1,1,17,12,0.010000," ","int(tan(d*x+c),x)","\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*ln(1+tan(d*x+c)^2)","A"
2,1,24,14,0.010000," ","int(tan(d*x+c)^2,x)","\frac{\tan \left(d x +c \right)}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"tan(d*x+c)/d-1/d*arctan(tan(d*x+c))","A"
3,1,31,25,0.010000," ","int(tan(d*x+c)^3,x)","\frac{\tan^{2}\left(d x +c \right)}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/2*tan(d*x+c)^2/d-1/2/d*ln(1+tan(d*x+c)^2)","A"
4,1,35,26,0.010000," ","int(tan(d*x+c)^4,x)","\frac{\tan^{3}\left(d x +c \right)}{3 d}-\frac{\tan \left(d x +c \right)}{d}+\frac{d x +c}{d}"," ",0,"1/3*tan(d*x+c)^3/d-tan(d*x+c)/d+1/d*(d*x+c)","A"
5,1,44,39,0.010000," ","int(tan(d*x+c)^5,x)","\frac{\tan^{4}\left(d x +c \right)}{4 d}-\frac{\tan^{2}\left(d x +c \right)}{2 d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/4*tan(d*x+c)^4/d-1/2*tan(d*x+c)^2/d+1/2/d*ln(1+tan(d*x+c)^2)","A"
6,1,50,40,0.011000," ","int(tan(d*x+c)^6,x)","\frac{\tan^{5}\left(d x +c \right)}{5 d}-\frac{\tan^{3}\left(d x +c \right)}{3 d}+\frac{\tan \left(d x +c \right)}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/5*tan(d*x+c)^5/d-1/3*tan(d*x+c)^3/d+tan(d*x+c)/d-1/d*arctan(tan(d*x+c))","A"
7,1,57,51,0.010000," ","int(tan(d*x+c)^7,x)","\frac{\tan^{6}\left(d x +c \right)}{6 d}-\frac{\tan^{4}\left(d x +c \right)}{4 d}+\frac{\tan^{2}\left(d x +c \right)}{2 d}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/6*tan(d*x+c)^6/d-1/4*tan(d*x+c)^4/d+1/2*tan(d*x+c)^2/d-1/2/d*ln(1+tan(d*x+c)^2)","A"
8,1,61,52,0.010000," ","int(tan(d*x+c)^8,x)","\frac{\tan^{7}\left(d x +c \right)}{7 d}-\frac{\tan^{5}\left(d x +c \right)}{5 d}+\frac{\tan^{3}\left(d x +c \right)}{3 d}-\frac{\tan \left(d x +c \right)}{d}+\frac{d x +c}{d}"," ",0,"1/7*tan(d*x+c)^7/d-1/5*tan(d*x+c)^5/d+1/3*tan(d*x+c)^3/d-tan(d*x+c)/d+1/d*(d*x+c)","A"
9,1,200,179,0.069000," ","int((b*tan(d*x+c))^(7/2),x)","\frac{2 b \left(b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}-\frac{2 b^{3} \sqrt{b \tan \left(d x +c \right)}}{d}+\frac{b^{3} \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{b^{3} \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}+\frac{b^{3} \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(d x +c \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)}{4 d}"," ",0,"2/5*b*(b*tan(d*x+c))^(5/2)/d-2*b^3*(b*tan(d*x+c))^(1/2)/d+1/2/d*b^3*(b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)-1/2/d*b^3*(b^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)+1/4/d*b^3*(b^2)^(1/4)*2^(1/2)*ln((b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(d*x+c)-(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))","A"
10,1,182,161,0.057000," ","int((b*tan(d*x+c))^(5/2),x)","\frac{2 b \left(b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{b^{3} \sqrt{2}\, \ln \left(\frac{b \tan \left(d x +c \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)}{4 d \left(b^{2}\right)^{\frac{1}{4}}}-\frac{b^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(b^{2}\right)^{\frac{1}{4}}}+\frac{b^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(b^{2}\right)^{\frac{1}{4}}}"," ",0,"2/3*b*(b*tan(d*x+c))^(3/2)/d-1/4/d*b^3/(b^2)^(1/4)*2^(1/2)*ln((b*tan(d*x+c)-(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))-1/2/d*b^3/(b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)+1/2/d*b^3/(b^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)","A"
11,1,176,161,0.064000," ","int((b*tan(d*x+c))^(3/2),x)","\frac{2 b \sqrt{b \tan \left(d x +c \right)}}{d}-\frac{b \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}+\frac{b \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{b \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(d x +c \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)}{4 d}"," ",0,"2*b*(b*tan(d*x+c))^(1/2)/d-1/2/d*b*(b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)+1/2/d*b*(b^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)-1/4/d*b*(b^2)^(1/4)*2^(1/2)*ln((b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(d*x+c)-(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))","A"
12,1,160,145,0.070000," ","int((b*tan(d*x+c))^(1/2),x)","\frac{b \sqrt{2}\, \ln \left(\frac{b \tan \left(d x +c \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)}{4 d \left(b^{2}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(b^{2}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(b^{2}\right)^{\frac{1}{4}}}"," ",0,"1/4/d*b/(b^2)^(1/4)*2^(1/2)*ln((b*tan(d*x+c)-(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))+1/2/d*b/(b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)-1/2/d*b/(b^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)","A"
13,1,166,145,0.078000," ","int(1/(b*tan(d*x+c))^(1/2),x)","\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(d x +c \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)}{4 d b}+\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d b}-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d b}"," ",0,"1/4/d/b*(b^2)^(1/4)*2^(1/2)*ln((b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(d*x+c)-(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))+1/2/d/b*(b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)-1/2/d/b*(b^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)","A"
14,1,184,163,0.062000," ","int(1/(b*tan(d*x+c))^(3/2),x)","-\frac{\sqrt{2}\, \ln \left(\frac{b \tan \left(d x +c \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)}{4 d b \left(b^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d b \left(b^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d b \left(b^{2}\right)^{\frac{1}{4}}}-\frac{2}{b d \sqrt{b \tan \left(d x +c \right)}}"," ",0,"-1/4/d/b/(b^2)^(1/4)*2^(1/2)*ln((b*tan(d*x+c)-(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))-1/2/d/b/(b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)+1/2/d/b/(b^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)-2/b/d/(b*tan(d*x+c))^(1/2)","A"
15,1,184,163,0.062000," ","int(1/(b*tan(d*x+c))^(5/2),x)","-\frac{2}{3 b d \left(b \tan \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(d x +c \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)}{4 d \,b^{3}}-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,b^{3}}+\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,b^{3}}"," ",0,"-2/3/b/d/(b*tan(d*x+c))^(3/2)-1/4/d/b^3*(b^2)^(1/4)*2^(1/2)*ln((b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(d*x+c)-(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))-1/2/d/b^3*(b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)+1/2/d/b^3*(b^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)","A"
16,1,202,181,0.066000," ","int(1/(b*tan(d*x+c))^(7/2),x)","\frac{\sqrt{2}\, \ln \left(\frac{b \tan \left(d x +c \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)}{4 d \,b^{3} \left(b^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,b^{3} \left(b^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}}{\left(b^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,b^{3} \left(b^{2}\right)^{\frac{1}{4}}}-\frac{2}{5 b d \left(b \tan \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{2}{b^{3} d \sqrt{b \tan \left(d x +c \right)}}"," ",0,"1/4/d/b^3/(b^2)^(1/4)*2^(1/2)*ln((b*tan(d*x+c)-(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))+1/2/d/b^3/(b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)-1/2/d/b^3/(b^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)+1)-2/5/b/d/(b*tan(d*x+c))^(5/2)+2/b^3/d/(b*tan(d*x+c))^(1/2)","A"
17,1,215,185,0.143000," ","int((b*tan(d*x+c))^(4/3),x)","\frac{3 b \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{d}+\frac{b \sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}-\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{4 d}-\frac{b \left(b^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{2 d}-\frac{b \left(b^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{\left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}\right)}{d}-\frac{b \sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}+\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{4 d}-\frac{b \left(b^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{2 d}"," ",0,"3*b*(b*tan(d*x+c))^(1/3)/d+1/4/d*b*3^(1/2)*(b^2)^(1/6)*ln((b*tan(d*x+c))^(2/3)-3^(1/2)*(b^2)^(1/6)*(b*tan(d*x+c))^(1/3)+(b^2)^(1/3))-1/2/d*b*(b^2)^(1/6)*arctan(2*(b*tan(d*x+c))^(1/3)/(b^2)^(1/6)-3^(1/2))-1/d*b*(b^2)^(1/6)*arctan((b*tan(d*x+c))^(1/3)/(b^2)^(1/6))-1/4/d*b*3^(1/2)*(b^2)^(1/6)*ln((b*tan(d*x+c))^(2/3)+3^(1/2)*(b^2)^(1/6)*(b*tan(d*x+c))^(1/3)+(b^2)^(1/3))-1/2/d*b*(b^2)^(1/6)*arctan(2*(b*tan(d*x+c))^(1/3)/(b^2)^(1/6)+3^(1/2))","A"
18,1,202,168,0.121000," ","int((b*tan(d*x+c))^(2/3),x)","\frac{\sqrt{3}\, \left(b^{2}\right)^{\frac{5}{6}} \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}-\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{4 d b}+\frac{b \arctan \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{2 d \left(b^{2}\right)^{\frac{1}{6}}}+\frac{b \arctan \left(\frac{\left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}\right)}{d \left(b^{2}\right)^{\frac{1}{6}}}-\frac{\sqrt{3}\, \left(b^{2}\right)^{\frac{5}{6}} \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}+\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{4 d b}+\frac{b \arctan \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{2 d \left(b^{2}\right)^{\frac{1}{6}}}"," ",0,"1/4/d/b*3^(1/2)*(b^2)^(5/6)*ln((b*tan(d*x+c))^(2/3)-3^(1/2)*(b^2)^(1/6)*(b*tan(d*x+c))^(1/3)+(b^2)^(1/3))+1/2/d*b/(b^2)^(1/6)*arctan(2*(b*tan(d*x+c))^(1/3)/(b^2)^(1/6)-3^(1/2))+1/d*b/(b^2)^(1/6)*arctan((b*tan(d*x+c))^(1/3)/(b^2)^(1/6))-1/4/d/b*3^(1/2)*(b^2)^(5/6)*ln((b*tan(d*x+c))^(2/3)+3^(1/2)*(b^2)^(1/6)*(b*tan(d*x+c))^(1/3)+(b^2)^(1/3))+1/2/d*b/(b^2)^(1/6)*arctan(2*(b*tan(d*x+c))^(1/3)/(b^2)^(1/6)+3^(1/2))","A"
19,1,114,98,0.054000," ","int((b*tan(d*x+c))^(1/3),x)","-\frac{b \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{2 d \left(b^{2}\right)^{\frac{1}{3}}}+\frac{b \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{4}{3}}-\left(b^{2}\right)^{\frac{1}{3}} \left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}+\left(b^{2}\right)^{\frac{2}{3}}\right)}{4 d \left(b^{2}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{\left(b^{2}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 d \left(b^{2}\right)^{\frac{1}{3}}}"," ",0,"-1/2/d*b/(b^2)^(1/3)*ln((b*tan(d*x+c))^(2/3)+(b^2)^(1/3))+1/4/d*b/(b^2)^(1/3)*ln((b*tan(d*x+c))^(4/3)-(b^2)^(1/3)*(b*tan(d*x+c))^(2/3)+(b^2)^(2/3))+1/2/d*b*3^(1/2)/(b^2)^(1/3)*arctan(1/3*3^(1/2)*(2/(b^2)^(1/3)*(b*tan(d*x+c))^(2/3)-1))","A"
20,1,114,98,0.053000," ","int(1/(b*tan(d*x+c))^(1/3),x)","\frac{b \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{2 d \left(b^{2}\right)^{\frac{2}{3}}}-\frac{b \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{4}{3}}-\left(b^{2}\right)^{\frac{1}{3}} \left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}+\left(b^{2}\right)^{\frac{2}{3}}\right)}{4 d \left(b^{2}\right)^{\frac{2}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}}{\left(b^{2}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 d \left(b^{2}\right)^{\frac{2}{3}}}"," ",0,"1/2/d*b/(b^2)^(2/3)*ln((b*tan(d*x+c))^(2/3)+(b^2)^(1/3))-1/4/d*b/(b^2)^(2/3)*ln((b*tan(d*x+c))^(4/3)-(b^2)^(1/3)*(b*tan(d*x+c))^(2/3)+(b^2)^(2/3))+1/2/d*b/(b^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(b^2)^(1/3)*(b*tan(d*x+c))^(2/3)-1))","A"
21,1,208,168,0.119000," ","int(1/(b*tan(d*x+c))^(2/3),x)","-\frac{\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}-\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{4 d b}+\frac{\left(b^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{2 d b}+\frac{\left(b^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{\left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}\right)}{d b}+\frac{\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}+\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{4 d b}+\frac{\left(b^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{2 d b}"," ",0,"-1/4/d/b*3^(1/2)*(b^2)^(1/6)*ln((b*tan(d*x+c))^(2/3)-3^(1/2)*(b^2)^(1/6)*(b*tan(d*x+c))^(1/3)+(b^2)^(1/3))+1/2/d/b*(b^2)^(1/6)*arctan(2*(b*tan(d*x+c))^(1/3)/(b^2)^(1/6)-3^(1/2))+1/d/b*(b^2)^(1/6)*arctan((b*tan(d*x+c))^(1/3)/(b^2)^(1/6))+1/4/d/b*3^(1/2)*(b^2)^(1/6)*ln((b*tan(d*x+c))^(2/3)+3^(1/2)*(b^2)^(1/6)*(b*tan(d*x+c))^(1/3)+(b^2)^(1/3))+1/2/d/b*(b^2)^(1/6)*arctan(2*(b*tan(d*x+c))^(1/3)/(b^2)^(1/6)+3^(1/2))","A"
22,1,227,187,0.119000," ","int(1/(b*tan(d*x+c))^(4/3),x)","-\frac{\sqrt{3}\, \left(b^{2}\right)^{\frac{5}{6}} \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}-\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{4 d \,b^{3}}-\frac{\arctan \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{2 d b \left(b^{2}\right)^{\frac{1}{6}}}-\frac{\arctan \left(\frac{\left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}\right)}{d b \left(b^{2}\right)^{\frac{1}{6}}}+\frac{\sqrt{3}\, \left(b^{2}\right)^{\frac{5}{6}} \ln \left(\left(b \tan \left(d x +c \right)\right)^{\frac{2}{3}}+\sqrt{3}\, \left(b^{2}\right)^{\frac{1}{6}} \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}+\left(b^{2}\right)^{\frac{1}{3}}\right)}{4 d \,b^{3}}-\frac{\arctan \left(\frac{2 \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}{\left(b^{2}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{2 d b \left(b^{2}\right)^{\frac{1}{6}}}-\frac{3}{b d \left(b \tan \left(d x +c \right)\right)^{\frac{1}{3}}}"," ",0,"-1/4/d/b^3*3^(1/2)*(b^2)^(5/6)*ln((b*tan(d*x+c))^(2/3)-3^(1/2)*(b^2)^(1/6)*(b*tan(d*x+c))^(1/3)+(b^2)^(1/3))-1/2/d/b/(b^2)^(1/6)*arctan(2*(b*tan(d*x+c))^(1/3)/(b^2)^(1/6)-3^(1/2))-1/d/b/(b^2)^(1/6)*arctan((b*tan(d*x+c))^(1/3)/(b^2)^(1/6))+1/4/d/b^3*3^(1/2)*(b^2)^(5/6)*ln((b*tan(d*x+c))^(2/3)+3^(1/2)*(b^2)^(1/6)*(b*tan(d*x+c))^(1/3)+(b^2)^(1/3))-1/2/d/b/(b^2)^(1/6)*arctan(2*(b*tan(d*x+c))^(1/3)/(b^2)^(1/6)+3^(1/2))-3/b/d/(b*tan(d*x+c))^(1/3)","A"
23,0,0,48,0.675000," ","int((b*tan(d*x+c))^n,x)","\int \left(b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((b*tan(d*x+c))^n,x)","F"
24,1,58,88,0.153000," ","int((b*tan(d*x+c)^2)^(5/2),x)","\frac{\left(b \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{5}{2}} \left(\tan^{4}\left(d x +c \right)-2 \left(\tan^{2}\left(d x +c \right)\right)+2 \ln \left(1+\tan^{2}\left(d x +c \right)\right)\right)}{4 d \tan \left(d x +c \right)^{5}}"," ",0,"1/4/d*(b*tan(d*x+c)^2)^(5/2)*(tan(d*x+c)^4-2*tan(d*x+c)^2+2*ln(1+tan(d*x+c)^2))/tan(d*x+c)^5","A"
25,1,48,55,0.115000," ","int((b*tan(d*x+c)^2)^(3/2),x)","-\frac{\left(b \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{3}{2}} \left(-\left(\tan^{2}\left(d x +c \right)\right)+\ln \left(1+\tan^{2}\left(d x +c \right)\right)\right)}{2 d \tan \left(d x +c \right)^{3}}"," ",0,"-1/2/d*(b*tan(d*x+c)^2)^(3/2)*(-tan(d*x+c)^2+ln(1+tan(d*x+c)^2))/tan(d*x+c)^3","A"
26,1,37,30,0.138000," ","int((b*tan(d*x+c)^2)^(1/2),x)","\frac{\sqrt{b \left(\tan^{2}\left(d x +c \right)\right)}\, \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \tan \left(d x +c \right)}"," ",0,"1/2/d*(b*tan(d*x+c)^2)^(1/2)/tan(d*x+c)*ln(1+tan(d*x+c)^2)","A"
27,1,47,29,0.158000," ","int(1/(b*tan(d*x+c)^2)^(1/2),x)","\frac{\tan \left(d x +c \right) \left(2 \ln \left(\tan \left(d x +c \right)\right)-\ln \left(1+\tan^{2}\left(d x +c \right)\right)\right)}{2 d \sqrt{b \left(\tan^{2}\left(d x +c \right)\right)}}"," ",0,"1/2/d*tan(d*x+c)*(2*ln(tan(d*x+c))-ln(1+tan(d*x+c)^2))/(b*tan(d*x+c)^2)^(1/2)","A"
28,1,64,60,0.151000," ","int(1/(b*tan(d*x+c)^2)^(3/2),x)","-\frac{\tan \left(d x +c \right) \left(2 \ln \left(\tan \left(d x +c \right)\right) \left(\tan^{2}\left(d x +c \right)\right)-\ln \left(1+\tan^{2}\left(d x +c \right)\right) \left(\tan^{2}\left(d x +c \right)\right)+1\right)}{2 d \left(b \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/d*tan(d*x+c)*(2*ln(tan(d*x+c))*tan(d*x+c)^2-ln(1+tan(d*x+c)^2)*tan(d*x+c)^2+1)/(b*tan(d*x+c)^2)^(3/2)","A"
29,1,74,87,0.147000," ","int(1/(b*tan(d*x+c)^2)^(5/2),x)","\frac{\tan \left(d x +c \right) \left(4 \ln \left(\tan \left(d x +c \right)\right) \left(\tan^{4}\left(d x +c \right)\right)-2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) \left(\tan^{4}\left(d x +c \right)\right)+2 \left(\tan^{2}\left(d x +c \right)\right)-1\right)}{4 d \left(b \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/4/d*tan(d*x+c)*(4*ln(tan(d*x+c))*tan(d*x+c)^4-2*ln(1+tan(d*x+c)^2)*tan(d*x+c)^4+2*tan(d*x+c)^2-1)/(b*tan(d*x+c)^2)^(5/2)","A"
30,1,266,306,0.124000," ","int((b*tan(d*x+c)^3)^(5/2),x)","\frac{\left(b \left(\tan^{3}\left(d x +c \right)\right)\right)^{\frac{5}{2}} \left(360 \left(b \tan \left(d x +c \right)\right)^{\frac{13}{2}}-520 b^{2} \left(b \tan \left(d x +c \right)\right)^{\frac{9}{2}}+936 \left(b \tan \left(d x +c \right)\right)^{\frac{5}{2}} b^{4}+585 b^{6} \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(-\frac{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}-b \tan \left(d x +c \right)-\sqrt{b^{2}}}\right)+1170 b^{6} \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}+\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+1170 b^{6} \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)-4680 \sqrt{b \tan \left(d x +c \right)}\, b^{6}\right)}{2340 d \tan \left(d x +c \right)^{5} \left(b \tan \left(d x +c \right)\right)^{\frac{5}{2}} b^{4}}"," ",0,"1/2340/d*(b*tan(d*x+c)^3)^(5/2)*(360*(b*tan(d*x+c))^(13/2)-520*b^2*(b*tan(d*x+c))^(9/2)+936*(b*tan(d*x+c))^(5/2)*b^4+585*b^6*(b^2)^(1/4)*2^(1/2)*ln(-(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/((b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)-b*tan(d*x+c)-(b^2)^(1/2)))+1170*b^6*(b^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+1170*b^6*(b^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))-4680*(b*tan(d*x+c))^(1/2)*b^6)/tan(d*x+c)^5/(b*tan(d*x+c))^(5/2)/b^4","A"
31,1,236,234,0.079000," ","int((b*tan(d*x+c)^3)^(3/2),x)","\frac{\left(b \left(\tan^{3}\left(d x +c \right)\right)\right)^{\frac{3}{2}} \left(24 \left(b \tan \left(d x +c \right)\right)^{\frac{7}{2}} \left(b^{2}\right)^{\frac{1}{4}}-56 \left(b \tan \left(d x +c \right)\right)^{\frac{3}{2}} b^{2} \left(b^{2}\right)^{\frac{1}{4}}+21 b^{4} \sqrt{2}\, \ln \left(-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}-b \tan \left(d x +c \right)-\sqrt{b^{2}}}{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)+42 b^{4} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}+\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+42 b^{4} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)\right)}{84 d \tan \left(d x +c \right)^{3} \left(b \tan \left(d x +c \right)\right)^{\frac{3}{2}} b^{2} \left(b^{2}\right)^{\frac{1}{4}}}"," ",0,"1/84/d*(b*tan(d*x+c)^3)^(3/2)*(24*(b*tan(d*x+c))^(7/2)*(b^2)^(1/4)-56*(b*tan(d*x+c))^(3/2)*b^2*(b^2)^(1/4)+21*b^4*2^(1/2)*ln(-((b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)-b*tan(d*x+c)-(b^2)^(1/2))/(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))+42*b^4*2^(1/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+42*b^4*2^(1/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4)))/tan(d*x+c)^3/(b*tan(d*x+c))^(3/2)/b^2/(b^2)^(1/4)","A"
32,1,208,209,0.103000," ","int((b*tan(d*x+c)^3)^(1/2),x)","-\frac{\sqrt{b \left(\tan^{3}\left(d x +c \right)\right)}\, \left(\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(-\frac{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}-b \tan \left(d x +c \right)-\sqrt{b^{2}}}\right)+2 \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}+\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+2 \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)-8 \sqrt{b \tan \left(d x +c \right)}\right)}{4 d \tan \left(d x +c \right) \sqrt{b \tan \left(d x +c \right)}}"," ",0,"-1/4/d*(b*tan(d*x+c)^3)^(1/2)*((b^2)^(1/4)*2^(1/2)*ln(-(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/((b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)-b*tan(d*x+c)-(b^2)^(1/2)))+2*(b^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+2*(b^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))-8*(b*tan(d*x+c))^(1/2))/tan(d*x+c)/(b*tan(d*x+c))^(1/2)","A"
33,1,211,209,0.118000," ","int(1/(b*tan(d*x+c)^3)^(1/2),x)","-\frac{\tan \left(d x +c \right) \left(\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}\, \ln \left(-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}-b \tan \left(d x +c \right)-\sqrt{b^{2}}}{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)+2 \sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}+\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+2 \sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+8 \left(b^{2}\right)^{\frac{1}{4}}\right)}{4 d \sqrt{b \left(\tan^{3}\left(d x +c \right)\right)}\, \left(b^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/4/d*tan(d*x+c)*(2^(1/2)*(b*tan(d*x+c))^(1/2)*ln(-((b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)-b*tan(d*x+c)-(b^2)^(1/2))/(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))+2*2^(1/2)*(b*tan(d*x+c))^(1/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+2*2^(1/2)*(b*tan(d*x+c))^(1/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))+8*(b^2)^(1/4))/(b*tan(d*x+c)^3)^(1/2)/(b^2)^(1/4)","A"
34,1,236,246,0.101000," ","int(1/(b*tan(d*x+c)^3)^(3/2),x)","\frac{\tan \left(d x +c \right) \left(21 \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \left(b \tan \left(d x +c \right)\right)^{\frac{7}{2}} \ln \left(-\frac{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}-b \tan \left(d x +c \right)-\sqrt{b^{2}}}\right)+42 \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \left(b \tan \left(d x +c \right)\right)^{\frac{7}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}+\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+42 \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \left(b \tan \left(d x +c \right)\right)^{\frac{7}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+56 b^{4} \left(\tan^{2}\left(d x +c \right)\right)-24 b^{4}\right)}{84 d \,b^{4} \left(b \left(\tan^{3}\left(d x +c \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/84/d*tan(d*x+c)/b^4*(21*(b^2)^(1/4)*2^(1/2)*(b*tan(d*x+c))^(7/2)*ln(-(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2))/((b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)-b*tan(d*x+c)-(b^2)^(1/2)))+42*(b^2)^(1/4)*2^(1/2)*(b*tan(d*x+c))^(7/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+42*(b^2)^(1/4)*2^(1/2)*(b*tan(d*x+c))^(7/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))+56*b^4*tan(d*x+c)^2-24*b^4)/(b*tan(d*x+c)^3)^(3/2)","A"
35,1,272,306,0.109000," ","int(1/(b*tan(d*x+c)^3)^(5/2),x)","\frac{\tan \left(d x +c \right) \left(585 \sqrt{2}\, \left(b \tan \left(d x +c \right)\right)^{\frac{13}{2}} \ln \left(-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}-b \tan \left(d x +c \right)-\sqrt{b^{2}}}{b \tan \left(d x +c \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(d x +c \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)+1170 \sqrt{2}\, \left(b \tan \left(d x +c \right)\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}+\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+1170 \sqrt{2}\, \left(b \tan \left(d x +c \right)\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(d x +c \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+4680 \left(b^{2}\right)^{\frac{1}{4}} \left(\tan^{6}\left(d x +c \right)\right) b^{6}-936 b^{6} \left(b^{2}\right)^{\frac{1}{4}} \left(\tan^{4}\left(d x +c \right)\right)+520 b^{6} \left(b^{2}\right)^{\frac{1}{4}} \left(\tan^{2}\left(d x +c \right)\right)-360 b^{6} \left(b^{2}\right)^{\frac{1}{4}}\right)}{2340 d \,b^{6} \left(b \left(\tan^{3}\left(d x +c \right)\right)\right)^{\frac{5}{2}} \left(b^{2}\right)^{\frac{1}{4}}}"," ",0,"1/2340/d*tan(d*x+c)/b^6*(585*2^(1/2)*(b*tan(d*x+c))^(13/2)*ln(-((b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)-b*tan(d*x+c)-(b^2)^(1/2))/(b*tan(d*x+c)+(b^2)^(1/4)*(b*tan(d*x+c))^(1/2)*2^(1/2)+(b^2)^(1/2)))+1170*2^(1/2)*(b*tan(d*x+c))^(13/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+1170*2^(1/2)*(b*tan(d*x+c))^(13/2)*arctan((2^(1/2)*(b*tan(d*x+c))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))+4680*(b^2)^(1/4)*tan(d*x+c)^6*b^6-936*b^6*(b^2)^(1/4)*tan(d*x+c)^4+520*b^6*(b^2)^(1/4)*tan(d*x+c)^2-360*b^6*(b^2)^(1/4))/(b*tan(d*x+c)^3)^(5/2)/(b^2)^(1/4)","A"
36,1,84,162,0.116000," ","int((b*tan(d*x+c)^4)^(5/2),x)","-\frac{\left(b \left(\tan^{4}\left(d x +c \right)\right)\right)^{\frac{5}{2}} \left(-35 \left(\tan^{9}\left(d x +c \right)\right)+45 \left(\tan^{7}\left(d x +c \right)\right)-63 \left(\tan^{5}\left(d x +c \right)\right)+105 \left(\tan^{3}\left(d x +c \right)\right)+315 \arctan \left(\tan \left(d x +c \right)\right)-315 \tan \left(d x +c \right)\right)}{315 d \tan \left(d x +c \right)^{10}}"," ",0,"-1/315/d*(b*tan(d*x+c)^4)^(5/2)*(-35*tan(d*x+c)^9+45*tan(d*x+c)^7-63*tan(d*x+c)^5+105*tan(d*x+c)^3+315*arctan(tan(d*x+c))-315*tan(d*x+c))/tan(d*x+c)^10","A"
37,1,64,98,0.074000," ","int((b*tan(d*x+c)^4)^(3/2),x)","-\frac{\left(b \left(\tan^{4}\left(d x +c \right)\right)\right)^{\frac{3}{2}} \left(-3 \left(\tan^{5}\left(d x +c \right)\right)+5 \left(\tan^{3}\left(d x +c \right)\right)+15 \arctan \left(\tan \left(d x +c \right)\right)-15 \tan \left(d x +c \right)\right)}{15 d \tan \left(d x +c \right)^{6}}"," ",0,"-1/15/d*(b*tan(d*x+c)^4)^(3/2)*(-3*tan(d*x+c)^5+5*tan(d*x+c)^3+15*arctan(tan(d*x+c))-15*tan(d*x+c))/tan(d*x+c)^6","A"
38,1,42,46,0.096000," ","int((b*tan(d*x+c)^4)^(1/2),x)","-\frac{\sqrt{b \left(\tan^{4}\left(d x +c \right)\right)}\, \left(-\tan \left(d x +c \right)+\arctan \left(\tan \left(d x +c \right)\right)\right)}{d \tan \left(d x +c \right)^{2}}"," ",0,"-1/d*(b*tan(d*x+c)^4)^(1/2)*(-tan(d*x+c)+arctan(tan(d*x+c)))/tan(d*x+c)^2","A"
39,1,40,47,0.122000," ","int(1/(b*tan(d*x+c)^4)^(1/2),x)","-\frac{\tan \left(d x +c \right) \left(\arctan \left(\tan \left(d x +c \right)\right) \tan \left(d x +c \right)+1\right)}{d \sqrt{b \left(\tan^{4}\left(d x +c \right)\right)}}"," ",0,"-1/d*tan(d*x+c)*(arctan(tan(d*x+c))*tan(d*x+c)+1)/(b*tan(d*x+c)^4)^(1/2)","A"
40,1,63,107,0.098000," ","int(1/(b*tan(d*x+c)^4)^(3/2),x)","-\frac{\tan \left(d x +c \right) \left(15 \arctan \left(\tan \left(d x +c \right)\right) \left(\tan^{5}\left(d x +c \right)\right)+15 \left(\tan^{4}\left(d x +c \right)\right)-5 \left(\tan^{2}\left(d x +c \right)\right)+3\right)}{15 d \left(b \left(\tan^{4}\left(d x +c \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/15/d*tan(d*x+c)*(15*arctan(tan(d*x+c))*tan(d*x+c)^5+15*tan(d*x+c)^4-5*tan(d*x+c)^2+3)/(b*tan(d*x+c)^4)^(3/2)","A"
41,1,83,163,0.105000," ","int(1/(b*tan(d*x+c)^4)^(5/2),x)","-\frac{\tan \left(d x +c \right) \left(315 \arctan \left(\tan \left(d x +c \right)\right) \left(\tan^{9}\left(d x +c \right)\right)+315 \left(\tan^{8}\left(d x +c \right)\right)-105 \left(\tan^{6}\left(d x +c \right)\right)+63 \left(\tan^{4}\left(d x +c \right)\right)-45 \left(\tan^{2}\left(d x +c \right)\right)+35\right)}{315 d \left(b \left(\tan^{4}\left(d x +c \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-1/315/d*tan(d*x+c)*(315*arctan(tan(d*x+c))*tan(d*x+c)^9+315*tan(d*x+c)^8-105*tan(d*x+c)^6+63*tan(d*x+c)^4-45*tan(d*x+c)^2+35)/(b*tan(d*x+c)^4)^(5/2)","A"
42,-1,0,55,180.000000," ","int((b*tan(d*x+c)^p)^n,x)","\int \left(b \left(\tan^{p}\left(d x +c \right)\right)\right)^{n}\, dx"," ",0,"int((b*tan(d*x+c)^p)^n,x)","F"
43,0,0,49,0.574000," ","int((b*tan(d*x+c)^2)^n,x)","\int \left(b \left(\tan^{2}\left(d x +c \right)\right)\right)^{n}\, dx"," ",0,"int((b*tan(d*x+c)^2)^n,x)","F"
44,0,0,53,0.888000," ","int((b*tan(d*x+c)^3)^n,x)","\int \left(b \left(\tan^{3}\left(d x +c \right)\right)\right)^{n}\, dx"," ",0,"int((b*tan(d*x+c)^3)^n,x)","F"
45,0,0,53,0.585000," ","int((b*tan(d*x+c)^4)^n,x)","\int \left(b \left(\tan^{4}\left(d x +c \right)\right)\right)^{n}\, dx"," ",0,"int((b*tan(d*x+c)^4)^n,x)","F"
46,0,0,63,3.414000," ","int((b*tan(d*x+c)^p)^(5/2),x)","\int \left(b \left(\tan^{p}\left(d x +c \right)\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((b*tan(d*x+c)^p)^(5/2),x)","F"
47,0,0,59,0.732000," ","int((b*tan(d*x+c)^p)^(3/2),x)","\int \left(b \left(\tan^{p}\left(d x +c \right)\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((b*tan(d*x+c)^p)^(3/2),x)","F"
48,0,0,52,0.706000," ","int((b*tan(d*x+c)^p)^(1/2),x)","\int \sqrt{b \left(\tan^{p}\left(d x +c \right)\right)}\, dx"," ",0,"int((b*tan(d*x+c)^p)^(1/2),x)","F"
49,0,0,54,0.602000," ","int(1/(b*tan(d*x+c)^p)^(1/2),x)","\int \frac{1}{\sqrt{b \left(\tan^{p}\left(d x +c \right)\right)}}\, dx"," ",0,"int(1/(b*tan(d*x+c)^p)^(1/2),x)","F"
50,0,0,63,0.752000," ","int(1/(b*tan(d*x+c)^p)^(3/2),x)","\int \frac{1}{\left(b \left(\tan^{p}\left(d x +c \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(b*tan(d*x+c)^p)^(3/2),x)","F"
51,0,0,63,0.766000," ","int(1/(b*tan(d*x+c)^p)^(5/2),x)","\int \frac{1}{\left(b \left(\tan^{p}\left(d x +c \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(b*tan(d*x+c)^p)^(5/2),x)","F"
52,-1,0,32,180.000000," ","int((b*tan(d*x+c)^p)^(1/p),x)","\int \left(b \left(\tan^{p}\left(d x +c \right)\right)\right)^{\frac{1}{p}}\, dx"," ",0,"int((b*tan(d*x+c)^p)^(1/p),x)","F"
53,-1,0,57,180.000000," ","int((a*(b*tan(d*x+c))^p)^n,x)","\int \left(a \left(b \tan \left(d x +c \right)\right)^{p}\right)^{n}\, dx"," ",0,"int((a*(b*tan(d*x+c))^p)^n,x)","F"
54,1,542,197,0.586000," ","int(sin(b*x+a)^4*(d*tan(b*x+a))^(1/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(21 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-21 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+8 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-8 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+21 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+21 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-22 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+22 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \sqrt{2}}{64 b \sin \left(b x +a \right)^{3}}"," ",0,"1/64/b*(-1+cos(b*x+a))*(21*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-21*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+8*cos(b*x+a)^4*2^(1/2)-8*cos(b*x+a)^3*2^(1/2)+21*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+21*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-22*cos(b*x+a)^2*2^(1/2)+22*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(1/2)/sin(b*x+a)^3*2^(1/2)","C"
55,1,516,171,0.482000," ","int(sin(b*x+a)^2*(d*tan(b*x+a))^(1/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-2 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \sqrt{2}}{8 b \sin \left(b x +a \right)^{3}}"," ",0,"-1/8/b*(-1+cos(b*x+a))*(3*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-3*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+2*cos(b*x+a)^2*2^(1/2)-2*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(1/2)/sin(b*x+a)^3*2^(1/2)","C"
56,1,38,16,0.491000," ","int(csc(b*x+a)^2*(d*tan(b*x+a))^(1/2),x)","-\frac{2 \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \cos \left(b x +a \right)}{b \sin \left(b x +a \right)}"," ",0,"-2/b*(d*sin(b*x+a)/cos(b*x+a))^(1/2)*cos(b*x+a)/sin(b*x+a)","B"
57,1,50,35,0.587000," ","int(csc(b*x+a)^4*(d*tan(b*x+a))^(1/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-5\right) \cos \left(b x +a \right) \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}{5 b \sin \left(b x +a \right)^{3}}"," ",0,"2/5/b*(4*cos(b*x+a)^2-5)*cos(b*x+a)*(d*sin(b*x+a)/cos(b*x+a))^(1/2)/sin(b*x+a)^3","A"
58,1,60,53,0.577000," ","int(csc(b*x+a)^6*(d*tan(b*x+a))^(1/2),x)","-\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)-72 \left(\cos^{2}\left(b x +a \right)\right)+45\right) \cos \left(b x +a \right) \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}{45 b \sin \left(b x +a \right)^{5}}"," ",0,"-2/45/b*(32*cos(b*x+a)^4-72*cos(b*x+a)^2+45)*cos(b*x+a)*(d*sin(b*x+a)/cos(b*x+a))^(1/2)/sin(b*x+a)^5","A"
59,1,216,116,0.545000," ","int(sin(b*x+a)^3*(d*tan(b*x+a))^(1/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(5 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+7 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-7 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \sqrt{2}}{12 b \sin \left(b x +a \right)^{4}}"," ",0,"-1/12/b*(-1+cos(b*x+a))*(5*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-2*cos(b*x+a)^4*2^(1/2)+2*cos(b*x+a)^3*2^(1/2)+7*cos(b*x+a)^2*2^(1/2)-7*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(1/2)/sin(b*x+a)^4*2^(1/2)","A"
60,1,188,92,0.413000," ","int(sin(b*x+a)*(d*tan(b*x+a))^(1/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(\sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-\cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \sqrt{2}}{2 b \sin \left(b x +a \right)^{4}}"," ",0,"-1/2/b*(-1+cos(b*x+a))*(sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+cos(b*x+a)^2*2^(1/2)-cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(1/2)/sin(b*x+a)^4*2^(1/2)","B"
61,1,157,69,0.505000," ","int(csc(b*x+a)*(d*tan(b*x+a))^(1/2),x)","-\frac{\sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{b \sin \left(b x +a \right)^{3}}"," ",0,"-1/b*(d*sin(b*x+a)/cos(b*x+a))^(1/2)*(-1+cos(b*x+a))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*(cos(b*x+a)+1)^2/sin(b*x+a)^3*2^(1/2)","B"
62,1,297,92,0.591000," ","int(csc(b*x+a)^3*(d*tan(b*x+a))^(1/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(2 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+2 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-\cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \sqrt{2}}{3 b \sin \left(b x +a \right)^{6}}"," ",0,"1/3/b*(-1+cos(b*x+a))^2*(2*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+2*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(1/2)/sin(b*x+a)^6*2^(1/2)","B"
63,1,550,116,0.599000," ","int(csc(b*x+a)^5*(d*tan(b*x+a))^(1/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(4 \left(\cos^{3}\left(b x +a \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+4 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)-4 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-4 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+3 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \sqrt{2}}{7 b \sin \left(b x +a \right)^{8}}"," ",0,"-1/7/b*(-1+cos(b*x+a))^2*(4*cos(b*x+a)^3*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+4*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)^2*sin(b*x+a)-4*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-4*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-2*cos(b*x+a)^3*2^(1/2)+3*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(1/2)/sin(b*x+a)^8*2^(1/2)","B"
64,1,702,213,0.543000," ","int(sin(b*x+a)^4*(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(45 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-45 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-8 \sqrt{2}\, \left(\cos^{5}\left(b x +a \right)\right)+8 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+45 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-90 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+45 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+34 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-34 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+64 \cos \left(b x +a \right) \sqrt{2}-64 \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{64 b \sin \left(b x +a \right)^{5}}"," ",0,"1/64/b*(-1+cos(b*x+a))*(45*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-45*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-8*2^(1/2)*cos(b*x+a)^5+8*cos(b*x+a)^4*2^(1/2)+45*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-90*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+45*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+34*cos(b*x+a)^3*2^(1/2)-34*cos(b*x+a)^2*2^(1/2)+64*cos(b*x+a)*2^(1/2)-64*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5*2^(1/2)","C"
65,1,676,187,0.424000," ","int(sin(b*x+a)^2*(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(-5 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+5 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+5 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+5 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-10 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+8 \cos \left(b x +a \right) \sqrt{2}-8 \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{8 b \sin \left(b x +a \right)^{5}}"," ",0,"1/8/b*(-1+cos(b*x+a))*(-5*I*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*I*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+5*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-10*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+2*cos(b*x+a)^3*2^(1/2)-2*cos(b*x+a)^2*2^(1/2)+8*cos(b*x+a)*2^(1/2)-8*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5*2^(1/2)","C"
66,1,58,16,0.500000," ","int(csc(b*x+a)^2*(d*tan(b*x+a))^(3/2),x)","\frac{2 \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \cos \left(b x +a \right) \left(-1+\cos \left(b x +a \right)\right)^{2} \left(\cos \left(b x +a \right)+1\right)^{2}}{b \sin \left(b x +a \right)^{5}}"," ",0,"2/b*(d*sin(b*x+a)/cos(b*x+a))^(3/2)*cos(b*x+a)*(-1+cos(b*x+a))^2*(cos(b*x+a)+1)^2/sin(b*x+a)^5","B"
67,1,50,35,0.559000," ","int(csc(b*x+a)^4*(d*tan(b*x+a))^(3/2),x)","-\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-3\right) \cos \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}{3 b \sin \left(b x +a \right)^{3}}"," ",0,"-2/3/b*(4*cos(b*x+a)^2-3)*cos(b*x+a)*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^3","A"
68,1,60,53,0.592000," ","int(csc(b*x+a)^6*(d*tan(b*x+a))^(3/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)-56 \left(\cos^{2}\left(b x +a \right)\right)+21\right) \cos \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}{21 b \sin \left(b x +a \right)^{5}}"," ",0,"2/21/b*(32*cos(b*x+a)^4-56*cos(b*x+a)^2+21)*cos(b*x+a)*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5","A"
69,1,540,123,0.466000," ","int(sin(b*x+a)^3*(d*tan(b*x+a))^(3/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-42 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-11 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+21 \cos \left(b x +a \right) \sqrt{2}-12 \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{12 b \sin \left(b x +a \right)^{6}}"," ",0,"-1/12/b*(-1+cos(b*x+a))^2*(2*cos(b*x+a)^4*2^(1/2)-42*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+21*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-42*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+21*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-11*cos(b*x+a)^2*2^(1/2)+21*cos(b*x+a)*2^(1/2)-12*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^6*2^(1/2)","B"
70,1,526,95,0.426000," ","int(sin(b*x+a)*(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-3 \cos \left(b x +a \right) \sqrt{2}+2 \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 b \sin \left(b x +a \right)^{6}}"," ",0,"1/2/b*(-1+cos(b*x+a))^2*(6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)^2*2^(1/2)-3*cos(b*x+a)*2^(1/2)+2*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^6*2^(1/2)","B"
71,1,511,95,0.487000," ","int(csc(b*x+a)*(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{2}+\sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{b \sin \left(b x +a \right)^{6}}"," ",0,"1/b*(-1+cos(b*x+a))^2*(2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*2^(1/2)+2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^6*2^(1/2)","B"
72,1,491,119,0.573000," ","int(csc(b*x+a)^3*(d*tan(b*x+a))^(3/2),x)","\frac{\left(4 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \cos \left(b x +a \right) \sqrt{2}+\sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{b \sin \left(b x +a \right)^{2}}"," ",0,"1/b*(4*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+4*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)*2^(1/2)+2^(1/2))*cos(b*x+a)*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^2*2^(1/2)","B"
73,1,590,213,0.509000," ","int(sin(b*x+a)^4*(d*tan(b*x+a))^(5/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(231 i \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-231 i \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-24 \sqrt{2}\, \left(\cos^{5}\left(b x +a \right)\right)+24 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-231 \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-231 \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+114 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-114 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+64 \cos \left(b x +a \right) \sqrt{2}-64 \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{192 b \sin \left(b x +a \right)^{5}}"," ",0,"1/192/b*(-1+cos(b*x+a))*(231*I*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-231*I*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-24*2^(1/2)*cos(b*x+a)^5+24*cos(b*x+a)^4*2^(1/2)-231*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-231*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+114*cos(b*x+a)^3*2^(1/2)-114*cos(b*x+a)^2*2^(1/2)+64*cos(b*x+a)*2^(1/2)-64*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^5*2^(1/2)","C"
74,1,564,187,0.411000," ","int(sin(b*x+a)^2*(d*tan(b*x+a))^(5/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(21 i \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-21 i \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-21 \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-21 \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-6 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+8 \cos \left(b x +a \right) \sqrt{2}-8 \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{24 b \sin \left(b x +a \right)^{5}}"," ",0,"1/24/b*(-1+cos(b*x+a))*(21*I*cos(b*x+a)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-21*I*cos(b*x+a)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-21*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-21*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+6*cos(b*x+a)^3*2^(1/2)-6*cos(b*x+a)^2*2^(1/2)+8*cos(b*x+a)*2^(1/2)-8*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^5*2^(1/2)","C"
75,1,38,16,0.485000," ","int(csc(b*x+a)^2*(d*tan(b*x+a))^(5/2),x)","\frac{2 \cos \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}{3 b \sin \left(b x +a \right)}"," ",0,"2/3/b*cos(b*x+a)*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)","B"
76,1,50,35,0.503000," ","int(csc(b*x+a)^4*(d*tan(b*x+a))^(5/2),x)","-\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \cos \left(b x +a \right)}{3 b \sin \left(b x +a \right)^{3}}"," ",0,"-2/3/b*(4*cos(b*x+a)^2-1)*(d*sin(b*x+a)/cos(b*x+a))^(5/2)*cos(b*x+a)/sin(b*x+a)^3","A"
77,1,60,53,0.530000," ","int(csc(b*x+a)^6*(d*tan(b*x+a))^(5/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)-40 \left(\cos^{2}\left(b x +a \right)\right)+5\right) \cos \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}{15 b \sin \left(b x +a \right)^{5}}"," ",0,"2/15/b*(32*cos(b*x+a)^4-40*cos(b*x+a)^2+5)*cos(b*x+a)*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^5","A"
78,1,246,146,0.461000," ","int(sin(b*x+a)^3*(d*tan(b*x+a))^(5/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(15 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-2 \sqrt{2}\, \left(\cos^{5}\left(b x +a \right)\right)+2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+13 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-13 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+4 \cos \left(b x +a \right) \sqrt{2}-4 \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{12 b \sin \left(b x +a \right)^{6}}"," ",0,"1/12/b*(-1+cos(b*x+a))*(15*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-2*2^(1/2)*cos(b*x+a)^5+2*cos(b*x+a)^4*2^(1/2)+13*cos(b*x+a)^3*2^(1/2)-13*cos(b*x+a)^2*2^(1/2)+4*cos(b*x+a)*2^(1/2)-4*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^6*2^(1/2)","A"
79,1,220,119,0.411000," ","int(sin(b*x+a)*(d*tan(b*x+a))^(5/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(5 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+3 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-3 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+2 \cos \left(b x +a \right) \sqrt{2}-2 \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{6 b \sin \left(b x +a \right)^{6}}"," ",0,"1/6/b*(-1+cos(b*x+a))*(5*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+3*cos(b*x+a)^3*2^(1/2)-3*cos(b*x+a)^2*2^(1/2)+2*cos(b*x+a)*2^(1/2)-2*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^6*2^(1/2)","A"
80,1,192,95,0.474000," ","int(csc(b*x+a)*(d*tan(b*x+a))^(5/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(\EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+\cos \left(b x +a \right) \sqrt{2}-\sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{3 b \sin \left(b x +a \right)^{6}}"," ",0,"1/3/b*(-1+cos(b*x+a))*(EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+cos(b*x+a)*2^(1/2)-2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^6*2^(1/2)","B"
81,1,192,95,0.510000," ","int(csc(b*x+a)^3*(d*tan(b*x+a))^(5/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(2 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-\cos \left(b x +a \right) \sqrt{2}+\sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{3 b \sin \left(b x +a \right)^{6}}"," ",0,"-1/3/b*(-1+cos(b*x+a))*(2*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-cos(b*x+a)*2^(1/2)+2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^6*2^(1/2)","B"
82,1,316,121,0.551000," ","int(csc(b*x+a)^5*(d*tan(b*x+a))^(5/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(4 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)+4 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+\sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{3 b \sin \left(b x +a \right)^{8}}"," ",0,"1/3/b*(-1+cos(b*x+a))^2*(4*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)^2*sin(b*x+a)+4*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-2*cos(b*x+a)^2*2^(1/2)+2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^8*2^(1/2)","B"
83,1,571,147,0.592000," ","int(csc(b*x+a)^7*(d*tan(b*x+a))^(5/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(40 \left(\cos^{4}\left(b x +a \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+40 \left(\cos^{3}\left(b x +a \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-40 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)-40 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-20 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+30 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-7 \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{21 b \sin \left(b x +a \right)^{10}}"," ",0,"-1/21/b*(-1+cos(b*x+a))^2*(40*cos(b*x+a)^4*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+40*cos(b*x+a)^3*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-40*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)^2*sin(b*x+a)-40*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-20*cos(b*x+a)^4*2^(1/2)+30*cos(b*x+a)^2*2^(1/2)-7*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^10*2^(1/2)","B"
84,1,688,197,0.510000," ","int(sin(b*x+a)^4/(d*tan(b*x+a))^(1/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(5 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-5 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+8 \sqrt{2}\, \left(\cos^{5}\left(b x +a \right)\right)-8 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-5 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-5 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+10 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-18 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+18 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{64 b \cos \left(b x +a \right) \sin \left(b x +a \right)^{3} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}"," ",0,"1/64/b*(-1+cos(b*x+a))*(5*I*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*I*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+8*2^(1/2)*cos(b*x+a)^5-8*cos(b*x+a)^4*2^(1/2)-5*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-5*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+10*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-18*cos(b*x+a)^3*2^(1/2)+18*cos(b*x+a)^2*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)/sin(b*x+a)^3/(d*sin(b*x+a)/cos(b*x+a))^(1/2)*2^(1/2)","C"
85,1,662,171,0.455000," ","int(sin(b*x+a)^2/(d*tan(b*x+a))^(1/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+2 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{8 b \cos \left(b x +a \right) \sin \left(b x +a \right)^{3} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}"," ",0,"1/8/b*(-1+cos(b*x+a))*(I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+2*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-2*cos(b*x+a)^3*2^(1/2)+2*cos(b*x+a)^2*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)/sin(b*x+a)^3/(d*sin(b*x+a)/cos(b*x+a))^(1/2)*2^(1/2)","C"
86,1,38,16,0.549000," ","int(csc(b*x+a)^2/(d*tan(b*x+a))^(1/2),x)","-\frac{2 \cos \left(b x +a \right)}{3 b \sin \left(b x +a \right) \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}"," ",0,"-2/3/b*cos(b*x+a)/sin(b*x+a)/(d*sin(b*x+a)/cos(b*x+a))^(1/2)","B"
87,1,50,35,0.614000," ","int(csc(b*x+a)^4/(d*tan(b*x+a))^(1/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-7\right) \cos \left(b x +a \right)}{21 b \sin \left(b x +a \right)^{3} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}"," ",0,"2/21/b*(4*cos(b*x+a)^2-7)*cos(b*x+a)/sin(b*x+a)^3/(d*sin(b*x+a)/cos(b*x+a))^(1/2)","A"
88,1,60,53,0.678000," ","int(csc(b*x+a)^6/(d*tan(b*x+a))^(1/2),x)","-\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)-88 \left(\cos^{2}\left(b x +a \right)\right)+77\right) \cos \left(b x +a \right)}{231 b \sin \left(b x +a \right)^{5} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}"," ",0,"-2/231/b*(32*cos(b*x+a)^4-88*cos(b*x+a)^2+77)*cos(b*x+a)/sin(b*x+a)^5/(d*sin(b*x+a)/cos(b*x+a))^(1/2)","A"
89,1,550,118,0.536000," ","int(sin(b*x+a)^5/(d*tan(b*x+a))^(1/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(12 \sqrt{2}\, \left(\cos^{6}\left(b x +a \right)\right)-38 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-21 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+42 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+42 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+47 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-21 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{120 b \cos \left(b x +a \right) \sin \left(b x +a \right)^{4} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}"," ",0,"-1/120/b*(-1+cos(b*x+a))^2*(12*2^(1/2)*cos(b*x+a)^6-38*cos(b*x+a)^4*2^(1/2)-21*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+42*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-21*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+42*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+47*cos(b*x+a)^2*2^(1/2)-21*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)/sin(b*x+a)^4/(d*sin(b*x+a)/cos(b*x+a))^(1/2)*2^(1/2)","B"
90,1,537,94,0.522000," ","int(sin(b*x+a)^3/(d*tan(b*x+a))^(1/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+5 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-3 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{12 b \sin \left(b x +a \right)^{4} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \cos \left(b x +a \right)}"," ",0,"-1/12/b*(-1+cos(b*x+a))^2*(6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^4*2^(1/2)+6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+5*cos(b*x+a)^2*2^(1/2)-3*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/sin(b*x+a)^4/(d*sin(b*x+a)/cos(b*x+a))^(1/2)/cos(b*x+a)*2^(1/2)","B"
91,1,523,69,0.434000," ","int(sin(b*x+a)/(d*tan(b*x+a))^(1/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-\cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{2 b \cos \left(b x +a \right) \sin \left(b x +a \right)^{4} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}"," ",0,"-1/2/b*(-1+cos(b*x+a))^2*(2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)^2*2^(1/2)-cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)/sin(b*x+a)^4/(d*sin(b*x+a)/cos(b*x+a))^(1/2)*2^(1/2)","B"
92,1,482,91,0.552000," ","int(csc(b*x+a)/(d*tan(b*x+a))^(1/2),x)","\frac{\left(2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{b \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}\, \cos \left(b x +a \right)}"," ",0,"1/b*(2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*2^(1/2))/(d*sin(b*x+a)/cos(b*x+a))^(1/2)/cos(b*x+a)*2^(1/2)","B"
93,1,972,113,0.618000," ","int(csc(b*x+a)^3/(d*tan(b*x+a))^(1/2),x)","-\frac{\left(4 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+4 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-4 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+2 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{5 b \cos \left(b x +a \right) \sin \left(b x +a \right)^{2} \sqrt{\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}}}"," ",0,"-1/5/b*(4*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+4*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-4*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*2^(1/2)-4*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)^2*2^(1/2)+2*cos(b*x+a)*2^(1/2))/cos(b*x+a)/sin(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(1/2)*2^(1/2)","B"
94,1,550,197,0.483000," ","int(sin(b*x+a)^4/(d*tan(b*x+a))^(3/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+8 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-8 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-6 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+6 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{64 b \cos \left(b x +a \right)^{2} \sin \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/64/b*(-1+cos(b*x+a))*(3*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-3*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+8*cos(b*x+a)^4*2^(1/2)-8*cos(b*x+a)^3*2^(1/2)-3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-6*cos(b*x+a)^2*2^(1/2)+6*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)^2/sin(b*x+a)/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","C"
95,1,522,171,0.463000," ","int(sin(b*x+a)^2/(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-2 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{8 b \cos \left(b x +a \right)^{2} \sin \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"1/8/b*(-1+cos(b*x+a))*(-I*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+I*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+2*cos(b*x+a)^2*2^(1/2)-2*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)^2/sin(b*x+a)/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","C"
96,1,38,16,0.504000," ","int(csc(b*x+a)^2/(d*tan(b*x+a))^(3/2),x)","-\frac{2 \cos \left(b x +a \right)}{5 b \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)}"," ",0,"-2/5/b*cos(b*x+a)/(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)","B"
97,1,50,35,0.576000," ","int(csc(b*x+a)^4/(d*tan(b*x+a))^(3/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-9\right) \cos \left(b x +a \right)}{45 b \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)^{3}}"," ",0,"2/45/b*(4*cos(b*x+a)^2-9)*cos(b*x+a)/(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^3","A"
98,1,60,53,0.660000," ","int(csc(b*x+a)^6/(d*tan(b*x+a))^(3/2),x)","-\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)-104 \left(\cos^{2}\left(b x +a \right)\right)+117\right) \cos \left(b x +a \right)}{585 b \sin \left(b x +a \right)^{5} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/585/b*(32*cos(b*x+a)^4-104*cos(b*x+a)^2+117)*cos(b*x+a)/sin(b*x+a)^5/(d*sin(b*x+a)/cos(b*x+a))^(3/2)","A"
99,1,222,123,0.492000," ","int(sin(b*x+a)^3/(d*tan(b*x+a))^(3/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+\sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+\cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{12 b \cos \left(b x +a \right)^{2} \sin \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/12/b*(-1+cos(b*x+a))*(2*cos(b*x+a)^4*2^(1/2)+sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-2*cos(b*x+a)^3*2^(1/2)-cos(b*x+a)^2*2^(1/2)+cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)^2/sin(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","A"
100,1,196,96,0.418000," ","int(sin(b*x+a)/(d*tan(b*x+a))^(3/2),x)","-\frac{\left(\cos \left(b x +a \right)+1\right)^{2} \left(-1+\cos \left(b x +a \right)\right) \left(\sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+\cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{2 b \cos \left(b x +a \right)^{2} \sin \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/2/b*(cos(b*x+a)+1)^2*(-1+cos(b*x+a))*(sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-cos(b*x+a)^2*2^(1/2)+cos(b*x+a)*2^(1/2))/cos(b*x+a)^2/sin(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","B"
101,1,302,97,0.493000," ","int(csc(b*x+a)/(d*tan(b*x+a))^(3/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(\EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+\sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+\cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{3 b \cos \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)^{4}}"," ",0,"-1/3/b*(-1+cos(b*x+a))^2*(EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^4*2^(1/2)","B"
102,1,558,123,0.587000," ","int(csc(b*x+a)^3/(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(2 \left(\cos^{3}\left(b x +a \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-2 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-\left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-2 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{21 b \cos \left(b x +a \right)^{2} \sin \left(b x +a \right)^{6} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"1/21/b*(-1+cos(b*x+a))^2*(2*cos(b*x+a)^3*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+2*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)^2*sin(b*x+a)-2*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-2*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-cos(b*x+a)^3*2^(1/2)-2*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)^2/sin(b*x+a)^6/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","B"
103,1,688,197,0.487000," ","int(sin(b*x+a)^4/(d*tan(b*x+a))^(5/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+8 \sqrt{2}\, \left(\cos^{5}\left(b x +a \right)\right)-8 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-6 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{64 b \cos \left(b x +a \right)^{3} \sin \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/64/b*(-1+cos(b*x+a))*(3*I*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+8*2^(1/2)*cos(b*x+a)^5-8*cos(b*x+a)^4*2^(1/2)+3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-6*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-2*cos(b*x+a)^3*2^(1/2)+2*cos(b*x+a)^2*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)^3/sin(b*x+a)/(d*sin(b*x+a)/cos(b*x+a))^(5/2)*2^(1/2)","C"
104,1,662,171,0.434000," ","int(sin(b*x+a)^2/(d*tan(b*x+a))^(5/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+6 \sin \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}+2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{8 b \cos \left(b x +a \right)^{3} \sin \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"1/8/b*(-1+cos(b*x+a))*(-3*I*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+6*sin(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)+2*cos(b*x+a)^3*2^(1/2)-2*cos(b*x+a)^2*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)^3/sin(b*x+a)/(d*sin(b*x+a)/cos(b*x+a))^(5/2)*2^(1/2)","C"
105,1,38,16,0.528000," ","int(csc(b*x+a)^2/(d*tan(b*x+a))^(5/2),x)","-\frac{2 \cos \left(b x +a \right)}{7 b \sin \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/7/b*cos(b*x+a)/sin(b*x+a)/(d*sin(b*x+a)/cos(b*x+a))^(5/2)","B"
106,1,50,35,0.591000," ","int(csc(b*x+a)^4/(d*tan(b*x+a))^(5/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-11\right) \cos \left(b x +a \right)}{77 b \sin \left(b x +a \right)^{3} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"2/77/b*(4*cos(b*x+a)^2-11)*cos(b*x+a)/sin(b*x+a)^3/(d*sin(b*x+a)/cos(b*x+a))^(5/2)","A"
107,1,60,53,0.639000," ","int(csc(b*x+a)^6/(d*tan(b*x+a))^(5/2),x)","-\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)-120 \left(\cos^{2}\left(b x +a \right)\right)+165\right) \cos \left(b x +a \right)}{1155 b \sin \left(b x +a \right)^{5} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/1155/b*(32*cos(b*x+a)^4-120*cos(b*x+a)^2+165)*cos(b*x+a)/sin(b*x+a)^5/(d*sin(b*x+a)/cos(b*x+a))^(5/2)","A"
108,1,563,151,0.555000," ","int(sin(b*x+a)^7/(d*tan(b*x+a))^(5/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(40 \sqrt{2}\, \left(\cos^{8}\left(b x +a \right)\right)-108 \sqrt{2}\, \left(\cos^{6}\left(b x +a \right)\right)+42 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+82 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+42 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+7 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-21 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{560 b \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{3}}"," ",0,"-1/560/b*(-1+cos(b*x+a))^2*(40*2^(1/2)*cos(b*x+a)^8-108*2^(1/2)*cos(b*x+a)^6+42*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-21*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+82*cos(b*x+a)^4*2^(1/2)+42*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-21*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+7*cos(b*x+a)^2*2^(1/2)-21*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/(d*sin(b*x+a)/cos(b*x+a))^(5/2)/sin(b*x+a)^2/cos(b*x+a)^3*2^(1/2)","B"
109,1,550,125,0.472000," ","int(sin(b*x+a)^5/(d*tan(b*x+a))^(5/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(4 \sqrt{2}\, \left(\cos^{6}\left(b x +a \right)\right)-6 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+3 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{40 b \cos \left(b x +a \right)^{3} \sin \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"1/40/b*(-1+cos(b*x+a))^2*(4*2^(1/2)*cos(b*x+a)^6-6*cos(b*x+a)^4*2^(1/2)-6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)^2*2^(1/2)+3*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/cos(b*x+a)^3/sin(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(5/2)*2^(1/2)","B"
110,1,537,99,0.528000," ","int(sin(b*x+a)^3/(d*tan(b*x+a))^(5/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right)^{2} \left(3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+3 \cos \left(b x +a \right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \sqrt{2}}{12 b \sin \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \cos \left(b x +a \right)^{3}}"," ",0,"1/12/b*(-1+cos(b*x+a))^2*(3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^4*2^(1/2)+3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)^2*2^(1/2)+3*cos(b*x+a)*2^(1/2))*(cos(b*x+a)+1)^2/sin(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(5/2)/cos(b*x+a)^3*2^(1/2)","B"
111,1,503,97,0.441000," ","int(sin(b*x+a)/(d*tan(b*x+a))^(5/2),x)","\frac{\left(6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-3 \cos \left(b x +a \right) \sqrt{2}\right) \left(\sin^{2}\left(b x +a \right)\right) \sqrt{2}}{2 b \cos \left(b x +a \right)^{3} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"1/2/b*(6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)^2*2^(1/2)-3*cos(b*x+a)*2^(1/2))*sin(b*x+a)^2/cos(b*x+a)^3/(d*sin(b*x+a)/cos(b*x+a))^(5/2)*2^(1/2)","B"
112,1,965,121,0.531000," ","int(csc(b*x+a)/(d*tan(b*x+a))^(5/2),x)","\frac{\left(6 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+3 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{5 b \cos \left(b x +a \right)^{3} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"1/5/b*(6*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)^3*2^(1/2)-6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)^2*2^(1/2)+3*cos(b*x+a)*2^(1/2))/cos(b*x+a)^3/(d*sin(b*x+a)/cos(b*x+a))^(5/2)*2^(1/2)","B"
113,1,1455,147,0.614000," ","int(csc(b*x+a)^3/(d*tan(b*x+a))^(5/2),x)","-\frac{\left(12 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{5}\left(b x +a \right)\right)-6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{5}\left(b x +a \right)\right)+12 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{4}\left(b x +a \right)\right)-6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{4}\left(b x +a \right)\right)-24 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+12 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-24 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+12 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{2}\, \left(\cos^{5}\left(b x +a \right)\right)+12 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \cos \left(b x +a \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+12 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+12 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-6 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{45 b \sin \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \cos \left(b x +a \right)^{3}}"," ",0,"-1/45/b*(12*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)^5-6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)^5+12*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)^4-6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)^4-24*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+12*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-24*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+12*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*2^(1/2)*cos(b*x+a)^5+12*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*cos(b*x+a)^4*2^(1/2)+12*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+12*cos(b*x+a)^3*2^(1/2)+2*cos(b*x+a)^2*2^(1/2)-6*cos(b*x+a)*2^(1/2))/sin(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(5/2)/cos(b*x+a)^3*2^(1/2)","B"
114,1,493,56,0.636000," ","int((a*sin(f*x+e))^(5/2)*(b*tan(f*x+e))^(1/2),x)","-\frac{\left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \left(5 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)-5 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)^{2}}\right)-4 \left(\cos^{3}\left(f x +e \right)\right)+5 \ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}-5 \ln \left(-\frac{2 \left(2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)^{2}}\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+20 \cos \left(f x +e \right)\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}{10 f \sin \left(f x +e \right)^{3}}"," ",0,"-1/10/f*(a*sin(f*x+e))^(5/2)*(5*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)-5*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)-4*cos(f*x+e)^3+5*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)-5*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+20*cos(f*x+e))*(b*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^3","B"
115,1,131,100,0.522000," ","int((a*sin(f*x+e))^(3/2)*(b*tan(f*x+e))^(1/2),x)","-\frac{2 \left(2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos^{2}\left(f x +e \right)-\cos \left(f x +e \right)\right) \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}{3 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}"," ",0,"-2/3/f*(2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+cos(f*x+e)^2-cos(f*x+e))*(a*sin(f*x+e))^(3/2)*(b*sin(f*x+e)/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))/sin(f*x+e)","C"
116,1,295,26,0.548000," ","int((a*sin(f*x+e))^(1/2)*(b*tan(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}-\ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)+\ln \left(-\frac{2 \left(2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)^{2}}\right)+4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) \cos \left(f x +e \right) \sqrt{a \sin \left(f x +e \right)}\, \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}{2 f \sin \left(f x +e \right)^{3} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}"," ",0,"1/2/f*(-1+cos(f*x+e))*(4*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)-ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)+ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)+4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)*(a*sin(f*x+e))^(1/2)*(b*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^3/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)","B"
117,1,88,70,0.427000," ","int((b*tan(f*x+e))^(1/2)/(a*sin(f*x+e))^(1/2),x)","\frac{2 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}{f \sqrt{a \sin \left(f x +e \right)}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}}"," ",0,"2*I/f/(a*sin(f*x+e))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)/(1/(1+cos(f*x+e)))^(1/2)*(b*sin(f*x+e)/cos(f*x+e))^(1/2)","C"
118,1,185,91,0.506000," ","int((b*tan(f*x+e))^(1/2)/(a*sin(f*x+e))^(3/2),x)","-\frac{\left(\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right)-\ln \left(-\frac{2 \left(2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)^{2}}\right)\right) \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}{2 f \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}"," ",0,"-1/2/f*(arctan(1/2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))-ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2))*(-1+cos(f*x+e))*cos(f*x+e)*(b*sin(f*x+e)/cos(f*x+e))^(1/2)/(a*sin(f*x+e))^(3/2)/sin(f*x+e)/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)","B"
119,1,178,102,0.507000," ","int((b*tan(f*x+e))^(1/2)/(a*sin(f*x+e))^(5/2),x)","\frac{\left(i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\cos \left(f x +e \right)\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}{f \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}}}"," ",0,"1/f*(I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-cos(f*x+e))*(b*sin(f*x+e)/cos(f*x+e))^(1/2)*sin(f*x+e)/(a*sin(f*x+e))^(5/2)","C"
120,1,338,132,0.536000," ","int((a*sin(f*x+e))^(5/2)*(b*tan(f*x+e))^(3/2),x)","\frac{2 \left(12 i \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-12 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+12 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-12 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\left(\cos^{4}\left(f x +e \right)\right)+8 \left(\cos^{2}\left(f x +e \right)\right)-12 \cos \left(f x +e \right)+5\right) \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)}{5 f \sin \left(f x +e \right)^{5}}"," ",0,"2/5/f*(12*I*sin(f*x+e)*cos(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-12*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+12*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-12*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-cos(f*x+e)^4+8*cos(f*x+e)^2-12*cos(f*x+e)+5)*(a*sin(f*x+e))^(5/2)*(b*sin(f*x+e)/cos(f*x+e))^(3/2)*cos(f*x+e)/sin(f*x+e)^5","C"
121,1,492,56,0.498000," ","int((a*sin(f*x+e))^(3/2)*(b*tan(f*x+e))^(3/2),x)","\frac{\left(-3 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)^{2}}\right)+3 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)+4 \left(\cos^{2}\left(f x +e \right)\right)-3 \ln \left(-\frac{2 \left(2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)^{2}}\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+3 \ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+12\right) \cos \left(f x +e \right) \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{6 f \sin \left(f x +e \right)^{3}}"," ",0,"1/6/f*(-3*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)+3*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)+4*cos(f*x+e)^2-3*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+3*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+12)*cos(f*x+e)*(a*sin(f*x+e))^(3/2)*(b*sin(f*x+e)/cos(f*x+e))^(3/2)/sin(f*x+e)^3","B"
122,1,326,100,0.521000," ","int((a*sin(f*x+e))^(1/2)*(b*tan(f*x+e))^(3/2),x)","\frac{2 \left(-2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+2 i \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \cos \left(f x +e \right)+1\right) \sqrt{a \sin \left(f x +e \right)}\, \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)}{f \sin \left(f x +e \right)^{3}}"," ",0,"2/f*(-2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+2*I*cos(f*x+e)*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+cos(f*x+e)^2-2*cos(f*x+e)+1)*(a*sin(f*x+e))^(1/2)*(b*sin(f*x+e)/cos(f*x+e))^(3/2)*cos(f*x+e)/sin(f*x+e)^3","C"
123,1,308,26,0.533000," ","int((b*tan(f*x+e))^(3/2)/(a*sin(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right) \ln \left(-\frac{2 \left(2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)^{2}}\right)-\cos \left(f x +e \right) \ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)+4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) \cos \left(f x +e \right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{2 f \sqrt{a \sin \left(f x +e \right)}\, \sin \left(f x +e \right)^{3} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}"," ",0,"-1/2/f*(-1+cos(f*x+e))*(cos(f*x+e)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)-cos(f*x+e)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)+4*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)*(b*sin(f*x+e)/cos(f*x+e))^(3/2)/(a*sin(f*x+e))^(1/2)/sin(f*x+e)^3/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)","B"
124,1,316,106,0.468000," ","int((b*tan(f*x+e))^(3/2)/(a*sin(f*x+e))^(3/2),x)","-\frac{2 \left(i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-i \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos \left(f x +e \right)-1\right) \cos \left(f x +e \right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{f \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sin \left(f x +e \right)}"," ",0,"-2/f*(I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-I*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-I*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+cos(f*x+e)-1)*cos(f*x+e)*(b*sin(f*x+e)/cos(f*x+e))^(3/2)/(a*sin(f*x+e))^(3/2)/sin(f*x+e)","C"
125,1,247,125,0.507000," ","int((b*tan(f*x+e))^(3/2)/(a*sin(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right) \ln \left(-\frac{2 \left(2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)^{2}}\right)+\cos \left(f x +e \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right)+4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) \cos \left(f x +e \right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{2 f \sin \left(f x +e \right) \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}"," ",0,"-1/2/f*(-1+cos(f*x+e))*(cos(f*x+e)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)+cos(f*x+e)*arctan(1/2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))+4*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)*(b*sin(f*x+e)/cos(f*x+e))^(3/2)/sin(f*x+e)/(a*sin(f*x+e))^(5/2)/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)","A"
126,1,349,129,0.584000," ","int((a*sin(f*x+e))^(9/2)/(b*tan(f*x+e))^(1/2),x)","\frac{2 \left(12 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-12 i \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-5 \left(\cos^{6}\left(f x +e \right)\right)+12 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-12 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+16 \left(\cos^{4}\left(f x +e \right)\right)-23 \left(\cos^{2}\left(f x +e \right)\right)+12 \cos \left(f x +e \right)\right) \left(a \sin \left(f x +e \right)\right)^{\frac{9}{2}}}{45 f \cos \left(f x +e \right) \sin \left(f x +e \right)^{5} \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"2/45/f*(12*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-12*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)-5*cos(f*x+e)^6+12*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-12*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+16*cos(f*x+e)^4-23*cos(f*x+e)^2+12*cos(f*x+e))*(a*sin(f*x+e))^(9/2)/cos(f*x+e)/sin(f*x+e)^5/(b*sin(f*x+e)/cos(f*x+e))^(1/2)","C"
127,1,60,56,0.500000," ","int((a*sin(f*x+e))^(7/2)/(b*tan(f*x+e))^(1/2),x)","\frac{2 \left(3 \left(\cos^{2}\left(f x +e \right)\right)-7\right) \left(a \sin \left(f x +e \right)\right)^{\frac{7}{2}} \cos \left(f x +e \right)}{21 f \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)^{3}}"," ",0,"2/21/f*(3*cos(f*x+e)^2-7)*(a*sin(f*x+e))^(7/2)*cos(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^3","A"
128,1,337,100,0.560000," ","int((a*sin(f*x+e))^(5/2)/(b*tan(f*x+e))^(1/2),x)","\frac{2 \left(2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-2 i \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos^{4}\left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)\right) \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}}}{5 f \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right)^{3}}"," ",0,"2/5/f*(2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-2*I*cos(f*x+e)*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+cos(f*x+e)^4-3*cos(f*x+e)^2+2*cos(f*x+e))*(a*sin(f*x+e))^(5/2)/(b*sin(f*x+e)/cos(f*x+e))^(1/2)/cos(f*x+e)/sin(f*x+e)^3","C"
129,1,48,26,0.466000," ","int((a*sin(f*x+e))^(3/2)/(b*tan(f*x+e))^(1/2),x)","-\frac{2 \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \cos \left(f x +e \right)}{3 f \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}"," ",0,"-2/3/f*(a*sin(f*x+e))^(3/2)*cos(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)","A"
130,1,327,70,0.532000," ","int((a*sin(f*x+e))^(1/2)/(b*tan(f*x+e))^(1/2),x)","\frac{2 \sqrt{a \sin \left(f x +e \right)}\, \left(i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-i \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+\cos \left(f x +e \right)\right)}{f \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \cos \left(f x +e \right)}"," ",0,"2/f*(a*sin(f*x+e))^(1/2)*(I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-I*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-I*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-cos(f*x+e)^2+cos(f*x+e))/(b*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)/cos(f*x+e)","C"
131,1,177,90,0.512000," ","int(1/(a*sin(f*x+e))^(1/2)/(b*tan(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right)+\ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)\right)}{2 f \sqrt{a \sin \left(f x +e \right)}\, \sin \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"-1/2/f*(-1+cos(f*x+e))*(arctan(1/2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))+ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2))/(a*sin(f*x+e))^(1/2)/sin(f*x+e)/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(b*sin(f*x+e)/cos(f*x+e))^(1/2)","A"
132,1,315,103,0.551000," ","int(1/(a*sin(f*x+e))^(3/2)/(b*tan(f*x+e))^(1/2),x)","-\frac{\left(i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-i \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}{f \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right)}"," ",0,"-1/f*(I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-I*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-I*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+cos(f*x+e))*sin(f*x+e)/(a*sin(f*x+e))^(3/2)/(b*sin(f*x+e)/cos(f*x+e))^(1/2)/cos(f*x+e)","C"
133,1,319,120,0.575000," ","int(1/(a*sin(f*x+e))^(5/2)/(b*tan(f*x+e))^(1/2),x)","-\frac{\left(4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\cos \left(f x +e \right) \ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)+\cos \left(f x +e \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right)-\ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)-\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right)\right) \sin \left(f x +e \right)}{8 f \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}"," ",0,"-1/8/f*(4*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+cos(f*x+e)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)+cos(f*x+e)*arctan(1/2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))-ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)-arctan(1/2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)))*sin(f*x+e)/(a*sin(f*x+e))^(5/2)/(b*sin(f*x+e)/cos(f*x+e))^(1/2)/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)","B"
134,1,70,122,0.486000," ","int((a*sin(f*x+e))^(13/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{2 \left(45 \left(\cos^{4}\left(f x +e \right)\right)-130 \left(\cos^{2}\left(f x +e \right)\right)+117\right) \left(a \sin \left(f x +e \right)\right)^{\frac{13}{2}} \cos \left(f x +e \right)}{585 f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{5}}"," ",0,"-2/585/f*(45*cos(f*x+e)^4-130*cos(f*x+e)^2+117)*(a*sin(f*x+e))^(13/2)*cos(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/sin(f*x+e)^5","A"
135,1,60,91,0.465000," ","int((a*sin(f*x+e))^(9/2)/(b*tan(f*x+e))^(3/2),x)","\frac{2 \left(a \sin \left(f x +e \right)\right)^{\frac{9}{2}} \left(5 \left(\cos^{2}\left(f x +e \right)\right)-9\right) \cos \left(f x +e \right)}{45 f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{3}}"," ",0,"2/45/f*(a*sin(f*x+e))^(9/2)*(5*cos(f*x+e)^2-9)*cos(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/sin(f*x+e)^3","A"
136,1,48,26,0.448000," ","int((a*sin(f*x+e))^(5/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{2 \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \cos \left(f x +e \right)}{5 f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}"," ",0,"-2/5/f*(a*sin(f*x+e))^(5/2)*cos(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/sin(f*x+e)","A"
137,1,237,121,0.542000," ","int((a*sin(f*x+e))^(1/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right)-\ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)+4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) \sqrt{a \sin \left(f x +e \right)}}{2 f \sin \left(f x +e \right) \cos \left(f x +e \right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}"," ",0,"-1/2/f*(-1+cos(f*x+e))*(4*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+arctan(1/2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))-ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)+4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))*(a*sin(f*x+e))^(1/2)/sin(f*x+e)/cos(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)","A"
138,1,320,125,0.514000," ","int(1/(a*sin(f*x+e))^(3/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{\left(\cos \left(f x +e \right) \ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)-\cos \left(f x +e \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right)+4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}-\ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right)+\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right)\right) \sin \left(f x +e \right)}{8 f \cos \left(f x +e \right) \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}"," ",0,"-1/8/f*(cos(f*x+e)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)-cos(f*x+e)*arctan(1/2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2))+4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)-ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)+arctan(1/2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)))*sin(f*x+e)/cos(f*x+e)/(a*sin(f*x+e))^(3/2)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)","B"
139,1,181,167,0.581000," ","int((a*sin(f*x+e))^(11/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{2 \left(-7 \left(\cos^{6}\left(f x +e \right)\right)+4 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+7 \left(\cos^{5}\left(f x +e \right)\right)+13 \left(\cos^{4}\left(f x +e \right)\right)-13 \left(\cos^{3}\left(f x +e \right)\right)-4 \left(\cos^{2}\left(f x +e \right)\right)+4 \cos \left(f x +e \right)\right) \left(a \sin \left(f x +e \right)\right)^{\frac{11}{2}}}{77 f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)^{2}}"," ",0,"-2/77/f*(-7*cos(f*x+e)^6+4*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+7*cos(f*x+e)^5+13*cos(f*x+e)^4-13*cos(f*x+e)^3-4*cos(f*x+e)^2+4*cos(f*x+e))*(a*sin(f*x+e))^(11/2)/(-1+cos(f*x+e))/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/sin(f*x+e)^3/cos(f*x+e)^2","C"
140,1,161,136,0.521000," ","int((a*sin(f*x+e))^(7/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{2 \left(2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+3 \left(\cos^{4}\left(f x +e \right)\right)-3 \left(\cos^{3}\left(f x +e \right)\right)-2 \left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)\right) \left(a \sin \left(f x +e \right)\right)^{\frac{7}{2}}}{21 f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right)^{2}}"," ",0,"-2/21/f*(2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+3*cos(f*x+e)^4-3*cos(f*x+e)^3-2*cos(f*x+e)^2+2*cos(f*x+e))*(a*sin(f*x+e))^(7/2)/(-1+cos(f*x+e))/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/sin(f*x+e)/cos(f*x+e)^2","C"
141,1,137,105,0.477000," ","int((a*sin(f*x+e))^(3/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{2 \sin \left(f x +e \right) \left(i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+\cos \left(f x +e \right)\right) \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2}}"," ",0,"-2/3/f*sin(f*x+e)*(I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-cos(f*x+e)^2+cos(f*x+e))*(a*sin(f*x+e))^(3/2)/(-1+cos(f*x+e))/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/cos(f*x+e)^2","C"
142,1,185,102,0.562000," ","int(1/(a*sin(f*x+e))^(1/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{\left(i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}{f \sqrt{a \sin \left(f x +e \right)}\, \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2}}"," ",0,"-1/f*(I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+cos(f*x+e))*sin(f*x+e)/(a*sin(f*x+e))^(1/2)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/cos(f*x+e)^2","C"
143,1,337,136,0.532000," ","int(1/(a*sin(f*x+e))^(5/2)/(b*tan(f*x+e))^(3/2),x)","\frac{\left(i \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\left(\cos^{3}\left(f x +e \right)\right)-\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}{6 f \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2}}"," ",0,"1/6/f*(I*sin(f*x+e)*cos(f*x+e)^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+I*sin(f*x+e)*cos(f*x+e)^2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-cos(f*x+e)^3-cos(f*x+e))*sin(f*x+e)/(a*sin(f*x+e))^(5/2)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/cos(f*x+e)^2","C"
144,1,487,167,0.600000," ","int(1/(a*sin(f*x+e))^(9/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{\left(5 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)+5 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-10 i \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-10 i \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+5 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+5 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-5 \left(\cos^{5}\left(f x +e \right)\right)+12 \left(\cos^{3}\left(f x +e \right)\right)+5 \cos \left(f x +e \right)\right) \sin \left(f x +e \right)}{60 f \left(a \sin \left(f x +e \right)\right)^{\frac{9}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2}}"," ",0,"-1/60/f*(5*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^5+5*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^4-10*I*sin(f*x+e)*cos(f*x+e)^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-10*I*sin(f*x+e)*cos(f*x+e)^2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+5*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+5*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-5*cos(f*x+e)^5+12*cos(f*x+e)^3+5*cos(f*x+e))*sin(f*x+e)/(a*sin(f*x+e))^(9/2)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/cos(f*x+e)^2","C"
145,0,0,52,0.710000," ","int((b*sin(f*x+e))^(4/3)*(d*tan(f*x+e))^(1/2),x)","\int \left(b \sin \left(f x +e \right)\right)^{\frac{4}{3}} \sqrt{d \tan \left(f x +e \right)}\, dx"," ",0,"int((b*sin(f*x+e))^(4/3)*(d*tan(f*x+e))^(1/2),x)","F"
146,0,0,52,0.507000," ","int((b*sin(f*x+e))^(1/3)*(d*tan(f*x+e))^(1/2),x)","\int \left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}} \sqrt{d \tan \left(f x +e \right)}\, dx"," ",0,"int((b*sin(f*x+e))^(1/3)*(d*tan(f*x+e))^(1/2),x)","F"
147,0,0,52,0.562000," ","int((d*tan(f*x+e))^(1/2)/(b*sin(f*x+e))^(1/3),x)","\int \frac{\sqrt{d \tan \left(f x +e \right)}}{\left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*tan(f*x+e))^(1/2)/(b*sin(f*x+e))^(1/3),x)","F"
148,0,0,52,0.489000," ","int((d*tan(f*x+e))^(1/2)/(b*sin(f*x+e))^(4/3),x)","\int \frac{\sqrt{d \tan \left(f x +e \right)}}{\left(b \sin \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((d*tan(f*x+e))^(1/2)/(b*sin(f*x+e))^(4/3),x)","F"
149,0,0,52,0.413000," ","int((b*sin(f*x+e))^(4/3)*(d*tan(f*x+e))^(3/2),x)","\int \left(b \sin \left(f x +e \right)\right)^{\frac{4}{3}} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((b*sin(f*x+e))^(4/3)*(d*tan(f*x+e))^(3/2),x)","F"
150,0,0,52,0.401000," ","int((b*sin(f*x+e))^(1/3)*(d*tan(f*x+e))^(3/2),x)","\int \left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((b*sin(f*x+e))^(1/3)*(d*tan(f*x+e))^(3/2),x)","F"
151,0,0,52,0.392000," ","int((d*tan(f*x+e))^(3/2)/(b*sin(f*x+e))^(1/3),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*tan(f*x+e))^(3/2)/(b*sin(f*x+e))^(1/3),x)","F"
152,0,0,52,0.393000," ","int((d*tan(f*x+e))^(3/2)/(b*sin(f*x+e))^(4/3),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(b \sin \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((d*tan(f*x+e))^(3/2)/(b*sin(f*x+e))^(4/3),x)","F"
153,0,0,52,0.423000," ","int((b*sin(f*x+e))^(1/2)*(d*tan(f*x+e))^(4/3),x)","\int \sqrt{b \sin \left(f x +e \right)}\, \left(d \tan \left(f x +e \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((b*sin(f*x+e))^(1/2)*(d*tan(f*x+e))^(4/3),x)","F"
154,0,0,52,0.559000," ","int((b*sin(f*x+e))^(1/2)*(d*tan(f*x+e))^(1/3),x)","\int \sqrt{b \sin \left(f x +e \right)}\, \left(d \tan \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((b*sin(f*x+e))^(1/2)*(d*tan(f*x+e))^(1/3),x)","F"
155,0,0,52,0.627000," ","int((b*sin(f*x+e))^(1/2)/(d*tan(f*x+e))^(1/3),x)","\int \frac{\sqrt{b \sin \left(f x +e \right)}}{\left(d \tan \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*sin(f*x+e))^(1/2)/(d*tan(f*x+e))^(1/3),x)","F"
156,0,0,52,0.518000," ","int((b*sin(f*x+e))^(1/2)/(d*tan(f*x+e))^(4/3),x)","\int \frac{\sqrt{b \sin \left(f x +e \right)}}{\left(d \tan \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((b*sin(f*x+e))^(1/2)/(d*tan(f*x+e))^(4/3),x)","F"
157,0,0,52,0.384000," ","int((b*sin(f*x+e))^(3/2)*(d*tan(f*x+e))^(4/3),x)","\int \left(b \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(d \tan \left(f x +e \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((b*sin(f*x+e))^(3/2)*(d*tan(f*x+e))^(4/3),x)","F"
158,0,0,52,0.433000," ","int((b*sin(f*x+e))^(3/2)*(d*tan(f*x+e))^(1/3),x)","\int \left(b \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(d \tan \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((b*sin(f*x+e))^(3/2)*(d*tan(f*x+e))^(1/3),x)","F"
159,0,0,52,0.363000," ","int((b*sin(f*x+e))^(3/2)/(d*tan(f*x+e))^(1/3),x)","\int \frac{\left(b \sin \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(d \tan \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*sin(f*x+e))^(3/2)/(d*tan(f*x+e))^(1/3),x)","F"
160,0,0,52,0.385000," ","int((b*sin(f*x+e))^(3/2)/(d*tan(f*x+e))^(4/3),x)","\int \frac{\left(b \sin \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(d \tan \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((b*sin(f*x+e))^(3/2)/(d*tan(f*x+e))^(4/3),x)","F"
161,0,0,46,0.520000," ","int((a*sin(f*x+e))^m*tan(f*x+e)^3,x)","\int \left(a \sin \left(f x +e \right)\right)^{m} \left(\tan^{3}\left(f x +e \right)\right)\, dx"," ",0,"int((a*sin(f*x+e))^m*tan(f*x+e)^3,x)","F"
162,0,0,46,1.000000," ","int((a*sin(f*x+e))^m*tan(f*x+e),x)","\int \left(a \sin \left(f x +e \right)\right)^{m} \tan \left(f x +e \right)\, dx"," ",0,"int((a*sin(f*x+e))^m*tan(f*x+e),x)","F"
163,1,18,17,0.065000," ","int(cot(f*x+e)*(a*sin(f*x+e))^m,x)","\frac{\left(a \sin \left(f x +e \right)\right)^{m}}{f m}"," ",0,"(a*sin(f*x+e))^m/f/m","A"
164,1,3161,46,1.658000," ","int(cot(f*x+e)^3*(a*sin(f*x+e))^m,x)","\text{output too large to display}"," ",0,"-1/(-2+m)/f/(exp(2*I*(f*x+e))-1)^2/m*(m/(2^m)*a^m*(exp(I*(f*x+e))+1)^m*(exp(I*(f*x+e))-1)^m/(exp(I*(Re(f*x)+Re(e)))^m)*exp(m*Im(f*x)+m*Im(e))*exp(-1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^3*Pi)*exp(-1/2*I*m*csgn(I*a*sin(f*x+e))^3*Pi)*exp(-1/2*I*m*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))*csgn(I*a)*Pi)*exp(-1/2*I*Pi*m)*exp(1/2*I*m*csgn(I*a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))+I)*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))^2*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))-I)*Pi)*exp(1/2*I*m*csgn(sin(f*x+e))^3*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))^2*csgn(I*a)*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))^3*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))*csgn(I*exp(-I*(f*x+e)))*Pi)*exp(1/2*I*m*csgn(sin(f*x+e))^2*csgn(I*exp(-I*(f*x+e)))*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))+I)*Pi)*exp(4*I*f*x)*exp(4*I*e)-2/(2^m)*a^m*(exp(I*(f*x+e))+1)^m*(exp(I*(f*x+e))-1)^m/(exp(I*(Re(f*x)+Re(e)))^m)*exp(m*Im(f*x)+m*Im(e))*exp(-1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^3*Pi)*exp(-1/2*I*m*csgn(I*a*sin(f*x+e))^3*Pi)*exp(-1/2*I*m*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))*csgn(I*a)*Pi)*exp(-1/2*I*Pi*m)*exp(1/2*I*m*csgn(I*a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))+I)*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))^2*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))-I)*Pi)*exp(1/2*I*m*csgn(sin(f*x+e))^3*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))^2*csgn(I*a)*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))^3*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))*csgn(I*exp(-I*(f*x+e)))*Pi)*exp(1/2*I*m*csgn(sin(f*x+e))^2*csgn(I*exp(-I*(f*x+e)))*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))+I)*Pi)*exp(4*I*f*x)*exp(4*I*e)+2*m/(2^m)*a^m*(exp(I*(f*x+e))+1)^m*(exp(I*(f*x+e))-1)^m/(exp(I*(Re(f*x)+Re(e)))^m)*exp(m*Im(f*x)+m*Im(e))*exp(-1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^3*Pi)*exp(-1/2*I*m*csgn(I*a*sin(f*x+e))^3*Pi)*exp(-1/2*I*m*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))*csgn(I*a)*Pi)*exp(-1/2*I*Pi*m)*exp(1/2*I*m*csgn(I*a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))+I)*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))^2*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))-I)*Pi)*exp(1/2*I*m*csgn(sin(f*x+e))^3*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))^2*csgn(I*a)*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))^3*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))*csgn(I*exp(-I*(f*x+e)))*Pi)*exp(1/2*I*m*csgn(sin(f*x+e))^2*csgn(I*exp(-I*(f*x+e)))*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))+I)*Pi)*exp(2*I*f*x)*exp(2*I*e)+4/(2^m)*a^m*(exp(I*(f*x+e))+1)^m*(exp(I*(f*x+e))-1)^m/(exp(I*(Re(f*x)+Re(e)))^m)*exp(m*Im(f*x)+m*Im(e))*exp(-1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^3*Pi)*exp(-1/2*I*m*csgn(I*a*sin(f*x+e))^3*Pi)*exp(-1/2*I*m*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))*csgn(I*a)*Pi)*exp(-1/2*I*Pi*m)*exp(1/2*I*m*csgn(I*a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))^2*Pi)*exp(-1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))+I)*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))^2*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))-I)*Pi)*exp(1/2*I*m*csgn(sin(f*x+e))^3*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))^2*csgn(I*a)*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))^3*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))*csgn(I*exp(-I*(f*x+e)))*Pi)*exp(1/2*I*m*csgn(sin(f*x+e))^2*csgn(I*exp(-I*(f*x+e)))*Pi)*exp(1/2*I*m*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))*Pi)*exp(1/2*I*m*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))+I)*Pi)*exp(2*I*f*x)*exp(2*I*e)+m/(2^m)*a^m*(exp(I*(f*x+e))+1)^m*(exp(I*(f*x+e))-1)^m/(exp(I*(Re(f*x)+Re(e)))^m)*exp(1/2*m*(-I*csgn(I*exp(2*I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))+I)*Pi+I*csgn(a*sin(f*x+e))^2*csgn(I*a)*Pi-I*Pi-I*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))*csgn(I*a)*Pi-I*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))^2*Pi+I*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))*csgn(I*exp(-I*(f*x+e)))*Pi+I*csgn(sin(f*x+e))^2*csgn(I*exp(-I*(f*x+e)))*Pi+I*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))-I)*Pi+I*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))+I)*Pi-I*csgn(I*a*sin(f*x+e))^3*Pi+I*csgn(I*a*sin(f*x+e))^2*Pi+I*csgn(sin(f*x+e))^3*Pi+I*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))*Pi+I*csgn(a*sin(f*x+e))^3*Pi+I*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))^2*Pi-I*csgn(I*exp(2*I*(f*x+e))-I)^3*Pi-I*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))^2*Pi+2*Im(f*x)+2*Im(e)))-2/(2^m)*a^m*(exp(I*(f*x+e))+1)^m*(exp(I*(f*x+e))-1)^m/(exp(I*(Re(f*x)+Re(e)))^m)*exp(1/2*m*(-I*csgn(I*exp(2*I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))-I)*csgn(I*exp(I*(f*x+e))+I)*Pi+I*csgn(a*sin(f*x+e))^2*csgn(I*a)*Pi-I*Pi-I*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))*csgn(I*a)*Pi-I*csgn(sin(f*x+e))*csgn(a*sin(f*x+e))^2*Pi+I*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))*csgn(I*exp(-I*(f*x+e)))*Pi+I*csgn(sin(f*x+e))^2*csgn(I*exp(-I*(f*x+e)))*Pi+I*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))-I)*Pi+I*csgn(I*exp(2*I*(f*x+e))-I)^2*csgn(I*exp(I*(f*x+e))+I)*Pi-I*csgn(I*a*sin(f*x+e))^3*Pi+I*csgn(I*a*sin(f*x+e))^2*Pi+I*csgn(sin(f*x+e))^3*Pi+I*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))*Pi+I*csgn(a*sin(f*x+e))^3*Pi+I*csgn(I*exp(2*I*(f*x+e))-I)*csgn(sin(f*x+e))^2*Pi-I*csgn(I*exp(2*I*(f*x+e))-I)^3*Pi-I*csgn(a*sin(f*x+e))*csgn(I*a*sin(f*x+e))^2*Pi+2*Im(f*x)+2*Im(e))))","C"
165,1,7964,72,1.270000," ","int(cot(f*x+e)^5*(a*sin(f*x+e))^m,x)","\text{output too large to display}"," ",0,"result too large to display","C"
166,0,0,62,0.409000," ","int((a*sin(f*x+e))^m*tan(f*x+e)^4,x)","\int \left(a \sin \left(f x +e \right)\right)^{m} \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((a*sin(f*x+e))^m*tan(f*x+e)^4,x)","F"
167,0,0,62,0.366000," ","int((a*sin(f*x+e))^m*tan(f*x+e)^2,x)","\int \left(a \sin \left(f x +e \right)\right)^{m} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((a*sin(f*x+e))^m*tan(f*x+e)^2,x)","F"
168,0,0,63,0.406000," ","int(cot(f*x+e)^2*(a*sin(f*x+e))^m,x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^2*(a*sin(f*x+e))^m,x)","F"
169,0,0,65,0.412000," ","int(cot(f*x+e)^4*(a*sin(f*x+e))^m,x)","\int \left(\cot^{4}\left(f x +e \right)\right) \left(a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^4*(a*sin(f*x+e))^m,x)","F"
170,0,0,67,0.443000," ","int((a*sin(f*x+e))^m*(b*tan(f*x+e))^(3/2),x)","\int \left(a \sin \left(f x +e \right)\right)^{m} \left(b \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a*sin(f*x+e))^m*(b*tan(f*x+e))^(3/2),x)","F"
171,0,0,67,0.469000," ","int((a*sin(f*x+e))^m*(b*tan(f*x+e))^(1/2),x)","\int \left(a \sin \left(f x +e \right)\right)^{m} \sqrt{b \tan \left(f x +e \right)}\, dx"," ",0,"int((a*sin(f*x+e))^m*(b*tan(f*x+e))^(1/2),x)","F"
172,0,0,67,0.438000," ","int((a*sin(f*x+e))^m/(b*tan(f*x+e))^(1/2),x)","\int \frac{\left(a \sin \left(f x +e \right)\right)^{m}}{\sqrt{b \tan \left(f x +e \right)}}\, dx"," ",0,"int((a*sin(f*x+e))^m/(b*tan(f*x+e))^(1/2),x)","F"
173,0,0,67,0.406000," ","int((a*sin(f*x+e))^m/(b*tan(f*x+e))^(3/2),x)","\int \frac{\left(a \sin \left(f x +e \right)\right)^{m}}{\left(b \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*sin(f*x+e))^m/(b*tan(f*x+e))^(3/2),x)","F"
174,0,0,81,1.449000," ","int((a*sin(f*x+e))^m*(b*tan(f*x+e))^n,x)","\int \left(a \sin \left(f x +e \right)\right)^{m} \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*sin(f*x+e))^m*(b*tan(f*x+e))^n,x)","F"
175,0,0,48,1.987000," ","int(sin(f*x+e)^4*(b*tan(f*x+e))^n,x)","\int \left(\sin^{4}\left(f x +e \right)\right) \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(sin(f*x+e)^4*(b*tan(f*x+e))^n,x)","F"
176,0,0,48,1.713000," ","int(sin(f*x+e)^2*(b*tan(f*x+e))^n,x)","\int \left(\sin^{2}\left(f x +e \right)\right) \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(sin(f*x+e)^2*(b*tan(f*x+e))^n,x)","F"
177,1,4284,25,3.656000," ","int(csc(f*x+e)^2*(b*tan(f*x+e))^n,x)","\text{output too large to display}"," ",0,"I/(-1+n)/f/(exp(2*I*(f*x+e))-1)*(1/((exp(I*(f*x+e))+I)^n)/((exp(I*(f*x+e))-I)^n)*(exp(I*(f*x+e))+1)^n*(exp(I*(f*x+e))-1)^n*b^n*exp(-1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I*exp(I*(f*x+e))-I))*exp(1/2*I*n*Pi*csgn(1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^2)*exp(1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^2*csgn(I*b))*exp(-1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^3)*exp(-1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^3)*exp(-1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^3)*exp(-1/2*I*n*Pi*csgn(1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^3)*exp(-1/2*I*Pi*n)*exp(-1/2*I*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^3*n)*exp(1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)*csgn(1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^2)*exp(1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I*exp(I*(f*x+e))+I))*exp(1/2*I*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I/(exp(I*(f*x+e))+I))*n)*exp(-1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)*csgn(1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b))*exp(1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I*exp(I*(f*x+e))-I))*exp(1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^2)*exp(1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2)*exp(1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)))*exp(-1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I*exp(I*(f*x+e))+I)*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)))*exp(1/2*I*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I/(exp(I*(f*x+e))-I))*n)*exp(-1/2*I*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I))*csgn(I/(exp(I*(f*x+e))+I))*n)*exp(-1/2*I*n*Pi*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)*csgn(I*b))*exp(2*I*f*x)*exp(2*I*e)+1/((exp(I*(f*x+e))+I)^n)/((exp(I*(f*x+e))-I)^n)*(exp(I*(f*x+e))+1)^n*(exp(I*(f*x+e))-1)^n*b^n*exp(-1/2*I*Pi*n*(-csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I/(exp(I*(f*x+e))-I))+csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^3+csgn(1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^3+csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I*exp(I*(f*x+e))-I)-csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I*exp(I*(f*x+e))-I)+csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^3-csgn(1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^2+csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)*csgn(I*b)-csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I/(exp(I*(f*x+e))+I))-csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2+csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^3+csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)*csgn(1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)+csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^3+csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I))*csgn(I/(exp(I*(f*x+e))+I))+csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I*exp(I*(f*x+e))+I)*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))-csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))-csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(I*(f*x+e))+I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))^2*csgn(I*exp(I*(f*x+e))+I)-csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I))*csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^2-csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^2*csgn(I*b)-csgn(I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-I/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)*csgn(1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b*exp(2*I*(f*x+e))-1/(exp(I*(f*x+e))-I)/(exp(I*(f*x+e))+I)*b)^2+1)))","C"
178,1,13019,53,1.475000," ","int(csc(f*x+e)^4*(b*tan(f*x+e))^n,x)","\text{output too large to display}"," ",0,"result too large to display","C"
179,1,26124,80,2.009000," ","int(csc(f*x+e)^6*(b*tan(f*x+e))^n,x)","\text{output too large to display}"," ",0,"result too large to display","C"
180,0,0,72,1.707000," ","int(sin(f*x+e)^3*(b*tan(f*x+e))^n,x)","\int \left(\sin^{3}\left(f x +e \right)\right) \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(sin(f*x+e)^3*(b*tan(f*x+e))^n,x)","F"
181,0,0,70,1.262000," ","int(sin(f*x+e)*(b*tan(f*x+e))^n,x)","\int \sin \left(f x +e \right) \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(sin(f*x+e)*(b*tan(f*x+e))^n,x)","F"
182,0,0,68,0.698000," ","int(csc(f*x+e)*(b*tan(f*x+e))^n,x)","\int \csc \left(f x +e \right) \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(csc(f*x+e)*(b*tan(f*x+e))^n,x)","F"
183,0,0,68,0.789000," ","int(csc(f*x+e)^3*(b*tan(f*x+e))^n,x)","\int \left(\csc^{3}\left(f x +e \right)\right) \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(csc(f*x+e)^3*(b*tan(f*x+e))^n,x)","F"
184,0,0,68,0.812000," ","int(csc(f*x+e)^5*(b*tan(f*x+e))^n,x)","\int \left(\csc^{5}\left(f x +e \right)\right) \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(csc(f*x+e)^5*(b*tan(f*x+e))^n,x)","F"
185,0,0,77,0.481000," ","int((a*sin(f*x+e))^(3/2)*(b*tan(f*x+e))^n,x)","\int \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*sin(f*x+e))^(3/2)*(b*tan(f*x+e))^n,x)","F"
186,0,0,77,0.467000," ","int((a*sin(f*x+e))^(1/2)*(b*tan(f*x+e))^n,x)","\int \sqrt{a \sin \left(f x +e \right)}\, \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*sin(f*x+e))^(1/2)*(b*tan(f*x+e))^n,x)","F"
187,0,0,77,0.427000," ","int((b*tan(f*x+e))^n/(a*sin(f*x+e))^(1/2),x)","\int \frac{\left(b \tan \left(f x +e \right)\right)^{n}}{\sqrt{a \sin \left(f x +e \right)}}\, dx"," ",0,"int((b*tan(f*x+e))^n/(a*sin(f*x+e))^(1/2),x)","F"
188,0,0,77,0.401000," ","int((b*tan(f*x+e))^n/(a*sin(f*x+e))^(3/2),x)","\int \frac{\left(b \tan \left(f x +e \right)\right)^{n}}{\left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((b*tan(f*x+e))^n/(a*sin(f*x+e))^(3/2),x)","F"
189,0,0,80,1.474000," ","int((a*cos(f*x+e))^m*(b*tan(f*x+e))^n,x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*cos(f*x+e))^m*(b*tan(f*x+e))^n,x)","F"
190,0,0,65,0.806000," ","int((a*tan(f*x+e))^m*(b*tan(f*x+e))^n,x)","\int \left(a \tan \left(f x +e \right)\right)^{m} \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*tan(f*x+e))^m*(b*tan(f*x+e))^n,x)","F"
191,1,728,179,0.754000," ","int((d*cot(f*x+e))^(1/2)*tan(f*x+e)^4,x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(5 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-5 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+12 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-12 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-2 \cos \left(f x +e \right) \sqrt{2}+2 \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}}{10 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)^{3}}"," ",0,"-1/10/f*(-1+cos(f*x+e))*(5*I*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-5*I*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+5*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+5*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-10*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+12*cos(f*x+e)^3*2^(1/2)-12*cos(f*x+e)^2*2^(1/2)-2*cos(f*x+e)*2^(1/2)+2*2^(1/2))*(1+cos(f*x+e))^2*(d*cos(f*x+e)/sin(f*x+e))^(1/2)/cos(f*x+e)^3/sin(f*x+e)^3*2^(1/2)","C"
192,1,548,163,0.676000," ","int((d*cot(f*x+e))^(1/2)*tan(f*x+e)^3,x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(3 i \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}}{6 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)^{2}}"," ",0,"1/6/f*(-1+cos(f*x+e))*(3*I*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))*(1+cos(f*x+e))^2*(d*cos(f*x+e)/sin(f*x+e))^(1/2)/sin(f*x+e)^2/cos(f*x+e)^2*2^(1/2)","C"
193,1,660,161,0.624000," ","int((d*cot(f*x+e))^(1/2)*tan(f*x+e)^2,x)","\frac{\sqrt{\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(i \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-i \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+\sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+\sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-2 \sin \left(f x +e \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \sqrt{2}}{2 f \cos \left(f x +e \right) \sin \left(f x +e \right)^{3}}"," ",0,"1/2/f*(d*cos(f*x+e)/sin(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))*(I*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-I*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-2*sin(f*x+e)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))/cos(f*x+e)/sin(f*x+e)^3*2^(1/2)","C"
194,1,292,145,0.506000," ","int((d*cot(f*x+e))^(1/2)*tan(f*x+e),x)","-\frac{\sqrt{\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{2 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)}"," ",0,"-1/2/f*(d*cos(f*x+e)/sin(f*x+e))^(1/2)*(-1+cos(f*x+e))*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2)))/sin(f*x+e)^2/cos(f*x+e)*(1+cos(f*x+e))^2*2^(1/2)","C"
195,1,160,145,0.137000," ","int((d*cot(f*x+e))^(1/2),x)","-\frac{d \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \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/f*d/(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2/f*d/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/2/f*d/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)","A"
196,1,172,160,0.117000," ","int(cot(f*x+e)*(d*cot(f*x+e))^(1/2),x)","-\frac{2 \sqrt{d \cot \left(f x +e \right)}}{f}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}"," ",0,"-2*(d*cot(f*x+e))^(1/2)/f+1/2/f*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/2/f*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/4/f*(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))","A"
197,1,178,163,0.185000," ","int(cot(f*x+e)^2*(d*cot(f*x+e))^(1/2),x)","-\frac{2 \left(d \cot \left(f x +e \right)\right)^{\frac{3}{2}}}{3 d f}+\frac{d \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \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*(d*cot(f*x+e))^(3/2)/d/f+1/4/f*d/(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2/f*d/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/2/f*d/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)","A"
198,1,190,178,0.184000," ","int(cot(f*x+e)^3*(d*cot(f*x+e))^(1/2),x)","-\frac{2 \left(d \cot \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d^{2} f}+\frac{2 \sqrt{d \cot \left(f x +e \right)}}{f}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}"," ",0,"-2/5*(d*cot(f*x+e))^(5/2)/d^2/f+2*(d*cot(f*x+e))^(1/2)/f-1/2/f*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/2/f*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/4/f*(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))","A"
199,1,728,181,0.684000," ","int((d*cot(f*x+e))^(3/2)*tan(f*x+e)^5,x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(5 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-5 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-12 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+12 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \left(\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}}{10 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)^{4}}"," ",0,"1/10/f*(-1+cos(f*x+e))*(5*I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)^2-5*I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)^2-5*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+10*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-5*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-12*cos(f*x+e)^3*2^(1/2)+12*cos(f*x+e)^2*2^(1/2)+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))*(1+cos(f*x+e))^2*(d*cos(f*x+e)/sin(f*x+e))^(3/2)/sin(f*x+e)^2/cos(f*x+e)^4*2^(1/2)","C"
200,1,548,163,0.671000," ","int((d*cot(f*x+e))^(3/2)*tan(f*x+e)^4,x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(3 i \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \cos \left(f x +e \right) \sqrt{2}+2 \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \left(\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}}{6 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"-1/6/f*(-1+cos(f*x+e))*(3*I*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*cos(f*x+e)*2^(1/2)+2*2^(1/2))*(1+cos(f*x+e))^2*(d*cos(f*x+e)/sin(f*x+e))^(3/2)/sin(f*x+e)/cos(f*x+e)^3*2^(1/2)","C"
201,1,660,163,0.630000," ","int((d*cot(f*x+e))^(3/2)*tan(f*x+e)^3,x)","\frac{\left(i \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-i \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+\sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+\sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-2 \sin \left(f x +e \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)^{2}}"," ",0,"1/2/f*(I*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-I*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-2*sin(f*x+e)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))*(1+cos(f*x+e))^2*(-1+cos(f*x+e))*(d*cos(f*x+e)/sin(f*x+e))^(3/2)/sin(f*x+e)^2/cos(f*x+e)^2*2^(1/2)","C"
202,1,292,145,0.588000," ","int((d*cot(f*x+e))^(3/2)*tan(f*x+e)^2,x)","-\frac{\left(1+\cos \left(f x +e \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{2}}"," ",0,"-1/2/f*(1+cos(f*x+e))^2*(I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-1+cos(f*x+e))*(d*cos(f*x+e)/sin(f*x+e))^(3/2)/sin(f*x+e)/cos(f*x+e)^2*2^(1/2)","C"
203,1,324,145,0.508000," ","int((d*cot(f*x+e))^(3/2)*tan(f*x+e),x)","-\frac{\left(1+\cos \left(f x +e \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{2}}"," ",0,"-1/2/f*(1+cos(f*x+e))^2*(I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-1+cos(f*x+e))*(d*cos(f*x+e)/sin(f*x+e))^(3/2)/sin(f*x+e)/cos(f*x+e)^2*2^(1/2)","C"
204,1,176,161,0.110000," ","int((d*cot(f*x+e))^(3/2),x)","-\frac{2 d \sqrt{d \cot \left(f x +e \right)}}{f}+\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}"," ",0,"-2*d*(d*cot(f*x+e))^(1/2)/f+1/2/f*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/2/f*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/4/f*d*(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))","A"
205,1,181,160,0.101000," ","int(cot(f*x+e)*(d*cot(f*x+e))^(3/2),x)","-\frac{2 \left(d \cot \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}+\frac{d^{2} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{d^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \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*(d*cot(f*x+e))^(3/2)/f+1/4/f*d^2/(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2/f*d^2/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/2/f*d^2/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)","A"
206,1,194,179,0.157000," ","int(cot(f*x+e)^2*(d*cot(f*x+e))^(3/2),x)","-\frac{2 \left(d \cot \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d f}+\frac{2 d \sqrt{d \cot \left(f x +e \right)}}{f}-\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}+\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f}-\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f}"," ",0,"-2/5*(d*cot(f*x+e))^(5/2)/d/f+2*d*(d*cot(f*x+e))^(1/2)/f-1/2/f*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/2/f*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/4/f*d*(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))","A"
207,1,728,178,0.699000," ","int(tan(f*x+e)^3/(d*cot(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(5 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-5 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+12 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-12 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-2 \cos \left(f x +e \right) \sqrt{2}+2 \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{10 f \sin \left(f x +e \right)^{4} \cos \left(f x +e \right)^{2} \sqrt{\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}}}"," ",0,"-1/10/f*(-1+cos(f*x+e))*(5*I*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-5*I*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+5*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+5*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-10*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+12*cos(f*x+e)^3*2^(1/2)-12*cos(f*x+e)^2*2^(1/2)-2*cos(f*x+e)*2^(1/2)+2*2^(1/2))*(1+cos(f*x+e))^2/sin(f*x+e)^4/cos(f*x+e)^2/(d*cos(f*x+e)/sin(f*x+e))^(1/2)*2^(1/2)","C"
208,1,548,161,0.644000," ","int(tan(f*x+e)^2/(d*cot(f*x+e))^(1/2),x)","\frac{\left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(3 i \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \sqrt{2}}{6 f \sin \left(f x +e \right)^{3} \sqrt{\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \cos \left(f x +e \right)}"," ",0,"1/6/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))*(3*I*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))/sin(f*x+e)^3/(d*cos(f*x+e)/sin(f*x+e))^(1/2)/cos(f*x+e)*2^(1/2)","C"
209,1,652,160,0.633000," ","int(tan(f*x+e)/(d*cot(f*x+e))^(1/2),x)","\frac{\left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(i \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-i \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+\sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+\sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-2 \sin \left(f x +e \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \sqrt{2}}{2 f \sin \left(f x +e \right)^{4} \sqrt{\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}}}"," ",0,"1/2/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))*(I*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-I*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-2*sin(f*x+e)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))/sin(f*x+e)^4/(d*cos(f*x+e)/sin(f*x+e))^(1/2)*2^(1/2)","C"
210,1,166,145,0.124000," ","int(1/(d*cot(f*x+e))^(1/2),x)","-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}"," ",0,"-1/4/f/d*(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2/f/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/2/f/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)","A"
211,1,157,145,0.127000," ","int(cot(f*x+e)/(d*cot(f*x+e))^(1/2),x)","-\frac{\sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \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/f/(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2/f/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/2/f/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)","A"
212,1,184,163,0.181000," ","int(cot(f*x+e)^2/(d*cot(f*x+e))^(1/2),x)","-\frac{2 \sqrt{d \cot \left(f x +e \right)}}{d f}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d}"," ",0,"-2*(d*cot(f*x+e))^(1/2)/d/f+1/2/f/d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/2/f/d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/4/f/d*(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))","A"
213,1,175,163,0.186000," ","int(cot(f*x+e)^3/(d*cot(f*x+e))^(1/2),x)","-\frac{2 \left(d \cot \left(f x +e \right)\right)^{\frac{3}{2}}}{3 d^{2} f}+\frac{\sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \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*(d*cot(f*x+e))^(3/2)/d^2/f+1/4/f/(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2/f/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/2/f/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)","A"
214,1,728,179,0.642000," ","int(tan(f*x+e)^2/(d*cot(f*x+e))^(3/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(5 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-5 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-12 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+12 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{10 f \left(\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"1/10/f*(-1+cos(f*x+e))*(5*I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)^2-5*I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)^2-5*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+10*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-5*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-12*cos(f*x+e)^3*2^(1/2)+12*cos(f*x+e)^2*2^(1/2)+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))*(1+cos(f*x+e))^2/(d*cos(f*x+e)/sin(f*x+e))^(3/2)/sin(f*x+e)^5/cos(f*x+e)*2^(1/2)","C"
215,1,540,160,0.587000," ","int(tan(f*x+e)/(d*cot(f*x+e))^(3/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(3 i \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{6 f \sin \left(f x +e \right)^{4} \left(\frac{d \cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"1/6/f*(-1+cos(f*x+e))*(3*I*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))*(1+cos(f*x+e))^2/sin(f*x+e)^4/(d*cos(f*x+e)/sin(f*x+e))^(3/2)*2^(1/2)","C"
216,1,184,163,0.109000," ","int(1/(d*cot(f*x+e))^(3/2),x)","\frac{\sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \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{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \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}{d f \sqrt{d \cot \left(f x +e \right)}}"," ",0,"1/4/f/d/(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2/f/d/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/2/f/d/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+2/d/f/(d*cot(f*x+e))^(1/2)","A"
217,1,166,145,0.102000," ","int(cot(f*x+e)/(d*cot(f*x+e))^(3/2),x)","-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{2}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}"," ",0,"-1/4/f*(d^2)^(1/4)/d^2*2^(1/2)*ln((d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2/f*(d^2)^(1/4)/d^2*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/2/f*(d^2)^(1/4)/d^2*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)","A"
218,1,166,145,0.152000," ","int(cot(f*x+e)^2/(d*cot(f*x+e))^(3/2),x)","-\frac{\sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \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{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/4/f/d/(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2/f/d/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/2/f/d/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)","A"
219,1,184,163,0.160000," ","int(cot(f*x+e)^3/(d*cot(f*x+e))^(3/2),x)","-\frac{2 \sqrt{d \cot \left(f x +e \right)}}{d^{2} f}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{2}}"," ",0,"-2*(d*cot(f*x+e))^(1/2)/d^2/f+1/2/f*(d^2)^(1/4)/d^2*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/2/f*(d^2)^(1/4)/d^2*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/4/f*(d^2)^(1/4)/d^2*2^(1/2)*ln((d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))","A"
220,1,184,163,0.145000," ","int(cot(f*x+e)^4/(d*cot(f*x+e))^(3/2),x)","-\frac{2 \left(d \cot \left(f x +e \right)\right)^{\frac{3}{2}}}{3 d^{3} f}+\frac{\sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \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{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f d \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3*(d*cot(f*x+e))^(3/2)/d^3/f+1/4/f/d/(d^2)^(1/4)*2^(1/2)*ln((d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))+1/2/f/d/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/2/f/d/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)","A"
221,1,202,181,0.150000," ","int(cot(f*x+e)^5/(d*cot(f*x+e))^(3/2),x)","-\frac{2 \left(d \cot \left(f x +e \right)\right)^{\frac{5}{2}}}{5 d^{4} f}+\frac{2 \sqrt{d \cot \left(f x +e \right)}}{d^{2} f}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}+\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \cot \left(f x +e \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 f \,d^{2}}-\frac{\left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \cot \left(f x +e \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \cot \left(f x +e \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \cot \left(f x +e \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 f \,d^{2}}"," ",0,"-2/5*(d*cot(f*x+e))^(5/2)/d^4/f+2*(d*cot(f*x+e))^(1/2)/d^2/f-1/2/f*(d^2)^(1/4)/d^2*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)+1/2/f*(d^2)^(1/4)/d^2*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)+1)-1/4/f*(d^2)^(1/4)/d^2*2^(1/2)*ln((d*cot(f*x+e)+(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*cot(f*x+e)-(d^2)^(1/4)*(d*cot(f*x+e))^(1/2)*2^(1/2)+(d^2)^(1/2)))","A"
222,0,0,60,0.908000," ","int(cot(f*x+e)^m*tan(f*x+e)^n,x)","\int \left(\cot^{m}\left(f x +e \right)\right) \left(\tan^{n}\left(f x +e \right)\right)\, dx"," ",0,"int(cot(f*x+e)^m*tan(f*x+e)^n,x)","F"
223,0,0,65,0.728000," ","int(cot(f*x+e)^m*(b*tan(f*x+e))^n,x)","\int \left(\cot^{m}\left(f x +e \right)\right) \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cot(f*x+e)^m*(b*tan(f*x+e))^n,x)","F"
224,0,0,62,0.856000," ","int((a*cot(f*x+e))^m*tan(f*x+e)^n,x)","\int \left(a \cot \left(f x +e \right)\right)^{m} \left(\tan^{n}\left(f x +e \right)\right)\, dx"," ",0,"int((a*cot(f*x+e))^m*tan(f*x+e)^n,x)","F"
225,0,0,67,0.737000," ","int((a*cot(f*x+e))^m*(b*tan(f*x+e))^n,x)","\int \left(a \cot \left(f x +e \right)\right)^{m} \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*cot(f*x+e))^m*(b*tan(f*x+e))^n,x)","F"
226,1,60,55,0.727000," ","int(sec(f*x+e)^6*(d*tan(f*x+e))^(1/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(f x +e \right)\right)+24 \left(\cos^{2}\left(f x +e \right)\right)+21\right) \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}{231 f \cos \left(f x +e \right)^{5}}"," ",0,"2/231/f*(32*cos(f*x+e)^4+24*cos(f*x+e)^2+21)*(d*sin(f*x+e)/cos(f*x+e))^(1/2)*sin(f*x+e)/cos(f*x+e)^5","A"
227,1,50,37,0.611000," ","int(sec(f*x+e)^4*(d*tan(f*x+e))^(1/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(f x +e \right)\right)+3\right) \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}{21 f \cos \left(f x +e \right)^{3}}"," ",0,"2/21/f*(4*cos(f*x+e)^2+3)*(d*sin(f*x+e)/cos(f*x+e))^(1/2)*sin(f*x+e)/cos(f*x+e)^3","A"
228,1,19,18,0.153000," ","int(sec(f*x+e)^2*(d*tan(f*x+e))^(1/2),x)","\frac{2 \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 d f}"," ",0,"2/3*(d*tan(f*x+e))^(3/2)/d/f","A"
229,1,160,145,0.084000," ","int((d*tan(f*x+e))^(1/2),x)","\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)}{4 f \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)}{2 f \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)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"1/4/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/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/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)","A"
230,1,522,171,0.555000," ","int(cos(f*x+e)^2*(d*tan(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+\EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+\EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-2 \cos \left(f x +e \right) \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{2}}{8 f \sin \left(f x +e \right)^{3}}"," ",0,"1/8/f*(-1+cos(f*x+e))*(I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-I*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*cos(f*x+e)^2*2^(1/2)-2*cos(f*x+e)*2^(1/2))*(1+cos(f*x+e))^2*(d*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^3*2^(1/2)","C"
231,1,559,118,0.566000," ","int(sec(f*x+e)^3*(d*tan(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(2 \left(\cos^{3}\left(f x +e \right)\right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-4 \left(\cos^{3}\left(f x +e \right)\right) \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+2 \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-4 \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+2 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\sqrt{2}\right) \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{5 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{5}}"," ",0,"-1/5/f*(-1+cos(f*x+e))^2*(2*cos(f*x+e)^3*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-4*cos(f*x+e)^3*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*cos(f*x+e)^2*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-4*cos(f*x+e)^2*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*cos(f*x+e)^3*2^(1/2)-cos(f*x+e)^2*2^(1/2)-2^(1/2))*(d*sin(f*x+e)/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2/cos(f*x+e)^2/sin(f*x+e)^5*2^(1/2)","B"
232,1,513,94,0.472000," ","int(sec(f*x+e)*(d*tan(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{d \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(2 \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-\EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+2 \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-\EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-\cos \left(f x +e \right) \sqrt{2}+\sqrt{2}\right) \sqrt{2}}{f \sin \left(f x +e \right)^{5}}"," ",0,"1/f*(d*sin(f*x+e)/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(2*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-cos(f*x+e)*2^(1/2)+2^(1/2))/sin(f*x+e)^5*2^(1/2)","B"
233,1,523,69,0.502000," ","int(cos(f*x+e)*(d*tan(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(2 \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-\EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+2 \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-\EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2 f \sin \left(f x +e \right)^{5}}"," ",0,"-1/2/f*(-1+cos(f*x+e))^2*(2*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2))*(1+cos(f*x+e))^2*(d*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^5*2^(1/2)","B"
234,1,537,96,0.575000," ","int(cos(f*x+e)^3*(d*tan(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(3 \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-6 \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}+3 \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-6 \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+3 \cos \left(f x +e \right) \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{2}}{12 f \sin \left(f x +e \right)^{5}}"," ",0,"1/12/f*(-1+cos(f*x+e))^2*(3*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-6*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-2*cos(f*x+e)^4*2^(1/2)+3*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-6*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-cos(f*x+e)^2*2^(1/2)+3*cos(f*x+e)*2^(1/2))*(1+cos(f*x+e))^2*(d*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^5*2^(1/2)","B"
235,1,550,122,0.533000," ","int(cos(f*x+e)^5*(d*tan(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(12 \left(\cos^{6}\left(f x +e \right)\right) \sqrt{2}+2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}+42 \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-21 \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+42 \EllipticE \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-21 \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+7 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-21 \cos \left(f x +e \right) \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{2}}{120 f \sin \left(f x +e \right)^{5}}"," ",0,"-1/120/f*(-1+cos(f*x+e))^2*(12*cos(f*x+e)^6*2^(1/2)+2*cos(f*x+e)^4*2^(1/2)+42*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-21*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+42*EllipticE((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-21*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+7*cos(f*x+e)^2*2^(1/2)-21*cos(f*x+e)*2^(1/2))*(1+cos(f*x+e))^2*(d*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^5*2^(1/2)","B"
236,1,60,55,0.674000," ","int(sec(b*x+a)^6*(d*tan(b*x+a))^(3/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)+40 \left(\cos^{2}\left(b x +a \right)\right)+45\right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)}{585 b \cos \left(b x +a \right)^{5}}"," ",0,"2/585/b*(32*cos(b*x+a)^4+40*cos(b*x+a)^2+45)*(d*sin(b*x+a)/cos(b*x+a))^(3/2)*sin(b*x+a)/cos(b*x+a)^5","A"
237,1,50,37,0.725000," ","int(sec(b*x+a)^4*(d*tan(b*x+a))^(3/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)+5\right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)}{45 b \cos \left(b x +a \right)^{3}}"," ",0,"2/45/b*(4*cos(b*x+a)^2+5)*(d*sin(b*x+a)/cos(b*x+a))^(3/2)*sin(b*x+a)/cos(b*x+a)^3","A"
238,1,19,18,0.106000," ","int(sec(b*x+a)^2*(d*tan(b*x+a))^(3/2),x)","\frac{2 \left(d \tan \left(b x +a \right)\right)^{\frac{5}{2}}}{5 b d}"," ",0,"2/5*(d*tan(b*x+a))^(5/2)/b/d","A"
239,1,176,161,0.087000," ","int((d*tan(b*x+a))^(3/2),x)","\frac{2 d \sqrt{d \tan \left(b x +a \right)}}{b}+\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(b x +a \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b}-\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d \tan \left(b x +a \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(b x +a \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(b x +a \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(b x +a \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 b}-\frac{d \left(d^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(b x +a \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b}"," ",0,"2*d*(d*tan(b*x+a))^(1/2)/b+1/2/b*d*(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(b*x+a))^(1/2)+1)-1/4/b*d*(d^2)^(1/4)*2^(1/2)*ln((d*tan(b*x+a)+(d^2)^(1/4)*(d*tan(b*x+a))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(b*x+a)-(d^2)^(1/4)*(d*tan(b*x+a))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2/b*d*(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(b*x+a))^(1/2)+1)","A"
240,1,670,169,0.470000," ","int(cos(b*x+a)^2*(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(i \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \cos \left(b x +a \right) \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{8 b \sin \left(b x +a \right)^{5}}"," ",0,"1/8/b*(-1+cos(b*x+a))*(I*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*2^(1/2)+2*cos(b*x+a)^2*2^(1/2))*(cos(b*x+a)+1)^2*cos(b*x+a)*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5*2^(1/2)","C"
241,1,251,143,0.589000," ","int(sec(b*x+a)^5*(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(4 \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(\cos^{5}\left(b x +a \right)\right) \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \left(\cos^{5}\left(b x +a \right)\right)+2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-\left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+7 \cos \left(b x +a \right) \sqrt{2}-7 \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{77 b \sin \left(b x +a \right)^{5} \cos \left(b x +a \right)^{4}}"," ",0,"1/77/b*(-1+cos(b*x+a))*(4*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)^5*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*2^(1/2)*cos(b*x+a)^5+2*cos(b*x+a)^4*2^(1/2)-cos(b*x+a)^3*2^(1/2)+cos(b*x+a)^2*2^(1/2)+7*cos(b*x+a)*2^(1/2)-7*2^(1/2))*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5/cos(b*x+a)^4*2^(1/2)","A"
242,1,225,119,0.606000," ","int(sec(b*x+a)^3*(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(2 \sin \left(b x +a \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(\cos^{3}\left(b x +a \right)\right)-\left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+3 \cos \left(b x +a \right) \sqrt{2}-3 \sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{21 b \sin \left(b x +a \right)^{5} \cos \left(b x +a \right)^{2}}"," ",0,"1/21/b*(-1+cos(b*x+a))*(2*sin(b*x+a)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)^3-cos(b*x+a)^3*2^(1/2)+cos(b*x+a)^2*2^(1/2)+3*cos(b*x+a)*2^(1/2)-3*2^(1/2))*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5/cos(b*x+a)^2*2^(1/2)","A"
243,1,188,95,0.416000," ","int(sec(b*x+a)*(d*tan(b*x+a))^(3/2),x)","\frac{\left(-1+\cos \left(b x +a \right)\right) \left(\sin \left(b x +a \right) \cos \left(b x +a \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+\cos \left(b x +a \right) \sqrt{2}-\sqrt{2}\right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{3 b \sin \left(b x +a \right)^{5}}"," ",0,"1/3/b*(-1+cos(b*x+a))*(sin(b*x+a)*cos(b*x+a)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+cos(b*x+a)*2^(1/2)-2^(1/2))*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5*2^(1/2)","A"
244,1,196,95,0.470000," ","int(cos(b*x+a)*(d*tan(b*x+a))^(3/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(\sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-\cos \left(b x +a \right) \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 b \sin \left(b x +a \right)^{5}}"," ",0,"-1/2/b*(-1+cos(b*x+a))*(sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)^2*2^(1/2)-cos(b*x+a)*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5*2^(1/2)","B"
245,1,222,119,0.504000," ","int(cos(b*x+a)^3*(d*tan(b*x+a))^(3/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(\sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+\cos \left(b x +a \right) \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{12 b \sin \left(b x +a \right)^{5}}"," ",0,"-1/12/b*(-1+cos(b*x+a))*(sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)^4*2^(1/2)-2*cos(b*x+a)^3*2^(1/2)-cos(b*x+a)^2*2^(1/2)+cos(b*x+a)*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5*2^(1/2)","A"
246,1,250,143,0.506000," ","int(cos(b*x+a)^5*(d*tan(b*x+a))^(3/2),x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(12 \sqrt{2}\, \left(\cos^{6}\left(b x +a \right)\right)-12 \sqrt{2}\, \left(\cos^{5}\left(b x +a \right)\right)-2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+5 \sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-5 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+5 \cos \left(b x +a \right) \sqrt{2}\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{120 b \sin \left(b x +a \right)^{5}}"," ",0,"-1/120/b*(-1+cos(b*x+a))*(12*cos(b*x+a)^6*2^(1/2)-12*2^(1/2)*cos(b*x+a)^5-2*cos(b*x+a)^4*2^(1/2)+5*sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)^3*2^(1/2)-5*cos(b*x+a)^2*2^(1/2)+5*cos(b*x+a)*2^(1/2))*cos(b*x+a)*(cos(b*x+a)+1)^2*(d*sin(b*x+a)/cos(b*x+a))^(3/2)/sin(b*x+a)^5*2^(1/2)","A"
247,1,60,55,0.678000," ","int(sec(f*x+e)^6*(d*tan(f*x+e))^(5/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(f x +e \right)\right)+56 \left(\cos^{2}\left(f x +e \right)\right)+77\right) \left(\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)}{1155 f \cos \left(f x +e \right)^{5}}"," ",0,"2/1155/f*(32*cos(f*x+e)^4+56*cos(f*x+e)^2+77)*(d*sin(f*x+e)/cos(f*x+e))^(5/2)*sin(f*x+e)/cos(f*x+e)^5","A"
248,1,50,37,0.584000," ","int(sec(f*x+e)^4*(d*tan(f*x+e))^(5/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(f x +e \right)\right)+7\right) \left(\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)}{77 f \cos \left(f x +e \right)^{3}}"," ",0,"2/77/f*(4*cos(f*x+e)^2+7)*(d*sin(f*x+e)/cos(f*x+e))^(5/2)*sin(f*x+e)/cos(f*x+e)^3","A"
249,1,19,18,0.121000," ","int(sec(f*x+e)^2*(d*tan(f*x+e))^(5/2),x)","\frac{2 \left(d \tan \left(f x +e \right)\right)^{\frac{7}{2}}}{7 d f}"," ",0,"2/7*(d*tan(f*x+e))^(7/2)/d/f","A"
250,1,182,161,0.069000," ","int((d*tan(f*x+e))^(5/2),x)","\frac{2 d \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}-\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)}{4 f \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)}{2 f \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)}{2 f \left(d^{2}\right)^{\frac{1}{4}}}"," ",0,"2/3*d*(d*tan(f*x+e))^(3/2)/f-1/4/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/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/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)","A"
251,1,532,169,0.546000," ","int(cos(f*x+e)^2*(d*tan(f*x+e))^(5/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(3 i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-3 i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+3 \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+3 \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+2 \cos \left(f x +e \right) \sqrt{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \left(1+\cos \left(f x +e \right)\right)^{2} \left(\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{2}}{8 f \sin \left(f x +e \right)^{5}}"," ",0,"1/8/f*(-1+cos(f*x+e))*(3*I*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+3*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)-2*cos(f*x+e)^2*2^(1/2)+2*cos(f*x+e)*2^(1/2))*cos(f*x+e)^2*(1+cos(f*x+e))^2*(d*sin(f*x+e)/cos(f*x+e))^(5/2)/sin(f*x+e)^5*2^(1/2)","C"
252,1,558,193,0.483000," ","int(cos(f*x+e)^4*(d*tan(f*x+e))^(5/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(3 i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-3 i \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-8 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}+8 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+3 \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+3 \EllipticPi \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}+6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-6 \cos \left(f x +e \right) \sqrt{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \left(1+\cos \left(f x +e \right)\right)^{2} \left(\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{2}}{64 f \sin \left(f x +e \right)^{5}}"," ",0,"1/64/f*(-1+cos(f*x+e))*(3*I*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-8*cos(f*x+e)^4*2^(1/2)+8*cos(f*x+e)^3*2^(1/2)+3*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+3*EllipticPi((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)+6*cos(f*x+e)^2*2^(1/2)-6*cos(f*x+e)*2^(1/2))*cos(f*x+e)^2*(1+cos(f*x+e))^2*(d*sin(f*x+e)/cos(f*x+e))^(5/2)/sin(f*x+e)^5*2^(1/2)","C"
253,1,224,120,0.706000," ","int(sec(f*x+e)^5/(d*tan(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(4 \sin \left(f x +e \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(\cos^{3}\left(f x +e \right)\right)-2 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}+\sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{7 f \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)^{4} \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"-1/7/f*(-1+cos(f*x+e))*(4*sin(f*x+e)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)^3-2*cos(f*x+e)^3*2^(1/2)+2*cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2)+2^(1/2))*(1+cos(f*x+e))^2/sin(f*x+e)^3/cos(f*x+e)^4/(d*sin(f*x+e)/cos(f*x+e))^(1/2)*2^(1/2)","A"
254,1,196,94,0.628000," ","int(sec(f*x+e)^3/(d*tan(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(2 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{2}+\sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{3 f \cos \left(f x +e \right)^{2} \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)^{3}}"," ",0,"-1/3/f*(-1+cos(f*x+e))*(2*cos(f*x+e)*sin(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*2^(1/2)+2^(1/2))*(1+cos(f*x+e))^2/cos(f*x+e)^2/(d*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^3*2^(1/2)","B"
255,1,167,69,0.444000," ","int(sec(f*x+e)/(d*tan(f*x+e))^(1/2),x)","-\frac{\EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right) \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"-1/f*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-1+cos(f*x+e))/sin(f*x+e)^2/cos(f*x+e)*(1+cos(f*x+e))^2/(d*sin(f*x+e)/cos(f*x+e))^(1/2)*2^(1/2)","B"
256,1,199,93,0.489000," ","int(cos(f*x+e)/(d*tan(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(-\sin \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{2 f \cos \left(f x +e \right) \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)^{3}}"," ",0,"1/2/f*(-1+cos(f*x+e))*(-sin(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2))*(1+cos(f*x+e))^2/cos(f*x+e)/(d*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^3*2^(1/2)","B"
257,1,226,120,0.577000," ","int(cos(f*x+e)^3/(d*tan(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}-5 \sin \left(f x +e \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+5 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-5 \cos \left(f x +e \right) \sqrt{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{2}}{12 f \cos \left(f x +e \right) \sqrt{\frac{d \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)^{3}}"," ",0,"1/12/f*(-1+cos(f*x+e))*(2*cos(f*x+e)^4*2^(1/2)-5*sin(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-2*cos(f*x+e)^3*2^(1/2)+5*cos(f*x+e)^2*2^(1/2)-5*cos(f*x+e)*2^(1/2))*(1+cos(f*x+e))^2/cos(f*x+e)/(d*sin(f*x+e)/cos(f*x+e))^(1/2)/sin(f*x+e)^3*2^(1/2)","A"
258,1,60,55,0.679000," ","int(sec(b*x+a)^6/(d*tan(b*x+a))^(3/2),x)","-\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)-8 \left(\cos^{2}\left(b x +a \right)\right)-3\right) \sin \left(b x +a \right)}{21 b \cos \left(b x +a \right)^{5} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/21/b*(32*cos(b*x+a)^4-8*cos(b*x+a)^2-3)*sin(b*x+a)/cos(b*x+a)^5/(d*sin(b*x+a)/cos(b*x+a))^(3/2)","A"
259,1,50,37,0.600000," ","int(sec(b*x+a)^4/(d*tan(b*x+a))^(3/2),x)","-\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \sin \left(b x +a \right)}{3 b \cos \left(b x +a \right)^{3} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/3/b*(4*cos(b*x+a)^2-1)*sin(b*x+a)/cos(b*x+a)^3/(d*sin(b*x+a)/cos(b*x+a))^(3/2)","A"
260,1,19,18,0.114000," ","int(sec(b*x+a)^2/(d*tan(b*x+a))^(3/2),x)","-\frac{2}{b d \sqrt{d \tan \left(b x +a \right)}}"," ",0,"-2/b/d/(d*tan(b*x+a))^(1/2)","A"
261,1,184,163,0.090000," ","int(1/(d*tan(b*x+a))^(3/2),x)","-\frac{\sqrt{2}\, \ln \left(\frac{d \tan \left(b x +a \right)-\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(b x +a \right)}\, \sqrt{2}+\sqrt{d^{2}}}{d \tan \left(b x +a \right)+\left(d^{2}\right)^{\frac{1}{4}} \sqrt{d \tan \left(b x +a \right)}\, \sqrt{2}+\sqrt{d^{2}}}\right)}{4 b d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d \tan \left(b x +a \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b d \left(d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{d \tan \left(b x +a \right)}}{\left(d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b d \left(d^{2}\right)^{\frac{1}{4}}}-\frac{2}{b d \sqrt{d \tan \left(b x +a \right)}}"," ",0,"-1/4/b/d/(d^2)^(1/4)*2^(1/2)*ln((d*tan(b*x+a)-(d^2)^(1/4)*(d*tan(b*x+a))^(1/2)*2^(1/2)+(d^2)^(1/2))/(d*tan(b*x+a)+(d^2)^(1/4)*(d*tan(b*x+a))^(1/2)*2^(1/2)+(d^2)^(1/2)))-1/2/b/d/(d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2)^(1/4)*(d*tan(b*x+a))^(1/2)+1)+1/2/b/d/(d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(d^2)^(1/4)*(d*tan(b*x+a))^(1/2)+1)-2/b/d/(d*tan(b*x+a))^(1/2)","A"
262,1,982,189,0.511000," ","int(cos(b*x+a)^2/(d*tan(b*x+a))^(3/2),x)","\frac{\left(5 i \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)-5 i \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)+5 \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)+5 i \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)-5 i \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-10 \cos \left(b x +a \right) \sqrt{2}\right) \sin \left(b x +a \right) \sqrt{2}}{8 b \cos \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"1/8/b*(5*I*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)-5*I*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)+5*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)+5*I*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)-5*I*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2*cos(b*x+a)^3*2^(1/2)-10*cos(b*x+a)*2^(1/2))*sin(b*x+a)/cos(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","C"
263,1,537,147,0.662000," ","int(sec(b*x+a)^5/(d*tan(b*x+a))^(3/2),x)","-\frac{\left(-24 \left(\cos^{3}\left(b x +a \right)\right) \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+12 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-24 \left(\cos^{2}\left(b x +a \right)\right) \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+12 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+12 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-6 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-\sqrt{2}\right) \sin \left(b x +a \right) \sqrt{2}}{5 b \cos \left(b x +a \right)^{4} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/5/b*(-24*cos(b*x+a)^3*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)+12*cos(b*x+a)^3*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-24*cos(b*x+a)^2*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)+12*cos(b*x+a)^2*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+12*cos(b*x+a)^3*2^(1/2)-6*cos(b*x+a)^2*2^(1/2)-2^(1/2))*sin(b*x+a)/cos(b*x+a)^4/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","B"
264,1,499,121,0.643000," ","int(sec(b*x+a)^3/(d*tan(b*x+a))^(3/2),x)","\frac{\left(4 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+4 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \cos \left(b x +a \right) \sqrt{2}+\sqrt{2}\right) \sin \left(b x +a \right) \sqrt{2}}{b \cos \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"1/b*(4*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-2*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+4*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-2*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-2*cos(b*x+a)*2^(1/2)+2^(1/2))*sin(b*x+a)/cos(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","B"
265,1,496,97,0.447000," ","int(sec(b*x+a)/(d*tan(b*x+a))^(3/2),x)","\frac{\left(2 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-\EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+2 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-\EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-\cos \left(b x +a \right) \sqrt{2}\right) \sin \left(b x +a \right) \sqrt{2}}{b \cos \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"1/b*(2*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+2*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-cos(b*x+a)*2^(1/2))*sin(b*x+a)/cos(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","B"
266,1,509,97,0.514000," ","int(cos(b*x+a)/(d*tan(b*x+a))^(3/2),x)","\frac{\left(6 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+6 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-3 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-3 \cos \left(b x +a \right) \sqrt{2}\right) \sin \left(b x +a \right) \sqrt{2}}{2 b \cos \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"1/2/b*(6*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-3*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+6*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-3*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+cos(b*x+a)^2*2^(1/2)-3*cos(b*x+a)*2^(1/2))*sin(b*x+a)/cos(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","B"
267,1,523,125,0.518000," ","int(cos(b*x+a)^3/(d*tan(b*x+a))^(3/2),x)","\frac{\left(2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+42 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-21 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+42 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-21 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+7 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-21 \cos \left(b x +a \right) \sqrt{2}\right) \sin \left(b x +a \right) \sqrt{2}}{12 b \cos \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"1/12/b*(2*cos(b*x+a)^4*2^(1/2)+42*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-21*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+42*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-21*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+7*cos(b*x+a)^2*2^(1/2)-21*cos(b*x+a)*2^(1/2))*sin(b*x+a)/cos(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","B"
268,1,536,151,0.543000," ","int(cos(b*x+a)^5/(d*tan(b*x+a))^(3/2),x)","\frac{\left(12 \sqrt{2}\, \left(\cos^{6}\left(b x +a \right)\right)+22 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-231 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+462 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-231 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+462 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+77 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-231 \cos \left(b x +a \right) \sqrt{2}\right) \sin \left(b x +a \right) \sqrt{2}}{120 b \cos \left(b x +a \right)^{2} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"1/120/b*(12*cos(b*x+a)^6*2^(1/2)+22*cos(b*x+a)^4*2^(1/2)-231*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+462*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-231*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+462*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+77*cos(b*x+a)^2*2^(1/2)-231*cos(b*x+a)*2^(1/2))*sin(b*x+a)/cos(b*x+a)^2/(d*sin(b*x+a)/cos(b*x+a))^(3/2)*2^(1/2)","B"
269,1,306,97,0.439000," ","int(sec(b*x+a)/(d*tan(b*x+a))^(5/2),x)","-\frac{\left(\cos \left(b x +a \right)+1\right)^{2} \left(-1+\cos \left(b x +a \right)\right)^{2} \left(\sin \left(b x +a \right) \cos \left(b x +a \right) \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+\sin \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{3 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{3} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/3/b*(cos(b*x+a)+1)^2*(-1+cos(b*x+a))^2*(sin(b*x+a)*cos(b*x+a)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+sin(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)*2^(1/2))/sin(b*x+a)^3/cos(b*x+a)^3/(d*sin(b*x+a)/cos(b*x+a))^(5/2)*2^(1/2)","B"
270,1,986,121,0.615000," ","int(sec(b*x+a)^3/(d*tan(b*x+a))^(7/2),x)","-\frac{\left(4 \left(\cos^{3}\left(b x +a \right)\right) \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+4 \left(\cos^{2}\left(b x +a \right)\right) \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-4 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+2 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-4 \EllipticE \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}+2 \EllipticF \left(\sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{-\frac{-\sin \left(b x +a \right)-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+2 \cos \left(b x +a \right) \sqrt{2}\right) \sin \left(b x +a \right) \sqrt{2}}{5 b \cos \left(b x +a \right)^{4} \left(\frac{d \sin \left(b x +a \right)}{\cos \left(b x +a \right)}\right)^{\frac{7}{2}}}"," ",0,"-1/5/b*(4*cos(b*x+a)^3*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)-2*cos(b*x+a)^3*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+4*cos(b*x+a)^2*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)-2*cos(b*x+a)^2*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-4*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+2*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*cos(b*x+a)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-4*EllipticE((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)+2*EllipticF((-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*(-(-sin(b*x+a)-1+cos(b*x+a))/sin(b*x+a))^(1/2)-2*cos(b*x+a)^3*2^(1/2)+cos(b*x+a)^2*2^(1/2)+2*cos(b*x+a)*2^(1/2))*sin(b*x+a)/cos(b*x+a)^4/(d*sin(b*x+a)/cos(b*x+a))^(7/2)*2^(1/2)","B"
271,0,0,43,0.253000," ","int(sec(f*x+e)^(4/3)*tan(f*x+e)^2,x)","\int \left(\sec^{\frac{4}{3}}\left(f x +e \right)\right) \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^(4/3)*tan(f*x+e)^2,x)","F"
272,0,0,43,0.247000," ","int(sec(f*x+e)^(2/3)*tan(f*x+e)^2,x)","\int \left(\sec^{\frac{2}{3}}\left(f x +e \right)\right) \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^(2/3)*tan(f*x+e)^2,x)","F"
273,0,0,43,0.241000," ","int(sec(f*x+e)^(1/3)*tan(f*x+e)^2,x)","\int \left(\sec^{\frac{1}{3}}\left(f x +e \right)\right) \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^(1/3)*tan(f*x+e)^2,x)","F"
274,0,0,43,0.213000," ","int(tan(f*x+e)^2/sec(f*x+e)^(1/3),x)","\int \frac{\tan^{2}\left(f x +e \right)}{\sec \left(f x +e \right)^{\frac{1}{3}}}\, dx"," ",0,"int(tan(f*x+e)^2/sec(f*x+e)^(1/3),x)","F"
275,0,0,43,0.222000," ","int(tan(f*x+e)^2/sec(f*x+e)^(2/3),x)","\int \frac{\tan^{2}\left(f x +e \right)}{\sec \left(f x +e \right)^{\frac{2}{3}}}\, dx"," ",0,"int(tan(f*x+e)^2/sec(f*x+e)^(2/3),x)","F"
276,0,0,43,0.317000," ","int(sec(f*x+e)^(4/3)*tan(f*x+e)^4,x)","\int \left(\sec^{\frac{4}{3}}\left(f x +e \right)\right) \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^(4/3)*tan(f*x+e)^4,x)","F"
277,0,0,43,0.316000," ","int(sec(f*x+e)^(2/3)*tan(f*x+e)^4,x)","\int \left(\sec^{\frac{2}{3}}\left(f x +e \right)\right) \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^(2/3)*tan(f*x+e)^4,x)","F"
278,0,0,43,0.307000," ","int(sec(f*x+e)^(1/3)*tan(f*x+e)^4,x)","\int \left(\sec^{\frac{1}{3}}\left(f x +e \right)\right) \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^(1/3)*tan(f*x+e)^4,x)","F"
279,0,0,43,0.267000," ","int(tan(f*x+e)^4/sec(f*x+e)^(1/3),x)","\int \frac{\tan^{4}\left(f x +e \right)}{\sec \left(f x +e \right)^{\frac{1}{3}}}\, dx"," ",0,"int(tan(f*x+e)^4/sec(f*x+e)^(1/3),x)","F"
280,0,0,43,0.279000," ","int(tan(f*x+e)^4/sec(f*x+e)^(2/3),x)","\int \frac{\tan^{4}\left(f x +e \right)}{\sec \left(f x +e \right)^{\frac{2}{3}}}\, dx"," ",0,"int(tan(f*x+e)^4/sec(f*x+e)^(2/3),x)","F"
281,0,0,47,0.240000," ","int((d*sec(f*x+e))^(4/3)*tan(f*x+e)^2,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{4}{3}} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(4/3)*tan(f*x+e)^2,x)","F"
282,0,0,47,0.227000," ","int((d*sec(f*x+e))^(2/3)*tan(f*x+e)^2,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(2/3)*tan(f*x+e)^2,x)","F"
283,0,0,47,0.230000," ","int((d*sec(f*x+e))^(1/3)*tan(f*x+e)^2,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)*tan(f*x+e)^2,x)","F"
284,0,0,47,0.206000," ","int(tan(f*x+e)^2/(d*sec(f*x+e))^(1/3),x)","\int \frac{\tan^{2}\left(f x +e \right)}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(tan(f*x+e)^2/(d*sec(f*x+e))^(1/3),x)","F"
285,0,0,47,0.214000," ","int(tan(f*x+e)^2/(d*sec(f*x+e))^(2/3),x)","\int \frac{\tan^{2}\left(f x +e \right)}{\left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(tan(f*x+e)^2/(d*sec(f*x+e))^(2/3),x)","F"
286,0,0,47,0.307000," ","int((d*sec(f*x+e))^(4/3)*tan(f*x+e)^4,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{4}{3}} \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(4/3)*tan(f*x+e)^4,x)","F"
287,0,0,47,0.307000," ","int((d*sec(f*x+e))^(2/3)*tan(f*x+e)^4,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}} \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(2/3)*tan(f*x+e)^4,x)","F"
288,0,0,47,0.289000," ","int((d*sec(f*x+e))^(1/3)*tan(f*x+e)^4,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)*tan(f*x+e)^4,x)","F"
289,0,0,47,0.263000," ","int(tan(f*x+e)^4/(d*sec(f*x+e))^(1/3),x)","\int \frac{\tan^{4}\left(f x +e \right)}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(tan(f*x+e)^4/(d*sec(f*x+e))^(1/3),x)","F"
290,0,0,47,0.270000," ","int(tan(f*x+e)^4/(d*sec(f*x+e))^(2/3),x)","\int \frac{\tan^{4}\left(f x +e \right)}{\left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(tan(f*x+e)^4/(d*sec(f*x+e))^(2/3),x)","F"
291,1,600,144,0.921000," ","int((d*sec(f*x+e))^(5/2)*(b*tan(f*x+e))^(1/2),x)","\frac{\left(i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \cos \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{8 f \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"1/8/f*(I*cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))*cos(f*x+e)*(d/cos(f*x+e))^(5/2)*(b*sin(f*x+e)/cos(f*x+e))^(1/2)*sin(f*x+e)/(-1+cos(f*x+e))*2^(1/2)","C"
292,1,572,112,0.901000," ","int((d*sec(f*x+e))^(3/2)*(b*tan(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right) \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+2 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-\cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-\cos \left(f x +e \right) \sqrt{2}+\sqrt{2}\right) \sqrt{2}}{2 f \sin \left(f x +e \right)}"," ",0,"1/2/f*(b*sin(f*x+e)/cos(f*x+e))^(1/2)*(d/cos(f*x+e))^(3/2)*cos(f*x+e)*(2*cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-cos(f*x+e)*2^(1/2)+2^(1/2))/sin(f*x+e)*2^(1/2)","C"
293,1,302,108,0.666000," ","int((d*sec(f*x+e))^(1/2)*(b*tan(f*x+e))^(1/2),x)","-\frac{\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(i \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right)}{2 f \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/2/f*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(d/cos(f*x+e))^(1/2)*(b*sin(f*x+e)/cos(f*x+e))^(1/2)*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)*(I*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2)))/(-1+cos(f*x+e))","C"
294,1,551,79,0.696000," ","int((b*tan(f*x+e))^(1/2)/(d*sec(f*x+e))^(1/2),x)","-\frac{\left(2 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-\cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{2}}{f \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}"," ",0,"-1/f*(2*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)*2^(1/2)-2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(1/2)/(d/cos(f*x+e))^(1/2)/sin(f*x+e)*2^(1/2)","C"
295,1,50,28,0.668000," ","int((b*tan(f*x+e))^(1/2)/(d*sec(f*x+e))^(3/2),x)","\frac{2 \sin \left(f x +e \right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}{3 f \cos \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"2/3/f*sin(f*x+e)*(b*sin(f*x+e)/cos(f*x+e))^(1/2)/cos(f*x+e)/(d/cos(f*x+e))^(3/2)","A"
296,1,571,111,0.782000," ","int((b*tan(f*x+e))^(1/2)/(d*sec(f*x+e))^(5/2),x)","-\frac{\left(4 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-2 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+4 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{2}}{5 f \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)}"," ",0,"-1/5/f*(4*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-2*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+cos(f*x+e)^3*2^(1/2)+4*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)*2^(1/2)-2*2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(1/2)/(d/cos(f*x+e))^(5/2)/cos(f*x+e)^2/sin(f*x+e)*2^(1/2)","C"
297,1,62,60,0.683000," ","int((b*tan(f*x+e))^(1/2)/(d*sec(f*x+e))^(7/2),x)","\frac{2 \left(3 \left(\cos^{2}\left(f x +e \right)\right)+4\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}{21 f \cos \left(f x +e \right)^{3} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}}}"," ",0,"2/21/f*(3*cos(f*x+e)^2+4)*(b*sin(f*x+e)/cos(f*x+e))^(1/2)*sin(f*x+e)/cos(f*x+e)^3/(d/cos(f*x+e))^(7/2)","A"
298,1,585,142,0.714000," ","int((b*tan(f*x+e))^(1/2)/(d*sec(f*x+e))^(9/2),x)","-\frac{\left(5 \sqrt{2}\, \left(\cos^{5}\left(f x +e \right)\right)-12 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+24 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-12 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+24 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+6 \cos \left(f x +e \right) \sqrt{2}-12 \sqrt{2}\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{2}}{45 f \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{9}{2}} \cos \left(f x +e \right)^{4} \sin \left(f x +e \right)}"," ",0,"-1/45/f*(5*2^(1/2)*cos(f*x+e)^5-12*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+24*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+cos(f*x+e)^3*2^(1/2)-12*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+24*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+6*cos(f*x+e)*2^(1/2)-12*2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(1/2)/(d/cos(f*x+e))^(9/2)/cos(f*x+e)^4/sin(f*x+e)*2^(1/2)","C"
299,1,239,141,0.730000," ","int((d*sec(f*x+e))^(5/2)*(b*tan(f*x+e))^(3/2),x)","\frac{\left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right) \left(i \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \sqrt{2}}{12 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}"," ",0,"1/12/f*(b*sin(f*x+e)/cos(f*x+e))^(3/2)*(d/cos(f*x+e))^(5/2)*cos(f*x+e)*(I*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)^3*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)^3*2^(1/2)+cos(f*x+e)^2*2^(1/2)+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))/(-1+cos(f*x+e))/sin(f*x+e)*2^(1/2)","C"
300,1,759,135,0.583000," ","int((d*sec(f*x+e))^(3/2)*(b*tan(f*x+e))^(3/2),x)","-\frac{\left(2 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \cos \left(f x +e \right) \sqrt{2}+2 \sqrt{2}\right) \cos \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}}{8 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}"," ",0,"-1/8/f*(2*I*cos(f*x+e)^2*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-I*cos(f*x+e)^2*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*cos(f*x+e)^2*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-cos(f*x+e)^2*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+cos(f*x+e)^2*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*cos(f*x+e)*2^(1/2)+2*2^(1/2))*cos(f*x+e)*(d/cos(f*x+e))^(3/2)*(b*sin(f*x+e)/cos(f*x+e))^(3/2)/(-1+cos(f*x+e))/sin(f*x+e)*2^(1/2)","C"
301,1,211,107,0.685000," ","int((d*sec(f*x+e))^(1/2)*(b*tan(f*x+e))^(3/2),x)","\frac{\left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(i \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}+\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\right) \sqrt{2}}{2 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}"," ",0,"1/2/f*(b*sin(f*x+e)/cos(f*x+e))^(3/2)*(d/cos(f*x+e))^(1/2)*cos(f*x+e)*(I*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)+cos(f*x+e)*2^(1/2)-2^(1/2))/(-1+cos(f*x+e))/sin(f*x+e)*2^(1/2)","C"
302,1,719,139,0.680000," ","int((b*tan(f*x+e))^(3/2)/(d*sec(f*x+e))^(1/2),x)","\frac{\left(2 i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \cos \left(f x +e \right) \sqrt{2}+2 \sqrt{2}\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right) \sqrt{2}}{2 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}"," ",0,"1/2/f*(2*I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*cos(f*x+e)*2^(1/2)+2*2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(3/2)*cos(f*x+e)/(-1+cos(f*x+e))/(d/cos(f*x+e))^(1/2)/sin(f*x+e)*2^(1/2)","C"
303,1,207,112,0.670000," ","int((b*tan(f*x+e))^(3/2)/(d*sec(f*x+e))^(3/2),x)","-\frac{\left(i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}}{3 f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}"," ",0,"-1/3/f*(I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)+cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(3/2)/(-1+cos(f*x+e))/(d/cos(f*x+e))^(3/2)/sin(f*x+e)*2^(1/2)","C"
304,1,50,28,0.595000," ","int((b*tan(f*x+e))^(3/2)/(d*sec(f*x+e))^(5/2),x)","\frac{2 \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}{5 f \cos \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"2/5/f*(b*sin(f*x+e)/cos(f*x+e))^(3/2)*sin(f*x+e)/cos(f*x+e)/(d/cos(f*x+e))^(5/2)","A"
305,1,241,141,0.728000," ","int((b*tan(f*x+e))^(3/2)/(d*sec(f*x+e))^(7/2),x)","-\frac{\left(2 i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}-3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+\cos \left(f x +e \right) \sqrt{2}\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}}{21 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{2} \sin \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}}}"," ",0,"-1/21/f*(2*I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*cos(f*x+e)^4*2^(1/2)-3*cos(f*x+e)^3*2^(1/2)-cos(f*x+e)^2*2^(1/2)+cos(f*x+e)*2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(3/2)/(-1+cos(f*x+e))/cos(f*x+e)^2/sin(f*x+e)/(d/cos(f*x+e))^(7/2)*2^(1/2)","C"
306,1,62,85,0.586000," ","int((b*tan(f*x+e))^(3/2)/(d*sec(f*x+e))^(9/2),x)","\frac{2 \left(5 \left(\cos^{2}\left(f x +e \right)\right)+4\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}{45 f \cos \left(f x +e \right)^{3} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{9}{2}}}"," ",0,"2/45/f*(5*cos(f*x+e)^2+4)*(b*sin(f*x+e)/cos(f*x+e))^(3/2)*sin(f*x+e)/cos(f*x+e)^3/(d/cos(f*x+e))^(9/2)","A"
307,1,628,168,0.637000," ","int((d*sec(f*x+e))^(5/2)*(b*tan(f*x+e))^(5/2),x)","-\frac{\left(3 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-8 \cos \left(f x +e \right) \sqrt{2}+8 \sqrt{2}\right) \cos \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{2}}{64 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}"," ",0,"-1/64/f*(3*I*cos(f*x+e)^4*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(f*x+e)^4*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*cos(f*x+e)^4*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*cos(f*x+e)^4*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+6*cos(f*x+e)^3*2^(1/2)-6*cos(f*x+e)^2*2^(1/2)-8*cos(f*x+e)*2^(1/2)+8*2^(1/2))*cos(f*x+e)*(d/cos(f*x+e))^(5/2)*(b*sin(f*x+e)/cos(f*x+e))^(5/2)/(-1+cos(f*x+e))/sin(f*x+e)*2^(1/2)","C"
308,1,593,141,0.590000," ","int((d*sec(f*x+e))^(3/2)*(b*tan(f*x+e))^(5/2),x)","-\frac{\left(6 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+5 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-2 \sqrt{2}\right) \cos \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{2}}{12 f \sin \left(f x +e \right)^{3}}"," ",0,"-1/12/f*(6*cos(f*x+e)^4*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^4*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+6*cos(f*x+e)^3*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^3*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^3*2^(1/2)+5*cos(f*x+e)^2*2^(1/2)-2*2^(1/2))*cos(f*x+e)*(d/cos(f*x+e))^(3/2)*(b*sin(f*x+e)/cos(f*x+e))^(5/2)/sin(f*x+e)^3*2^(1/2)","C"
309,1,602,135,0.640000," ","int((d*sec(f*x+e))^(1/2)*(b*tan(f*x+e))^(5/2),x)","-\frac{\left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(3 i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \cos \left(f x +e \right) \sqrt{2}+2 \sqrt{2}\right) \sqrt{2}}{8 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}"," ",0,"-1/8/f*(b*sin(f*x+e)/cos(f*x+e))^(5/2)*(d/cos(f*x+e))^(1/2)*cos(f*x+e)*(3*I*cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*cos(f*x+e)*2^(1/2)+2*2^(1/2))/(-1+cos(f*x+e))/sin(f*x+e)*2^(1/2)","C"
310,1,585,108,0.715000," ","int((b*tan(f*x+e))^(5/2)/(d*sec(f*x+e))^(1/2),x)","\frac{\left(6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+6 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-3 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-3 \cos \left(f x +e \right) \sqrt{2}+\sqrt{2}\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{2}}{2 f \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)^{3}}"," ",0,"1/2/f*(6*cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-3*cos(f*x+e)^2*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+6*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-3*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*cos(f*x+e)^2*2^(1/2)-3*cos(f*x+e)*2^(1/2)+2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(5/2)*cos(f*x+e)/(d/cos(f*x+e))^(1/2)/sin(f*x+e)^3*2^(1/2)","C"
311,1,570,138,0.695000," ","int((b*tan(f*x+e))^(5/2)/(d*sec(f*x+e))^(3/2),x)","\frac{\left(3 i \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-3 i \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-3 \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-3 \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-2 \cos \left(f x +e \right) \sqrt{2}+2 \sqrt{2}\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{2}}{6 f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}"," ",0,"1/6/f*(3*I*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-3*I*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-3*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-3*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-2*cos(f*x+e)*2^(1/2)+2*2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(5/2)*cos(f*x+e)/(-1+cos(f*x+e))/(d/cos(f*x+e))^(3/2)/sin(f*x+e)*2^(1/2)","C"
312,1,565,112,0.712000," ","int((b*tan(f*x+e))^(5/2)/(d*sec(f*x+e))^(5/2),x)","-\frac{\left(6 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-3 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+6 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+4 \cos \left(f x +e \right) \sqrt{2}-3 \sqrt{2}\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{2}}{5 f \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)^{3}}"," ",0,"-1/5/f*(6*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-3*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+6*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)^3*2^(1/2)+4*cos(f*x+e)*2^(1/2)-3*2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(5/2)/(d/cos(f*x+e))^(5/2)/sin(f*x+e)^3*2^(1/2)","C"
313,1,50,28,0.562000," ","int((b*tan(f*x+e))^(5/2)/(d*sec(f*x+e))^(7/2),x)","\frac{2 \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)}{7 f \cos \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}}}"," ",0,"2/7/f*(b*sin(f*x+e)/cos(f*x+e))^(5/2)*sin(f*x+e)/cos(f*x+e)/(d/cos(f*x+e))^(7/2)","A"
314,1,586,141,0.646000," ","int((b*tan(f*x+e))^(5/2)/(d*sec(f*x+e))^(9/2),x)","\frac{\left(5 \sqrt{2}\, \left(\cos^{5}\left(f x +e \right)\right)+6 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-12 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-8 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+6 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{2}+6 \sqrt{2}\right) \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{2}}{45 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{3} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{9}{2}}}"," ",0,"1/45/f*(5*2^(1/2)*cos(f*x+e)^5+6*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-12*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-8*cos(f*x+e)^3*2^(1/2)+6*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-12*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)*2^(1/2)+6*2^(1/2))*(b*sin(f*x+e)/cos(f*x+e))^(5/2)/cos(f*x+e)^2/sin(f*x+e)^3/(d/cos(f*x+e))^(9/2)*2^(1/2)","C"
315,1,758,144,0.649000," ","int((d*sec(f*x+e))^(7/2)/(b*tan(f*x+e))^(1/2),x)","\frac{\left(6 i \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 i \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}}{8 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"1/8/f*(6*I*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)^2*sin(f*x+e)-3*I*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(f*x+e)^2*sin(f*x+e)-3*I*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^2*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*cos(f*x+e)^2*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(f*x+e)*2^(1/2)-2*2^(1/2))*(d/cos(f*x+e))^(7/2)*sin(f*x+e)*cos(f*x+e)/(-1+cos(f*x+e))/(b*sin(f*x+e)/cos(f*x+e))^(1/2)*2^(1/2)","C"
316,1,208,113,0.641000," ","int((d*sec(f*x+e))^(5/2)/(b*tan(f*x+e))^(1/2),x)","-\frac{\left(i \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}-\cos \left(f x +e \right) \sqrt{2}+\sqrt{2}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}}{2 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"-1/2/f*(I*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)-cos(f*x+e)*2^(1/2)+2^(1/2))*(d/cos(f*x+e))^(5/2)*sin(f*x+e)*cos(f*x+e)/(-1+cos(f*x+e))/(b*sin(f*x+e)/cos(f*x+e))^(1/2)*2^(1/2)","C"
317,1,344,107,0.628000," ","int((d*sec(f*x+e))^(3/2)/(b*tan(f*x+e))^(1/2),x)","\frac{\sqrt{2}\, \left(2 i \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\sin^{2}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}}{2 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"1/2/f*2^(1/2)*(2*I*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-I*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2)))*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*(d/cos(f*x+e))^(3/2)*sin(f*x+e)^2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)/(-1+cos(f*x+e))/(b*sin(f*x+e)/cos(f*x+e))^(1/2)","C"
318,1,175,79,0.632000," ","int((d*sec(f*x+e))^(1/2)/(b*tan(f*x+e))^(1/2),x)","-\frac{i \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \left(\sin^{2}\left(f x +e \right)\right) \sqrt{2}}{f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"-I/f*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(d/cos(f*x+e))^(1/2)*sin(f*x+e)^2*2^(1/2)/(-1+cos(f*x+e))/(b*sin(f*x+e)/cos(f*x+e))^(1/2)","C"
319,1,50,28,0.592000," ","int(1/(d*sec(f*x+e))^(1/2)/(b*tan(f*x+e))^(1/2),x)","\frac{2 \sin \left(f x +e \right)}{f \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right)}"," ",0,"2/f*sin(f*x+e)/(d/cos(f*x+e))^(1/2)/(b*sin(f*x+e)/cos(f*x+e))^(1/2)/cos(f*x+e)","A"
320,1,213,111,0.644000," ","int(1/(d*sec(f*x+e))^(3/2)/(b*tan(f*x+e))^(1/2),x)","-\frac{\left(2 i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+\cos \left(f x +e \right) \sqrt{2}\right) \sin \left(f x +e \right) \sqrt{2}}{3 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{2} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"-1/3/f*(2*I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)^2*2^(1/2)+cos(f*x+e)*2^(1/2))*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^2/(d/cos(f*x+e))^(3/2)/(b*sin(f*x+e)/cos(f*x+e))^(1/2)*2^(1/2)","C"
321,1,60,60,0.592000," ","int(1/(d*sec(f*x+e))^(5/2)/(b*tan(f*x+e))^(1/2),x)","\frac{2 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)+4\right)}{5 f \cos \left(f x +e \right)^{3} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}}}"," ",0,"2/5/f*sin(f*x+e)*(cos(f*x+e)^2+4)/cos(f*x+e)^3/(d/cos(f*x+e))^(5/2)/(b*sin(f*x+e)/cos(f*x+e))^(1/2)","A"
322,1,1061,143,0.615000," ","int((d*sec(f*x+e))^(5/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{\left(i \cos \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \cos \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-i \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+2 \sqrt{2}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}}{2 f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/2/f*(I*cos(f*x+e)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*cos(f*x+e)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-cos(f*x+e)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-cos(f*x+e)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*2^(1/2))*(d/cos(f*x+e))^(5/2)*sin(f*x+e)*cos(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)*2^(1/2)","C"
323,1,535,117,0.586000," ","int((d*sec(f*x+e))^(3/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{\left(-2 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+\cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right) \sqrt{2}}{f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/f*(-2*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+2^(1/2))*(d/cos(f*x+e))^(3/2)*sin(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)*2^(1/2)","C"
324,1,50,28,0.546000," ","int((d*sec(f*x+e))^(1/2)/(b*tan(f*x+e))^(3/2),x)","-\frac{2 \sin \left(f x +e \right) \sqrt{\frac{d}{\cos \left(f x +e \right)}}}{f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)}"," ",0,"-2/f*sin(f*x+e)*(d/cos(f*x+e))^(1/2)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/cos(f*x+e)","A"
325,1,556,111,0.636000," ","int(1/(d*sec(f*x+e))^(1/2)/(b*tan(f*x+e))^(3/2),x)","\frac{\left(4 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}-2 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+4 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(f x +e \right) \sqrt{2}-2 \sqrt{2}\right) \sin \left(f x +e \right) \sqrt{2}}{f \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2}}"," ",0,"1/f*(4*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-2*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+4*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)*2^(1/2)-2*2^(1/2))*sin(f*x+e)/(d/cos(f*x+e))^(1/2)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/cos(f*x+e)^2*2^(1/2)","C"
326,1,60,60,0.533000," ","int(1/(d*sec(f*x+e))^(3/2)/(b*tan(f*x+e))^(3/2),x)","\frac{2 \sin \left(f x +e \right) \left(-4+\cos^{2}\left(f x +e \right)\right)}{3 f \cos \left(f x +e \right)^{3} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"2/3/f*sin(f*x+e)*(-4+cos(f*x+e)^2)/cos(f*x+e)^3/(d/cos(f*x+e))^(3/2)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)","A"
327,1,570,142,0.635000," ","int(1/(d*sec(f*x+e))^(5/2)/(b*tan(f*x+e))^(3/2),x)","\frac{\left(-12 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+24 \cos \left(f x +e \right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}+\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-12 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+24 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+6 \cos \left(f x +e \right) \sqrt{2}-12 \sqrt{2}\right) \sin \left(f x +e \right) \sqrt{2}}{5 f \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{4}}"," ",0,"1/5/f*(-12*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+24*cos(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+cos(f*x+e)^3*2^(1/2)-12*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+24*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+6*cos(f*x+e)*2^(1/2)-12*2^(1/2))*sin(f*x+e)/(d/cos(f*x+e))^(5/2)/(b*sin(f*x+e)/cos(f*x+e))^(3/2)/cos(f*x+e)^4*2^(1/2)","C"
328,1,1367,142,0.657000," ","int((d*sec(f*x+e))^(7/2)/(b*tan(f*x+e))^(5/2),x)","\frac{\left(3 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 i \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}+3 i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}}{6 f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"1/6/f*(3*I*cos(f*x+e)*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*cos(f*x+e)*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*I*cos(f*x+e)*sin(f*x+e)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+3*I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(f*x+e)*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*2^(1/2))*(d/cos(f*x+e))^(7/2)*sin(f*x+e)*cos(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(5/2)*2^(1/2)","C"
329,1,314,117,0.589000," ","int((d*sec(f*x+e))^(5/2)/(b*tan(f*x+e))^(5/2),x)","-\frac{\left(-i \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}-i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(f x +e \right) \sqrt{2}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right) \sqrt{2}}{3 f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/3/f*(-I*cos(f*x+e)*sin(f*x+e)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-I*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+cos(f*x+e)*2^(1/2))*(d/cos(f*x+e))^(5/2)*sin(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(5/2)*2^(1/2)","C"
330,1,50,28,0.493000," ","int((d*sec(f*x+e))^(3/2)/(b*tan(f*x+e))^(5/2),x)","-\frac{2 \sin \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{3 f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)}"," ",0,"-2/3/f*sin(f*x+e)*(d/cos(f*x+e))^(3/2)/(b*sin(f*x+e)/cos(f*x+e))^(5/2)/cos(f*x+e)","A"
331,1,322,111,0.625000," ","int((d*sec(f*x+e))^(1/2)/(b*tan(f*x+e))^(5/2),x)","-\frac{\left(2 i \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}+2 i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(f x +e \right) \sqrt{2}\right) \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{3 f \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{2}}"," ",0,"-1/3/f*(2*I*cos(f*x+e)*sin(f*x+e)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+2*I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)*2^(1/2))*(d/cos(f*x+e))^(1/2)*sin(f*x+e)/(b*sin(f*x+e)/cos(f*x+e))^(5/2)/cos(f*x+e)^2*2^(1/2)","C"
332,1,62,57,0.575000," ","int(1/(d*sec(f*x+e))^(1/2)/(b*tan(f*x+e))^(5/2),x)","\frac{2 \sin \left(f x +e \right) \left(3 \left(\cos^{2}\left(f x +e \right)\right)-4\right)}{3 f \cos \left(f x +e \right)^{3} \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"2/3/f*sin(f*x+e)*(3*cos(f*x+e)^2-4)/cos(f*x+e)^3/(d/cos(f*x+e))^(1/2)/(b*sin(f*x+e)/cos(f*x+e))^(5/2)","A"
333,1,336,142,0.625000," ","int(1/(d*sec(f*x+e))^(3/2)/(b*tan(f*x+e))^(5/2),x)","-\frac{\left(4 i \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}+4 i \sin \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-i-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)-i+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+2 \cos \left(f x +e \right) \sqrt{2}\right) \sin \left(f x +e \right) \sqrt{2}}{3 f \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{4}}"," ",0,"-1/3/f*(4*I*cos(f*x+e)*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)+4*I*sin(f*x+e)*((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-I-sin(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)-I+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-cos(f*x+e)^3*2^(1/2)+2*cos(f*x+e)*2^(1/2))*sin(f*x+e)/(d/cos(f*x+e))^(3/2)/(b*sin(f*x+e)/cos(f*x+e))^(5/2)/cos(f*x+e)^4*2^(1/2)","C"
334,1,72,88,0.557000," ","int(1/(d*sec(f*x+e))^(5/2)/(b*tan(f*x+e))^(5/2),x)","\frac{2 \sin \left(f x +e \right) \left(3 \left(\cos^{4}\left(f x +e \right)\right)+24 \left(\cos^{2}\left(f x +e \right)\right)-32\right)}{15 f \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\frac{b \sin \left(f x +e \right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{5}}"," ",0,"2/15/f*sin(f*x+e)*(3*cos(f*x+e)^4+24*cos(f*x+e)^2-32)/(d/cos(f*x+e))^(5/2)/(b*sin(f*x+e)/cos(f*x+e))^(5/2)/cos(f*x+e)^5","A"
335,0,0,52,0.584000," ","int((b*sec(f*x+e))^(4/3)*(d*tan(f*x+e))^(1/2),x)","\int \left(b \sec \left(f x +e \right)\right)^{\frac{4}{3}} \sqrt{d \tan \left(f x +e \right)}\, dx"," ",0,"int((b*sec(f*x+e))^(4/3)*(d*tan(f*x+e))^(1/2),x)","F"
336,0,0,52,0.690000," ","int((b*sec(f*x+e))^(1/3)*(d*tan(f*x+e))^(1/2),x)","\int \left(b \sec \left(f x +e \right)\right)^{\frac{1}{3}} \sqrt{d \tan \left(f x +e \right)}\, dx"," ",0,"int((b*sec(f*x+e))^(1/3)*(d*tan(f*x+e))^(1/2),x)","F"
337,0,0,52,0.634000," ","int((d*tan(f*x+e))^(1/2)/(b*sec(f*x+e))^(1/3),x)","\int \frac{\sqrt{d \tan \left(f x +e \right)}}{\left(b \sec \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*tan(f*x+e))^(1/2)/(b*sec(f*x+e))^(1/3),x)","F"
338,0,0,52,0.622000," ","int((d*tan(f*x+e))^(1/2)/(b*sec(f*x+e))^(4/3),x)","\int \frac{\sqrt{d \tan \left(f x +e \right)}}{\left(b \sec \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((d*tan(f*x+e))^(1/2)/(b*sec(f*x+e))^(4/3),x)","F"
339,0,0,52,0.498000," ","int((b*sec(f*x+e))^(4/3)*(d*tan(f*x+e))^(3/2),x)","\int \left(b \sec \left(f x +e \right)\right)^{\frac{4}{3}} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((b*sec(f*x+e))^(4/3)*(d*tan(f*x+e))^(3/2),x)","F"
340,0,0,52,0.513000," ","int((b*sec(f*x+e))^(1/3)*(d*tan(f*x+e))^(3/2),x)","\int \left(b \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((b*sec(f*x+e))^(1/3)*(d*tan(f*x+e))^(3/2),x)","F"
341,0,0,52,0.506000," ","int((d*tan(f*x+e))^(3/2)/(b*sec(f*x+e))^(1/3),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(b \sec \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*tan(f*x+e))^(3/2)/(b*sec(f*x+e))^(1/3),x)","F"
342,0,0,52,0.605000," ","int((d*tan(f*x+e))^(3/2)/(b*sec(f*x+e))^(4/3),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(b \sec \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((d*tan(f*x+e))^(3/2)/(b*sec(f*x+e))^(4/3),x)","F"
343,0,0,52,0.533000," ","int((b*sec(f*x+e))^(1/2)*(d*tan(f*x+e))^(4/3),x)","\int \sqrt{b \sec \left(f x +e \right)}\, \left(d \tan \left(f x +e \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((b*sec(f*x+e))^(1/2)*(d*tan(f*x+e))^(4/3),x)","F"
344,0,0,52,0.692000," ","int((b*sec(f*x+e))^(1/2)*(d*tan(f*x+e))^(1/3),x)","\int \sqrt{b \sec \left(f x +e \right)}\, \left(d \tan \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((b*sec(f*x+e))^(1/2)*(d*tan(f*x+e))^(1/3),x)","F"
345,0,0,52,0.582000," ","int((b*sec(f*x+e))^(1/2)/(d*tan(f*x+e))^(1/3),x)","\int \frac{\sqrt{b \sec \left(f x +e \right)}}{\left(d \tan \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*sec(f*x+e))^(1/2)/(d*tan(f*x+e))^(1/3),x)","F"
346,0,0,52,0.458000," ","int((b*sec(f*x+e))^(1/2)/(d*tan(f*x+e))^(4/3),x)","\int \frac{\sqrt{b \sec \left(f x +e \right)}}{\left(d \tan \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((b*sec(f*x+e))^(1/2)/(d*tan(f*x+e))^(4/3),x)","F"
347,0,0,52,0.499000," ","int((b*sec(f*x+e))^(3/2)*(d*tan(f*x+e))^(4/3),x)","\int \left(b \sec \left(f x +e \right)\right)^{\frac{3}{2}} \left(d \tan \left(f x +e \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((b*sec(f*x+e))^(3/2)*(d*tan(f*x+e))^(4/3),x)","F"
348,0,0,52,0.464000," ","int((b*sec(f*x+e))^(3/2)*(d*tan(f*x+e))^(1/3),x)","\int \left(b \sec \left(f x +e \right)\right)^{\frac{3}{2}} \left(d \tan \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((b*sec(f*x+e))^(3/2)*(d*tan(f*x+e))^(1/3),x)","F"
349,0,0,52,0.404000," ","int((b*sec(f*x+e))^(3/2)/(d*tan(f*x+e))^(1/3),x)","\int \frac{\left(b \sec \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(d \tan \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*sec(f*x+e))^(3/2)/(d*tan(f*x+e))^(1/3),x)","F"
350,0,0,52,0.413000," ","int((b*sec(f*x+e))^(3/2)/(d*tan(f*x+e))^(4/3),x)","\int \frac{\left(b \sec \left(f x +e \right)\right)^{\frac{3}{2}}}{\left(d \tan \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((b*sec(f*x+e))^(3/2)/(d*tan(f*x+e))^(4/3),x)","F"
351,1,6797,67,1.067000," ","int((b*sec(f*x+e))^m*tan(f*x+e)^5,x)","\text{output too large to display}"," ",0,"result too large to display","C"
352,1,2707,43,0.536000," ","int((b*sec(f*x+e))^m*tan(f*x+e)^3,x)","\text{Expression too large to display}"," ",0,"-1/(2+m)/f/(exp(2*I*(f*x+e))+1)^2/m*(m/((exp(2*I*(f*x+e))+1)^m)*exp(I*(Re(f*x)+Re(e)))^m*2^m*b^m*exp(-m*Im(f*x)-m*Im(e))*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*exp(I*(f*x+e)))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))*csgn(I*b)*m)*exp(-1/2*I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^3*m)*exp(1/2*I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*csgn(I*b)*m)*exp(4*I*f*x)*exp(4*I*e)+2/((exp(2*I*(f*x+e))+1)^m)*exp(I*(Re(f*x)+Re(e)))^m*2^m*b^m*exp(-m*Im(f*x)-m*Im(e))*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*exp(I*(f*x+e)))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))*csgn(I*b)*m)*exp(-1/2*I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^3*m)*exp(1/2*I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*csgn(I*b)*m)*exp(4*I*f*x)*exp(4*I*e)-2*m/((exp(2*I*(f*x+e))+1)^m)*exp(I*(Re(f*x)+Re(e)))^m*2^m*b^m*exp(-m*Im(f*x)-m*Im(e))*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*exp(I*(f*x+e)))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))*csgn(I*b)*m)*exp(-1/2*I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^3*m)*exp(1/2*I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*csgn(I*b)*m)*exp(2*I*f*x)*exp(2*I*e)+4/((exp(2*I*(f*x+e))+1)^m)*exp(I*(Re(f*x)+Re(e)))^m*2^m*b^m*exp(-m*Im(f*x)-m*Im(e))*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*exp(I*(f*x+e)))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))*csgn(I*b)*m)*exp(-1/2*I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^3*m)*exp(1/2*I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*csgn(I*b)*m)*exp(2*I*f*x)*exp(2*I*e)+m/((exp(2*I*(f*x+e))+1)^m)*exp(I*(Re(f*x)+Re(e)))^m*2^m*b^m*exp(-1/2*m*(I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3-I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*exp(I*(f*x+e)))-I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))+I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I/(exp(2*I*(f*x+e))+1))-I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2+I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))*csgn(I*b)+I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^3-I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*csgn(I*b)+2*Im(e)+2*Im(f*x)))+2/((exp(2*I*(f*x+e))+1)^m)*exp(I*(Re(f*x)+Re(e)))^m*2^m*b^m*exp(-1/2*m*(I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3-I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*exp(I*(f*x+e)))-I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))+I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I/(exp(2*I*(f*x+e))+1))-I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2+I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))*csgn(I*b)+I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^3-I*Pi*csgn(I*b/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2*csgn(I*b)+2*Im(e)+2*Im(f*x))))","C"
353,1,18,17,0.058000," ","int((b*sec(f*x+e))^m*tan(f*x+e),x)","\frac{\left(b \sec \left(f x +e \right)\right)^{m}}{f m}"," ",0,"(b*sec(f*x+e))^m/f/m","A"
354,0,0,38,1.111000," ","int(cot(f*x+e)*(b*sec(f*x+e))^m,x)","\int \cot \left(f x +e \right) \left(b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)*(b*sec(f*x+e))^m,x)","F"
355,0,0,37,0.765000," ","int(cot(f*x+e)^3*(b*sec(f*x+e))^m,x)","\int \left(\cot^{3}\left(f x +e \right)\right) \left(b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^3*(b*sec(f*x+e))^m,x)","F"
356,0,0,38,0.431000," ","int(cot(f*x+e)^5*(b*sec(f*x+e))^m,x)","\int \left(\cot^{5}\left(f x +e \right)\right) \left(b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^5*(b*sec(f*x+e))^m,x)","F"
357,0,0,55,0.377000," ","int((b*sec(f*x+e))^m*tan(f*x+e)^4,x)","\int \left(b \sec \left(f x +e \right)\right)^{m} \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((b*sec(f*x+e))^m*tan(f*x+e)^4,x)","F"
358,0,0,55,0.556000," ","int((b*sec(f*x+e))^m*tan(f*x+e)^2,x)","\int \left(b \sec \left(f x +e \right)\right)^{m} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((b*sec(f*x+e))^m*tan(f*x+e)^2,x)","F"
359,0,0,53,0.610000," ","int(cot(f*x+e)^2*(b*sec(f*x+e))^m,x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^2*(b*sec(f*x+e))^m,x)","F"
360,0,0,55,0.398000," ","int(cot(f*x+e)^4*(b*sec(f*x+e))^m,x)","\int \left(\cot^{4}\left(f x +e \right)\right) \left(b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^4*(b*sec(f*x+e))^m,x)","F"
361,0,0,55,0.430000," ","int(cot(f*x+e)^6*(b*sec(f*x+e))^m,x)","\int \left(\cot^{6}\left(f x +e \right)\right) \left(b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^6*(b*sec(f*x+e))^m,x)","F"
362,0,0,80,1.464000," ","int((a*sec(f*x+e))^m*(b*tan(f*x+e))^n,x)","\int \left(a \sec \left(f x +e \right)\right)^{m} \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*sec(f*x+e))^m*(b*tan(f*x+e))^n,x)","F"
363,0,0,74,0.626000," ","int(sec(b*x+a)^6*(d*tan(b*x+a))^n,x)","\int \left(\sec^{6}\left(b x +a \right)\right) \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int(sec(b*x+a)^6*(d*tan(b*x+a))^n,x)","F"
364,0,0,49,0.499000," ","int(sec(b*x+a)^4*(d*tan(b*x+a))^n,x)","\int \left(\sec^{4}\left(b x +a \right)\right) \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int(sec(b*x+a)^4*(d*tan(b*x+a))^n,x)","F"
365,1,25,24,0.107000," ","int(sec(b*x+a)^2*(d*tan(b*x+a))^n,x)","\frac{\left(d \tan \left(b x +a \right)\right)^{1+n}}{b d \left(1+n \right)}"," ",0,"(d*tan(b*x+a))^(1+n)/b/d/(1+n)","A"
366,0,0,48,0.723000," ","int((d*tan(b*x+a))^n,x)","\int \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int((d*tan(b*x+a))^n,x)","F"
367,0,0,48,1.494000," ","int(cos(b*x+a)^2*(d*tan(b*x+a))^n,x)","\int \left(\cos^{2}\left(b x +a \right)\right) \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int(cos(b*x+a)^2*(d*tan(b*x+a))^n,x)","F"
368,0,0,48,1.522000," ","int(cos(b*x+a)^4*(d*tan(b*x+a))^n,x)","\int \left(\cos^{4}\left(b x +a \right)\right) \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int(cos(b*x+a)^4*(d*tan(b*x+a))^n,x)","F"
369,0,0,72,0.465000," ","int(sec(b*x+a)^5*(d*tan(b*x+a))^n,x)","\int \left(\sec^{5}\left(b x +a \right)\right) \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int(sec(b*x+a)^5*(d*tan(b*x+a))^n,x)","F"
370,0,0,72,0.429000," ","int(sec(b*x+a)^3*(d*tan(b*x+a))^n,x)","\int \left(\sec^{3}\left(b x +a \right)\right) \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int(sec(b*x+a)^3*(d*tan(b*x+a))^n,x)","F"
371,0,0,70,0.689000," ","int(sec(b*x+a)*(d*tan(b*x+a))^n,x)","\int \sec \left(b x +a \right) \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int(sec(b*x+a)*(d*tan(b*x+a))^n,x)","F"
372,0,0,66,1.300000," ","int(cos(b*x+a)*(d*tan(b*x+a))^n,x)","\int \cos \left(b x +a \right) \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int(cos(b*x+a)*(d*tan(b*x+a))^n,x)","F"
373,0,0,72,1.890000," ","int(cos(b*x+a)^3*(d*tan(b*x+a))^n,x)","\int \left(\cos^{3}\left(b x +a \right)\right) \left(d \tan \left(b x +a \right)\right)^{n}\, dx"," ",0,"int(cos(b*x+a)^3*(d*tan(b*x+a))^n,x)","F"
374,0,0,38,0.487000," ","int((b*csc(f*x+e))^m*tan(f*x+e)^3,x)","\int \left(b \csc \left(f x +e \right)\right)^{m} \left(\tan^{3}\left(f x +e \right)\right)\, dx"," ",0,"int((b*csc(f*x+e))^m*tan(f*x+e)^3,x)","F"
375,0,0,37,0.968000," ","int((b*csc(f*x+e))^m*tan(f*x+e),x)","\int \left(b \csc \left(f x +e \right)\right)^{m} \tan \left(f x +e \right)\, dx"," ",0,"int((b*csc(f*x+e))^m*tan(f*x+e),x)","F"
376,1,19,18,0.053000," ","int(cot(f*x+e)*(b*csc(f*x+e))^m,x)","-\frac{\left(b \csc \left(f x +e \right)\right)^{m}}{f m}"," ",0,"-(b*csc(f*x+e))^m/f/m","A"
377,1,6612,43,1.263000," ","int(cot(f*x+e)^3*(b*csc(f*x+e))^m,x)","\text{output too large to display}"," ",0,"result too large to display","C"
378,1,16599,69,1.127000," ","int(cot(f*x+e)^5*(b*csc(f*x+e))^m,x)","\text{output too large to display}"," ",0,"result too large to display","C"
379,0,0,55,0.475000," ","int((b*csc(f*x+e))^m*tan(f*x+e)^4,x)","\int \left(b \csc \left(f x +e \right)\right)^{m} \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((b*csc(f*x+e))^m*tan(f*x+e)^4,x)","F"
380,0,0,52,0.405000," ","int((b*csc(f*x+e))^m*tan(f*x+e)^2,x)","\int \left(b \csc \left(f x +e \right)\right)^{m} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((b*csc(f*x+e))^m*tan(f*x+e)^2,x)","F"
381,0,0,55,0.425000," ","int(cot(f*x+e)^2*(b*csc(f*x+e))^m,x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(b \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^2*(b*csc(f*x+e))^m,x)","F"
382,0,0,55,0.447000," ","int(cot(f*x+e)^4*(b*csc(f*x+e))^m,x)","\int \left(\cot^{4}\left(f x +e \right)\right) \left(b \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^4*(b*csc(f*x+e))^m,x)","F"
383,0,0,67,0.549000," ","int((b*csc(f*x+e))^m*(d*tan(f*x+e))^(3/2),x)","\int \left(b \csc \left(f x +e \right)\right)^{m} \left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((b*csc(f*x+e))^m*(d*tan(f*x+e))^(3/2),x)","F"
384,0,0,67,0.573000," ","int((b*csc(f*x+e))^m*(d*tan(f*x+e))^(1/2),x)","\int \left(b \csc \left(f x +e \right)\right)^{m} \sqrt{d \tan \left(f x +e \right)}\, dx"," ",0,"int((b*csc(f*x+e))^m*(d*tan(f*x+e))^(1/2),x)","F"
385,0,0,67,0.542000," ","int((b*csc(f*x+e))^m/(d*tan(f*x+e))^(1/2),x)","\int \frac{\left(b \csc \left(f x +e \right)\right)^{m}}{\sqrt{d \tan \left(f x +e \right)}}\, dx"," ",0,"int((b*csc(f*x+e))^m/(d*tan(f*x+e))^(1/2),x)","F"
386,0,0,67,0.533000," ","int((b*csc(f*x+e))^m/(d*tan(f*x+e))^(3/2),x)","\int \frac{\left(b \csc \left(f x +e \right)\right)^{m}}{\left(d \tan \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((b*csc(f*x+e))^m/(d*tan(f*x+e))^(3/2),x)","F"
387,0,0,83,1.532000," ","int((a*csc(f*x+e))^m*(b*tan(f*x+e))^n,x)","\int \left(a \csc \left(f x +e \right)\right)^{m} \left(b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*csc(f*x+e))^m*(b*tan(f*x+e))^n,x)","F"