+1/f/(a^2+b^2)/(c^2+d^2)^(1/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b*c-1/4/f/(a^2+b^2)/(c^2+d^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c+1/4/f/(a^2+b^2)/(c^2+d^2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c+1/4/f/(a^2+b^2)/(c^2+d^2)^(3/2)*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c^2+1/4/f/d^2/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-2/f*d^3/(a^2+b^2)/(c^2+d^2)^(3/2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a+2/f*b^2/(a^2+b^2)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))","B"
1252,1,6548,212,0.405000," ","int(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
1253,1,20054,287,0.361000," ","int((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1254,1,16343,194,0.314000," ","int((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1255,1,11618,128,0.293000," ","int((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1256,1,7951,118,0.250000," ","int((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1257,1,8702,181,0.431000," ","int(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1258,1,12889,280,0.428000," ","int(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1259,1,33851,258,0.431000," ","int((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1260,1,26303,193,0.364000," ","int((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1261,1,19430,169,0.302000," ","int((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1262,1,12836,162,0.268000," ","int((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1263,1,13982,238,0.451000," ","int(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1264,1,21275,387,0.454000," ","int(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1265,-1,0,277,180.000000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(5/2),x)","\int \sqrt{c +d \tan \left(f x +e \right)}\, \left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(5/2),x)","F"
1266,-1,0,208,180.000000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(3/2),x)","\int \sqrt{c +d \tan \left(f x +e \right)}\, \left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(3/2),x)","F"
1267,-1,0,172,180.000000," ","int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2),x)","\int \sqrt{a +b \tan \left(f x +e \right)}\, \sqrt{c +d \tan \left(f x +e \right)}\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2),x)","F"
1268,-1,0,129,180.000000," ","int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(1/2),x)","\int \frac{\sqrt{c +d \tan \left(f x +e \right)}}{\sqrt{a +b \tan \left(f x +e \right)}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(1/2),x)","F"
1269,-1,0,168,180.000000," ","int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x)","\int \frac{\sqrt{c +d \tan \left(f x +e \right)}}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x)","F"
1270,-1,0,234,180.000000," ","int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x)","\int \frac{\sqrt{c +d \tan \left(f x +e \right)}}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x)","F"
1271,-1,0,270,180.000000," ","int((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x)","F"
1272,-1,0,208,180.000000," ","int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2),x)","\int \sqrt{a +b \tan \left(f x +e \right)}\, \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2),x)","F"
1273,-1,0,172,180.000000," ","int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(1/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\sqrt{a +b \tan \left(f x +e \right)}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(1/2),x)","F"
1274,-1,0,175,180.000000," ","int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(3/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(3/2),x)","F"
1275,-1,0,231,180.000000," ","int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(5/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(5/2),x)","F"
1276,-1,0,339,180.000000," ","int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(7/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(7/2),x)","F"
1277,-1,0,363,180.000000," ","int((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x)","F"
1278,-1,0,279,180.000000," ","int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2),x)","\int \sqrt{a +b \tan \left(f x +e \right)}\, \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2),x)","F"
1279,-1,0,214,180.000000," ","int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(1/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{\sqrt{a +b \tan \left(f x +e \right)}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(1/2),x)","F"
1280,-1,0,223,180.000000," ","int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(3/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(3/2),x)","F"
1281,-1,0,246,180.000000," ","int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(5/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(5/2),x)","F"
1282,-1,0,346,180.000000," ","int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(7/2),x)","\int \frac{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(7/2),x)","F"
1283,-1,0,214,180.000000," ","int((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{\sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(1/2),x)","F"
1284,-1,0,172,180.000000," ","int((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(1/2),x)","F"
1285,-1,0,129,180.000000," ","int((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{\sqrt{a +b \tan \left(f x +e \right)}}{\sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x)","F"
1286,-1,0,129,180.000000," ","int(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{1}{\sqrt{a +b \tan \left(f x +e \right)}\, \sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x)","F"
1287,-1,0,180,180.000000," ","int(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x)","\int \frac{1}{\sqrt{c +d \tan \left(f x +e \right)}\, \left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x)","F"
1288,-1,0,249,180.000000," ","int(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x)","\int \frac{1}{\sqrt{c +d \tan \left(f x +e \right)}\, \left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x)","F"
1289,-1,0,302,180.000000," ","int((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
1290,-1,0,223,180.000000," ","int((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
1291,-1,0,175,180.000000," ","int((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
1292,-1,0,168,180.000000," ","int((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{\sqrt{a +b \tan \left(f x +e \right)}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
1293,-1,0,180,180.000000," ","int(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{1}{\sqrt{a +b \tan \left(f x +e \right)}\, \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
1294,-1,0,259,180.000000," ","int(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{1}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
1295,-1,0,365,180.000000," ","int(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{1}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x)","F"
1296,-1,0,408,180.000000," ","int((a+b*tan(f*x+e))^(9/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{9}{2}}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(9/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
1297,-1,0,291,180.000000," ","int((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
1298,-1,0,246,180.000000," ","int((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
1299,-1,0,230,180.000000," ","int((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
1300,-1,0,237,180.000000," ","int((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\sqrt{a +b \tan \left(f x +e \right)}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
1301,-1,0,249,180.000000," ","int(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{1}{\sqrt{a +b \tan \left(f x +e \right)}\, \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
1302,-1,0,383,180.000000," ","int(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{1}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
1303,-1,0,540,180.000000," ","int(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{1}{\left(a +b \tan \left(f x +e \right)\right)^{\frac{5}{2}} \left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x)","F"
1304,0,0,249,1.127000," ","int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x)","F"
1305,0,0,208,1.398000," ","int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x)","F"
1306,0,0,170,1.113000," ","int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x)","F"
1307,0,0,137,1.653000," ","int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e)),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e)),x)","F"
1308,0,0,155,0.703000," ","int((a+b*tan(f*x+e))^m,x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*tan(f*x+e))^m,x)","F"
1309,0,0,219,1.604000," ","int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e)),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{m}}{c +d \tan \left(f x +e \right)}\, dx"," ",0,"int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e)),x)","F"
1310,0,0,297,1.762000," ","int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{m}}{\left(c +d \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x)","F"
1311,0,0,445,2.072000," ","int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{m}}{\left(c +d \tan \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x)","F"
1312,0,0,263,1.331000," ","int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x)","\int \left(a +b \tan \left(f x +e \right)\right)^{m} \left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x)","F"
1313,0,0,241,1.159000," ","int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^m,x)","\int \sqrt{c +d \tan \left(f x +e \right)}\, \left(a +b \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^m,x)","F"
1314,0,0,241,1.244000," ","int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{m}}{\sqrt{c +d \tan \left(f x +e \right)}}\, dx"," ",0,"int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x)","F"
1315,0,0,263,1.154000," ","int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{m}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x)","F"
1316,0,0,267,1.132000," ","int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{m}}{\left(c +d \tan \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x)","F"
1317,0,0,95,4.144000," ","int((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^m,x)","\int \left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^m,x)","F"
1318,0,0,132,2.302000," ","int((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^3,x)","\int \left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^3,x)","F"
1319,-1,0,94,180.000000," ","int((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^2,x)","\int \left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^2,x)","F"
1320,-1,0,55,180.000000," ","int((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e)),x)","\int \left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n} \left(a +i a \tan \left(f x +e \right)\right)\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e)),x)","F"
1321,-1,0,125,180.000000," ","int((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e)),x)","\int \frac{\left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n}}{a +i a \tan \left(f x +e \right)}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e)),x)","F"
1322,-1,0,219,180.000000," ","int((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e))^2,x)","\int \frac{\left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n}}{\left(a +i a \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e))^2,x)","F"
1323,0,0,195,1.788000," ","int((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^m,x)","\int \left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^m,x)","F"
1324,0,0,211,1.974000," ","int((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^3,x)","\int \left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^3,x)","F"
1325,-1,0,163,180.000000," ","int((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^2,x)","\int \left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^2,x)","F"
1326,0,0,119,14.120000," ","int((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e)),x)","\int \left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \tan \left(f x +e \right)\right)\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e)),x)","F"
1327,0,0,210,3.646000," ","int((c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e)),x)","\int \frac{\left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n}}{a +b \tan \left(f x +e \right)}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e)),x)","F"
1328,0,0,289,3.851000," ","int((c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e))^2,x)","\int \frac{\left(c \left(d \tan \left(f x +e \right)\right)^{p}\right)^{n}}{\left(a +b \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e))^2,x)","F"