1,1,58,88,0.287000," ","int((b*tan(f*x+e)^2)^(5/2),x)","\frac{\left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(\tan^{4}\left(f x +e \right)-2 \left(\tan^{2}\left(f x +e \right)\right)+2 \ln \left(1+\tan^{2}\left(f x +e \right)\right)\right)}{4 f \tan \left(f x +e \right)^{5}}"," ",0,"1/4/f*(b*tan(f*x+e)^2)^(5/2)*(tan(f*x+e)^4-2*tan(f*x+e)^2+2*ln(1+tan(f*x+e)^2))/tan(f*x+e)^5","A"
2,1,48,55,0.263000," ","int((b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-\left(\tan^{2}\left(f x +e \right)\right)+\ln \left(1+\tan^{2}\left(f x +e \right)\right)\right)}{2 f \tan \left(f x +e \right)^{3}}"," ",0,"-1/2/f*(b*tan(f*x+e)^2)^(3/2)*(-tan(f*x+e)^2+ln(1+tan(f*x+e)^2))/tan(f*x+e)^3","A"
3,1,37,30,0.325000," ","int((b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{b \left(\tan^{2}\left(f x +e \right)\right)}\, \ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \tan \left(f x +e \right)}"," ",0,"1/2/f*(b*tan(f*x+e)^2)^(1/2)/tan(f*x+e)*ln(1+tan(f*x+e)^2)","A"
4,1,47,29,0.408000," ","int(1/(b*tan(f*x+e)^2)^(1/2),x)","\frac{\tan \left(f x +e \right) \left(2 \ln \left(\tan \left(f x +e \right)\right)-\ln \left(1+\tan^{2}\left(f x +e \right)\right)\right)}{2 f \sqrt{b \left(\tan^{2}\left(f x +e \right)\right)}}"," ",0,"1/2/f*tan(f*x+e)*(2*ln(tan(f*x+e))-ln(1+tan(f*x+e)^2))/(b*tan(f*x+e)^2)^(1/2)","A"
5,1,64,60,0.307000," ","int(1/(b*tan(f*x+e)^2)^(3/2),x)","-\frac{\tan \left(f x +e \right) \left(2 \ln \left(\tan \left(f x +e \right)\right) \left(\tan^{2}\left(f x +e \right)\right)-\ln \left(1+\tan^{2}\left(f x +e \right)\right) \left(\tan^{2}\left(f x +e \right)\right)+1\right)}{2 f \left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/f*tan(f*x+e)*(2*ln(tan(f*x+e))*tan(f*x+e)^2-ln(1+tan(f*x+e)^2)*tan(f*x+e)^2+1)/(b*tan(f*x+e)^2)^(3/2)","A"
6,1,74,87,0.348000," ","int(1/(b*tan(f*x+e)^2)^(5/2),x)","\frac{\tan \left(f x +e \right) \left(4 \ln \left(\tan \left(f x +e \right)\right) \left(\tan^{4}\left(f x +e \right)\right)-2 \ln \left(1+\tan^{2}\left(f x +e \right)\right) \left(\tan^{4}\left(f x +e \right)\right)+2 \left(\tan^{2}\left(f x +e \right)\right)-1\right)}{4 f \left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/4/f*tan(f*x+e)*(4*ln(tan(f*x+e))*tan(f*x+e)^4-2*ln(1+tan(f*x+e)^2)*tan(f*x+e)^4+2*tan(f*x+e)^2-1)/(b*tan(f*x+e)^2)^(5/2)","A"
7,1,263,306,0.253000," ","int((b*tan(f*x+e)^3)^(5/2),x)","\frac{\left(b \left(\tan^{3}\left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(360 \left(b \tan \left(f x +e \right)\right)^{\frac{13}{2}}-520 b^{2} \left(b \tan \left(f x +e \right)\right)^{\frac{9}{2}}+585 b^{6} \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{b \tan \left(f x +e \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(f x +e \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}+\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(f x +e \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(f x +e \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+936 \left(b \tan \left(f x +e \right)\right)^{\frac{5}{2}} b^{4}-4680 b^{6} \sqrt{b \tan \left(f x +e \right)}\right)}{2340 f \tan \left(f x +e \right)^{5} \left(b \tan \left(f x +e \right)\right)^{\frac{5}{2}} b^{4}}"," ",0,"1/2340/f*(b*tan(f*x+e)^3)^(5/2)*(360*(b*tan(f*x+e))^(13/2)-520*b^2*(b*tan(f*x+e))^(9/2)+585*b^6*(b^2)^(1/4)*2^(1/2)*ln((b*tan(f*x+e)+(b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(f*x+e)-(b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)+(b^2)^(1/2)))+1170*b^6*(b^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(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(f*x+e))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))+936*(b*tan(f*x+e))^(5/2)*b^4-4680*b^6*(b*tan(f*x+e))^(1/2))/tan(f*x+e)^5/(b*tan(f*x+e))^(5/2)/b^4","A"
8,1,236,234,0.165000," ","int((b*tan(f*x+e)^3)^(3/2),x)","\frac{\left(b \left(\tan^{3}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(24 \left(b \tan \left(f x +e \right)\right)^{\frac{7}{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(f x +e \right)}\, \sqrt{2}-b \tan \left(f x +e \right)-\sqrt{b^{2}}}{b \tan \left(f x +e \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)+42 b^{4} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(f x +e \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(f x +e \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)-56 \left(b \tan \left(f x +e \right)\right)^{\frac{3}{2}} b^{2} \left(b^{2}\right)^{\frac{1}{4}}\right)}{84 f \tan \left(f x +e \right)^{3} \left(b \tan \left(f x +e \right)\right)^{\frac{3}{2}} b^{2} \left(b^{2}\right)^{\frac{1}{4}}}"," ",0,"1/84/f*(b*tan(f*x+e)^3)^(3/2)*(24*(b*tan(f*x+e))^(7/2)*(b^2)^(1/4)+21*b^4*2^(1/2)*ln(-((b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)-b*tan(f*x+e)-(b^2)^(1/2))/(b*tan(f*x+e)+(b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)+(b^2)^(1/2)))+42*b^4*2^(1/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+42*b^4*2^(1/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))-56*(b*tan(f*x+e))^(3/2)*b^2*(b^2)^(1/4))/tan(f*x+e)^3/(b*tan(f*x+e))^(3/2)/b^2/(b^2)^(1/4)","A"
9,1,206,209,0.229000," ","int((b*tan(f*x+e)^3)^(1/2),x)","\frac{\sqrt{b \left(\tan^{3}\left(f x +e \right)\right)}\, \left(-2 \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(f x +e \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(f x +e \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{b \tan \left(f x +e \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(f x +e \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)+8 \sqrt{b \tan \left(f x +e \right)}\right)}{4 f \tan \left(f x +e \right) \sqrt{b \tan \left(f x +e \right)}}"," ",0,"1/4/f*(b*tan(f*x+e)^3)^(1/2)*(-2*(b^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))-2*(b^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))-(b^2)^(1/4)*2^(1/2)*ln((b*tan(f*x+e)+(b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(f*x+e)-(b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)+(b^2)^(1/2)))+8*(b*tan(f*x+e))^(1/2))/tan(f*x+e)/(b*tan(f*x+e))^(1/2)","A"
10,1,211,209,0.310000," ","int(1/(b*tan(f*x+e)^3)^(1/2),x)","-\frac{\tan \left(f x +e \right) \left(\sqrt{2}\, \sqrt{b \tan \left(f x +e \right)}\, \ln \left(-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}-b \tan \left(f x +e \right)-\sqrt{b^{2}}}{b \tan \left(f x +e \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)+2 \sqrt{2}\, \sqrt{b \tan \left(f x +e \right)}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(f x +e \right)}+\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+2 \sqrt{2}\, \sqrt{b \tan \left(f x +e \right)}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(f x +e \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 f \sqrt{b \left(\tan^{3}\left(f x +e \right)\right)}\, \left(b^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/4/f*tan(f*x+e)*(2^(1/2)*(b*tan(f*x+e))^(1/2)*ln(-((b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)-b*tan(f*x+e)-(b^2)^(1/2))/(b*tan(f*x+e)+(b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)+(b^2)^(1/2)))+2*2^(1/2)*(b*tan(f*x+e))^(1/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+2*2^(1/2)*(b*tan(f*x+e))^(1/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))+8*(b^2)^(1/4))/(b*tan(f*x+e)^3)^(1/2)/(b^2)^(1/4)","A"
11,1,233,246,0.211000," ","int(1/(b*tan(f*x+e)^3)^(3/2),x)","\frac{\tan \left(f x +e \right) \left(21 \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \left(b \tan \left(f x +e \right)\right)^{\frac{7}{2}} \ln \left(\frac{b \tan \left(f x +e \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{b^{2}}}{b \tan \left(f x +e \right)-\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)+42 \left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \left(b \tan \left(f x +e \right)\right)^{\frac{7}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(f x +e \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(f x +e \right)\right)^{\frac{7}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(f x +e \right)}-\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+56 \left(\tan^{2}\left(f x +e \right)\right) b^{4}-24 b^{4}\right)}{84 f \,b^{4} \left(b \left(\tan^{3}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/84/f*tan(f*x+e)/b^4*(21*(b^2)^(1/4)*2^(1/2)*(b*tan(f*x+e))^(7/2)*ln((b*tan(f*x+e)+(b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)+(b^2)^(1/2))/(b*tan(f*x+e)-(b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)+(b^2)^(1/2)))+42*(b^2)^(1/4)*2^(1/2)*(b*tan(f*x+e))^(7/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+42*(b^2)^(1/4)*2^(1/2)*(b*tan(f*x+e))^(7/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))+56*tan(f*x+e)^2*b^4-24*b^4)/(b*tan(f*x+e)^3)^(3/2)","A"
12,1,272,306,0.231000," ","int(1/(b*tan(f*x+e)^3)^(5/2),x)","\frac{\tan \left(f x +e \right) \left(585 \sqrt{2}\, \left(b \tan \left(f x +e \right)\right)^{\frac{13}{2}} \ln \left(-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}-b \tan \left(f x +e \right)-\sqrt{b^{2}}}{b \tan \left(f x +e \right)+\left(b^{2}\right)^{\frac{1}{4}} \sqrt{b \tan \left(f x +e \right)}\, \sqrt{2}+\sqrt{b^{2}}}\right)+1170 \sqrt{2}\, \left(b \tan \left(f x +e \right)\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(f x +e \right)}+\left(b^{2}\right)^{\frac{1}{4}}}{\left(b^{2}\right)^{\frac{1}{4}}}\right)+1170 \sqrt{2}\, \left(b \tan \left(f x +e \right)\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{b \tan \left(f x +e \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(f x +e \right)\right) b^{6}-936 b^{6} \left(b^{2}\right)^{\frac{1}{4}} \left(\tan^{4}\left(f x +e \right)\right)+520 b^{6} \left(b^{2}\right)^{\frac{1}{4}} \left(\tan^{2}\left(f x +e \right)\right)-360 b^{6} \left(b^{2}\right)^{\frac{1}{4}}\right)}{2340 f \,b^{6} \left(b \left(\tan^{3}\left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(b^{2}\right)^{\frac{1}{4}}}"," ",0,"1/2340/f*tan(f*x+e)/b^6*(585*2^(1/2)*(b*tan(f*x+e))^(13/2)*ln(-((b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)-b*tan(f*x+e)-(b^2)^(1/2))/(b*tan(f*x+e)+(b^2)^(1/4)*(b*tan(f*x+e))^(1/2)*2^(1/2)+(b^2)^(1/2)))+1170*2^(1/2)*(b*tan(f*x+e))^(13/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)+(b^2)^(1/4))/(b^2)^(1/4))+1170*2^(1/2)*(b*tan(f*x+e))^(13/2)*arctan((2^(1/2)*(b*tan(f*x+e))^(1/2)-(b^2)^(1/4))/(b^2)^(1/4))+4680*(b^2)^(1/4)*tan(f*x+e)^6*b^6-936*b^6*(b^2)^(1/4)*tan(f*x+e)^4+520*b^6*(b^2)^(1/4)*tan(f*x+e)^2-360*b^6*(b^2)^(1/4))/(b*tan(f*x+e)^3)^(5/2)/(b^2)^(1/4)","A"
13,1,84,162,0.218000," ","int((b*tan(f*x+e)^4)^(5/2),x)","-\frac{\left(b \left(\tan^{4}\left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-35 \left(\tan^{9}\left(f x +e \right)\right)+45 \left(\tan^{7}\left(f x +e \right)\right)-63 \left(\tan^{5}\left(f x +e \right)\right)+105 \left(\tan^{3}\left(f x +e \right)\right)+315 \arctan \left(\tan \left(f x +e \right)\right)-315 \tan \left(f x +e \right)\right)}{315 f \tan \left(f x +e \right)^{10}}"," ",0,"-1/315/f*(b*tan(f*x+e)^4)^(5/2)*(-35*tan(f*x+e)^9+45*tan(f*x+e)^7-63*tan(f*x+e)^5+105*tan(f*x+e)^3+315*arctan(tan(f*x+e))-315*tan(f*x+e))/tan(f*x+e)^10","A"
14,1,64,98,0.208000," ","int((b*tan(f*x+e)^4)^(3/2),x)","-\frac{\left(b \left(\tan^{4}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-3 \left(\tan^{5}\left(f x +e \right)\right)+5 \left(\tan^{3}\left(f x +e \right)\right)+15 \arctan \left(\tan \left(f x +e \right)\right)-15 \tan \left(f x +e \right)\right)}{15 f \tan \left(f x +e \right)^{6}}"," ",0,"-1/15/f*(b*tan(f*x+e)^4)^(3/2)*(-3*tan(f*x+e)^5+5*tan(f*x+e)^3+15*arctan(tan(f*x+e))-15*tan(f*x+e))/tan(f*x+e)^6","A"
15,1,42,46,0.230000," ","int((b*tan(f*x+e)^4)^(1/2),x)","-\frac{\sqrt{b \left(\tan^{4}\left(f x +e \right)\right)}\, \left(-\tan \left(f x +e \right)+\arctan \left(\tan \left(f x +e \right)\right)\right)}{f \tan \left(f x +e \right)^{2}}"," ",0,"-1/f*(b*tan(f*x+e)^4)^(1/2)*(-tan(f*x+e)+arctan(tan(f*x+e)))/tan(f*x+e)^2","A"
16,1,40,47,0.270000," ","int(1/(b*tan(f*x+e)^4)^(1/2),x)","-\frac{\tan \left(f x +e \right) \left(\arctan \left(\tan \left(f x +e \right)\right) \tan \left(f x +e \right)+1\right)}{f \sqrt{b \left(\tan^{4}\left(f x +e \right)\right)}}"," ",0,"-1/f*tan(f*x+e)*(arctan(tan(f*x+e))*tan(f*x+e)+1)/(b*tan(f*x+e)^4)^(1/2)","A"
17,1,63,107,0.227000," ","int(1/(b*tan(f*x+e)^4)^(3/2),x)","-\frac{\tan \left(f x +e \right) \left(15 \arctan \left(\tan \left(f x +e \right)\right) \left(\tan^{5}\left(f x +e \right)\right)+15 \left(\tan^{4}\left(f x +e \right)\right)-5 \left(\tan^{2}\left(f x +e \right)\right)+3\right)}{15 f \left(b \left(\tan^{4}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/15/f*tan(f*x+e)*(15*arctan(tan(f*x+e))*tan(f*x+e)^5+15*tan(f*x+e)^4-5*tan(f*x+e)^2+3)/(b*tan(f*x+e)^4)^(3/2)","A"
18,1,83,163,0.246000," ","int(1/(b*tan(f*x+e)^4)^(5/2),x)","-\frac{\tan \left(f x +e \right) \left(315 \arctan \left(\tan \left(f x +e \right)\right) \left(\tan^{9}\left(f x +e \right)\right)+315 \left(\tan^{8}\left(f x +e \right)\right)-105 \left(\tan^{6}\left(f x +e \right)\right)+63 \left(\tan^{4}\left(f x +e \right)\right)-45 \left(\tan^{2}\left(f x +e \right)\right)+35\right)}{315 f \left(b \left(\tan^{4}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-1/315/f*tan(f*x+e)*(315*arctan(tan(f*x+e))*tan(f*x+e)^9+315*tan(f*x+e)^8-105*tan(f*x+e)^6+63*tan(f*x+e)^4-45*tan(f*x+e)^2+35)/(b*tan(f*x+e)^4)^(5/2)","A"
19,0,0,63,12.309000," ","int((b*tan(f*x+e)^n)^(5/2),x)","\int \left(b \left(\tan^{n}\left(f x +e \right)\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((b*tan(f*x+e)^n)^(5/2),x)","F"
20,0,0,59,1.216000," ","int((b*tan(f*x+e)^n)^(3/2),x)","\int \left(b \left(\tan^{n}\left(f x +e \right)\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((b*tan(f*x+e)^n)^(3/2),x)","F"
21,0,0,52,1.274000," ","int((b*tan(f*x+e)^n)^(1/2),x)","\int \sqrt{b \left(\tan^{n}\left(f x +e \right)\right)}\, dx"," ",0,"int((b*tan(f*x+e)^n)^(1/2),x)","F"
22,0,0,54,1.308000," ","int(1/(b*tan(f*x+e)^n)^(1/2),x)","\int \frac{1}{\sqrt{b \left(\tan^{n}\left(f x +e \right)\right)}}\, dx"," ",0,"int(1/(b*tan(f*x+e)^n)^(1/2),x)","F"
23,0,0,63,1.234000," ","int(1/(b*tan(f*x+e)^n)^(3/2),x)","\int \frac{1}{\left(b \left(\tan^{n}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(b*tan(f*x+e)^n)^(3/2),x)","F"
24,0,0,63,1.075000," ","int(1/(b*tan(f*x+e)^n)^(5/2),x)","\int \frac{1}{\left(b \left(\tan^{n}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(b*tan(f*x+e)^n)^(5/2),x)","F"
25,-1,0,55,180.000000," ","int((b*tan(f*x+e)^n)^p,x)","\int \left(b \left(\tan^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((b*tan(f*x+e)^n)^p,x)","F"
26,0,0,49,1.228000," ","int((b*tan(f*x+e)^2)^p,x)","\int \left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((b*tan(f*x+e)^2)^p,x)","F"
27,0,0,53,1.579000," ","int((b*tan(f*x+e)^3)^p,x)","\int \left(b \left(\tan^{3}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((b*tan(f*x+e)^3)^p,x)","F"
28,0,0,53,1.186000," ","int((b*tan(f*x+e)^4)^p,x)","\int \left(b \left(\tan^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((b*tan(f*x+e)^4)^p,x)","F"
29,-1,0,32,180.000000," ","int((b*tan(f*x+e)^n)^(1/n),x)","\int \left(b \left(\tan^{n}\left(f x +e \right)\right)\right)^{\frac{1}{n}}\, dx"," ",0,"int((b*tan(f*x+e)^n)^(1/n),x)","F"
30,1,92,66,0.669000," ","int(sin(f*x+e)^5*(a+b*tan(f*x+e)^2),x)","\frac{-\frac{a \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+b \left(\frac{\sin^{8}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)\right)}{f}"," ",0,"1/f*(-1/5*a*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+b*(sin(f*x+e)^8/cos(f*x+e)+(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)))","A"
31,1,72,46,0.602000," ","int(sin(f*x+e)^3*(a+b*tan(f*x+e)^2),x)","\frac{-\frac{a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+b \left(\frac{\sin^{6}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)\right)}{f}"," ",0,"1/f*(-1/3*a*(2+sin(f*x+e)^2)*cos(f*x+e)+b*(sin(f*x+e)^6/cos(f*x+e)+(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)))","A"
32,1,52,28,0.448000," ","int(sin(f*x+e)*(a+b*tan(f*x+e)^2),x)","\frac{-a \cos \left(f x +e \right)+b \left(\frac{\sin^{4}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)\right)}{f}"," ",0,"1/f*(-a*cos(f*x+e)+b*(sin(f*x+e)^4/cos(f*x+e)+(2+sin(f*x+e)^2)*cos(f*x+e)))","A"
33,1,36,25,0.433000," ","int(csc(f*x+e)*(a+b*tan(f*x+e)^2),x)","\frac{a \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}+\frac{b}{f \cos \left(f x +e \right)}"," ",0,"1/f*a*ln(csc(f*x+e)-cot(f*x+e))+1/f*b/cos(f*x+e)","A"
34,1,76,47,0.565000," ","int(csc(f*x+e)^3*(a+b*tan(f*x+e)^2),x)","-\frac{a \cot \left(f x +e \right) \csc \left(f x +e \right)}{2 f}+\frac{a \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}+\frac{b}{f \cos \left(f x +e \right)}+\frac{b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}"," ",0,"-1/2*a*cot(f*x+e)*csc(f*x+e)/f+1/2/f*a*ln(csc(f*x+e)-cot(f*x+e))+1/f*b/cos(f*x+e)+1/f*b*ln(csc(f*x+e)-cot(f*x+e))","A"
35,1,120,73,0.526000," ","int(csc(f*x+e)^5*(a+b*tan(f*x+e)^2),x)","-\frac{a \cot \left(f x +e \right) \left(\csc^{3}\left(f x +e \right)\right)}{4 f}-\frac{3 a \cot \left(f x +e \right) \csc \left(f x +e \right)}{8 f}+\frac{3 a \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{8 f}-\frac{b}{2 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)}+\frac{3 b}{2 f \cos \left(f x +e \right)}+\frac{3 b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}"," ",0,"-1/4/f*a*cot(f*x+e)*csc(f*x+e)^3-3/8*a*cot(f*x+e)*csc(f*x+e)/f+3/8/f*a*ln(csc(f*x+e)-cot(f*x+e))-1/2/f*b/sin(f*x+e)^2/cos(f*x+e)+3/2/f*b/cos(f*x+e)+3/2/f*b*ln(csc(f*x+e)-cot(f*x+e))","A"
36,1,122,94,0.679000," ","int(sin(f*x+e)^6*(a+b*tan(f*x+e)^2),x)","\frac{a \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+b \left(\frac{\sin^{9}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\sin^{7}\left(f x +e \right)+\frac{7 \left(\sin^{5}\left(f x +e \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(f x +e \right)\right)}{24}+\frac{35 \sin \left(f x +e \right)}{16}\right) \cos \left(f x +e \right)-\frac{35 f x}{16}-\frac{35 e}{16}\right)}{f}"," ",0,"1/f*(a*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+b*(sin(f*x+e)^9/cos(f*x+e)+(sin(f*x+e)^7+7/6*sin(f*x+e)^5+35/24*sin(f*x+e)^3+35/16*sin(f*x+e))*cos(f*x+e)-35/16*f*x-35/16*e))","A"
37,1,102,68,0.581000," ","int(sin(f*x+e)^4*(a+b*tan(f*x+e)^2),x)","\frac{a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+b \left(\frac{\sin^{7}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)-\frac{15 f x}{8}-\frac{15 e}{8}\right)}{f}"," ",0,"1/f*(a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+b*(sin(f*x+e)^7/cos(f*x+e)+(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)-15/8*f*x-15/8*e))","A"
38,1,81,42,0.447000," ","int(sin(f*x+e)^2*(a+b*tan(f*x+e)^2),x)","\frac{a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+b \left(\frac{\sin^{5}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)-\frac{3 f x}{2}-\frac{3 e}{2}\right)}{f}"," ",0,"1/f*(a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+b*(sin(f*x+e)^5/cos(f*x+e)+(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/2*f*x-3/2*e))","A"
39,1,29,19,0.025000," ","int(a+b*tan(f*x+e)^2,x)","a x +\frac{b \tan \left(f x +e \right)}{f}-\frac{b \arctan \left(\tan \left(f x +e \right)\right)}{f}"," ",0,"a*x+b*tan(f*x+e)/f-b/f*arctan(tan(f*x+e))","A"
40,1,23,24,0.568000," ","int(csc(f*x+e)^2*(a+b*tan(f*x+e)^2),x)","\frac{-a \cot \left(f x +e \right)+b \tan \left(f x +e \right)}{f}"," ",0,"1/f*(-a*cot(f*x+e)+b*tan(f*x+e))","A"
41,1,54,40,0.712000," ","int(csc(f*x+e)^4*(a+b*tan(f*x+e)^2),x)","\frac{a \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(f x +e \right)\right)}{3}\right) \cot \left(f x +e \right)+b \left(\frac{1}{\sin \left(f x +e \right) \cos \left(f x +e \right)}-2 \cot \left(f x +e \right)\right)}{f}"," ",0,"1/f*(a*(-2/3-1/3*csc(f*x+e)^2)*cot(f*x+e)+b*(1/sin(f*x+e)/cos(f*x+e)-2*cot(f*x+e)))","A"
42,1,83,60,0.707000," ","int(csc(f*x+e)^6*(a+b*tan(f*x+e)^2),x)","\frac{a \left(-\frac{8}{15}-\frac{\left(\csc^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\csc^{2}\left(f x +e \right)\right)}{15}\right) \cot \left(f x +e \right)+b \left(-\frac{1}{3 \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)}+\frac{4}{3 \sin \left(f x +e \right) \cos \left(f x +e \right)}-\frac{8 \cot \left(f x +e \right)}{3}\right)}{f}"," ",0,"1/f*(a*(-8/15-1/5*csc(f*x+e)^4-4/15*csc(f*x+e)^2)*cot(f*x+e)+b*(-1/3/sin(f*x+e)^3/cos(f*x+e)+4/3/sin(f*x+e)/cos(f*x+e)-8/3*cot(f*x+e)))","A"
43,1,185,101,0.744000," ","int(sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x)","\frac{-\frac{a^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+2 a b \left(\frac{\sin^{8}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)\right)+b^{2} \left(\frac{\sin^{10}\left(f x +e \right)}{3 \cos \left(f x +e \right)^{3}}-\frac{7 \left(\sin^{10}\left(f x +e \right)\right)}{3 \cos \left(f x +e \right)}-\frac{7 \left(\frac{128}{35}+\sin^{8}\left(f x +e \right)+\frac{8 \left(\sin^{6}\left(f x +e \right)\right)}{7}+\frac{48 \left(\sin^{4}\left(f x +e \right)\right)}{35}+\frac{64 \left(\sin^{2}\left(f x +e \right)\right)}{35}\right) \cos \left(f x +e \right)}{3}\right)}{f}"," ",0,"1/f*(-1/5*a^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+2*a*b*(sin(f*x+e)^8/cos(f*x+e)+(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e))+b^2*(1/3*sin(f*x+e)^10/cos(f*x+e)^3-7/3*sin(f*x+e)^10/cos(f*x+e)-7/3*(128/35+sin(f*x+e)^8+8/7*sin(f*x+e)^6+48/35*sin(f*x+e)^4+64/35*sin(f*x+e)^2)*cos(f*x+e)))","A"
44,1,155,76,0.867000," ","int(sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x)","\frac{-\frac{a^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 a b \left(\frac{\sin^{6}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)\right)+b^{2} \left(\frac{\sin^{8}\left(f x +e \right)}{3 \cos \left(f x +e \right)^{3}}-\frac{5 \left(\sin^{8}\left(f x +e \right)\right)}{3 \cos \left(f x +e \right)}-\frac{5 \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{3}\right)}{f}"," ",0,"1/f*(-1/3*a^2*(2+sin(f*x+e)^2)*cos(f*x+e)+2*a*b*(sin(f*x+e)^6/cos(f*x+e)+(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e))+b^2*(1/3*sin(f*x+e)^8/cos(f*x+e)^3-5/3*sin(f*x+e)^8/cos(f*x+e)-5/3*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)))","B"
45,1,125,52,0.716000," ","int(sin(f*x+e)*(a+b*tan(f*x+e)^2)^2,x)","\frac{-\cos \left(f x +e \right) a^{2}+2 a b \left(\frac{\sin^{4}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)\right)+b^{2} \left(\frac{\sin^{6}\left(f x +e \right)}{3 \cos \left(f x +e \right)^{3}}-\frac{\sin^{6}\left(f x +e \right)}{\cos \left(f x +e \right)}-\left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)\right)}{f}"," ",0,"1/f*(-cos(f*x+e)*a^2+2*a*b*(sin(f*x+e)^4/cos(f*x+e)+(2+sin(f*x+e)^2)*cos(f*x+e))+b^2*(1/3*sin(f*x+e)^6/cos(f*x+e)^3-sin(f*x+e)^6/cos(f*x+e)-(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)))","B"
46,1,124,50,0.551000," ","int(csc(f*x+e)*(a+b*tan(f*x+e)^2)^2,x)","\frac{a^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}+\frac{2 a b}{f \cos \left(f x +e \right)}+\frac{b^{2} \left(\sin^{4}\left(f x +e \right)\right)}{3 f \cos \left(f x +e \right)^{3}}-\frac{b^{2} \left(\sin^{4}\left(f x +e \right)\right)}{3 f \cos \left(f x +e \right)}-\frac{b^{2} \left(\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3 f}-\frac{2 \cos \left(f x +e \right) b^{2}}{3 f}"," ",0,"1/f*a^2*ln(csc(f*x+e)-cot(f*x+e))+2/f*a*b/cos(f*x+e)+1/3/f*b^2*sin(f*x+e)^4/cos(f*x+e)^3-1/3/f*b^2*sin(f*x+e)^4/cos(f*x+e)-1/3/f*b^2*sin(f*x+e)^2*cos(f*x+e)-2/3/f*cos(f*x+e)*b^2","B"
47,1,100,74,0.739000," ","int(csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x)","-\frac{a^{2} \csc \left(f x +e \right) \cot \left(f x +e \right)}{2 f}+\frac{a^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}+\frac{2 a b}{f \cos \left(f x +e \right)}+\frac{2 a b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}+\frac{b^{2}}{3 f \cos \left(f x +e \right)^{3}}"," ",0,"-1/2/f*a^2*csc(f*x+e)*cot(f*x+e)+1/2/f*a^2*ln(csc(f*x+e)-cot(f*x+e))+2/f*a*b/cos(f*x+e)+2/f*a*b*ln(csc(f*x+e)-cot(f*x+e))+1/3/f*b^2/cos(f*x+e)^3","A"
48,1,183,113,0.642000," ","int(csc(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x)","-\frac{a^{2} \cot \left(f x +e \right) \left(\csc^{3}\left(f x +e \right)\right)}{4 f}-\frac{3 a^{2} \csc \left(f x +e \right) \cot \left(f x +e \right)}{8 f}+\frac{3 a^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{8 f}-\frac{a b}{f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)}+\frac{3 a b}{f \cos \left(f x +e \right)}+\frac{3 a b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}+\frac{b^{2}}{3 f \cos \left(f x +e \right)^{3}}+\frac{b^{2}}{f \cos \left(f x +e \right)}+\frac{b^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}"," ",0,"-1/4/f*a^2*cot(f*x+e)*csc(f*x+e)^3-3/8/f*a^2*csc(f*x+e)*cot(f*x+e)+3/8/f*a^2*ln(csc(f*x+e)-cot(f*x+e))-1/f*a*b/sin(f*x+e)^2/cos(f*x+e)+3/f*a*b/cos(f*x+e)+3/f*a*b*ln(csc(f*x+e)-cot(f*x+e))+1/3/f*b^2/cos(f*x+e)^3+1/f*b^2/cos(f*x+e)+1/f*b^2*ln(csc(f*x+e)-cot(f*x+e))","A"
49,1,199,112,0.776000," ","int(sin(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+2 a b \left(\frac{\sin^{7}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)-\frac{15 f x}{8}-\frac{15 e}{8}\right)+b^{2} \left(\frac{\sin^{9}\left(f x +e \right)}{3 \cos \left(f x +e \right)^{3}}-\frac{2 \left(\sin^{9}\left(f x +e \right)\right)}{\cos \left(f x +e \right)}-2 \left(\sin^{7}\left(f x +e \right)+\frac{7 \left(\sin^{5}\left(f x +e \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(f x +e \right)\right)}{24}+\frac{35 \sin \left(f x +e \right)}{16}\right) \cos \left(f x +e \right)+\frac{35 f x}{8}+\frac{35 e}{8}\right)}{f}"," ",0,"1/f*(a^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+2*a*b*(sin(f*x+e)^7/cos(f*x+e)+(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)-15/8*f*x-15/8*e)+b^2*(1/3*sin(f*x+e)^9/cos(f*x+e)^3-2*sin(f*x+e)^9/cos(f*x+e)-2*(sin(f*x+e)^7+7/6*sin(f*x+e)^5+35/24*sin(f*x+e)^3+35/16*sin(f*x+e))*cos(f*x+e)+35/8*f*x+35/8*e))","A"
50,1,168,77,0.705000," ","int(sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x)","\frac{a^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+2 a b \left(\frac{\sin^{5}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)-\frac{3 f x}{2}-\frac{3 e}{2}\right)+b^{2} \left(\frac{\sin^{7}\left(f x +e \right)}{3 \cos \left(f x +e \right)^{3}}-\frac{4 \left(\sin^{7}\left(f x +e \right)\right)}{3 \cos \left(f x +e \right)}-\frac{4 \left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{3}+\frac{5 f x}{2}+\frac{5 e}{2}\right)}{f}"," ",0,"1/f*(a^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2*a*b*(sin(f*x+e)^5/cos(f*x+e)+(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/2*f*x-3/2*e)+b^2*(1/3*sin(f*x+e)^7/cos(f*x+e)^3-4/3*sin(f*x+e)^7/cos(f*x+e)-4/3*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/2*f*x+5/2*e))","B"
51,1,87,44,0.025000," ","int((a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{2 a b \tan \left(f x +e \right)}{f}-\frac{b^{2} \tan \left(f x +e \right)}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2}}{f}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f}"," ",0,"1/3*b^2*tan(f*x+e)^3/f+2*a*b*tan(f*x+e)/f-b^2*tan(f*x+e)/f+1/f*arctan(tan(f*x+e))*a^2-2/f*arctan(tan(f*x+e))*a*b+1/f*arctan(tan(f*x+e))*b^2","A"
52,1,48,44,0.633000," ","int(csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x)","\frac{-a^{2} \cot \left(f x +e \right)+2 a b \tan \left(f x +e \right)+\frac{b^{2} \left(\sin^{3}\left(f x +e \right)\right)}{3 \cos \left(f x +e \right)^{3}}}{f}"," ",0,"1/f*(-a^2*cot(f*x+e)+2*a*b*tan(f*x+e)+1/3*b^2*sin(f*x+e)^3/cos(f*x+e)^3)","A"
53,1,81,66,0.903000," ","int(csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x)","\frac{a^{2} \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(f x +e \right)\right)}{3}\right) \cot \left(f x +e \right)+2 a b \left(\frac{1}{\sin \left(f x +e \right) \cos \left(f x +e \right)}-2 \cot \left(f x +e \right)\right)-b^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(a^2*(-2/3-1/3*csc(f*x+e)^2)*cot(f*x+e)+2*a*b*(1/sin(f*x+e)/cos(f*x+e)-2*cot(f*x+e))-b^2*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e))","A"
54,1,136,87,0.740000," ","int(csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,x)","\frac{a^{2} \left(-\frac{8}{15}-\frac{\left(\csc^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\csc^{2}\left(f x +e \right)\right)}{15}\right) \cot \left(f x +e \right)+2 a b \left(-\frac{1}{3 \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)}+\frac{4}{3 \sin \left(f x +e \right) \cos \left(f x +e \right)}-\frac{8 \cot \left(f x +e \right)}{3}\right)+b^{2} \left(\frac{1}{3 \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}+\frac{4}{3 \sin \left(f x +e \right) \cos \left(f x +e \right)}-\frac{8 \cot \left(f x +e \right)}{3}\right)}{f}"," ",0,"1/f*(a^2*(-8/15-1/5*csc(f*x+e)^4-4/15*csc(f*x+e)^2)*cot(f*x+e)+2*a*b*(-1/3/sin(f*x+e)^3/cos(f*x+e)+4/3/sin(f*x+e)/cos(f*x+e)-8/3*cot(f*x+e))+b^2*(1/3/sin(f*x+e)/cos(f*x+e)^3+4/3/sin(f*x+e)/cos(f*x+e)-8/3*cot(f*x+e)))","A"
55,1,205,105,0.519000," ","int(sin(f*x+e)^5/(a+b*tan(f*x+e)^2),x)","-\frac{\left(\cos^{5}\left(f x +e \right)\right) a^{2}}{5 f \left(a -b \right)^{3}}+\frac{2 \left(\cos^{5}\left(f x +e \right)\right) a b}{5 f \left(a -b \right)^{3}}-\frac{\left(\cos^{5}\left(f x +e \right)\right) b^{2}}{5 f \left(a -b \right)^{3}}+\frac{2 \left(\cos^{3}\left(f x +e \right)\right) a^{2}}{3 f \left(a -b \right)^{3}}-\frac{\left(\cos^{3}\left(f x +e \right)\right) a b}{f \left(a -b \right)^{3}}+\frac{\left(\cos^{3}\left(f x +e \right)\right) b^{2}}{3 f \left(a -b \right)^{3}}-\frac{a^{2} \cos \left(f x +e \right)}{\left(a -b \right)^{3} f}+\frac{a^{2} b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \left(a -b \right)^{3} \sqrt{\left(a -b \right) b}}"," ",0,"-1/5/f/(a-b)^3*cos(f*x+e)^5*a^2+2/5/f/(a-b)^3*cos(f*x+e)^5*a*b-1/5/f/(a-b)^3*cos(f*x+e)^5*b^2+2/3/f/(a-b)^3*cos(f*x+e)^3*a^2-1/f/(a-b)^3*cos(f*x+e)^3*a*b+1/3/f/(a-b)^3*cos(f*x+e)^3*b^2-a^2*cos(f*x+e)/(a-b)^3/f+1/f*a^2*b/(a-b)^3/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))","A"
56,1,107,74,0.570000," ","int(sin(f*x+e)^3/(a+b*tan(f*x+e)^2),x)","\frac{a \left(\cos^{3}\left(f x +e \right)\right)}{3 f \left(a -b \right)^{2}}-\frac{b \left(\cos^{3}\left(f x +e \right)\right)}{3 f \left(a -b \right)^{2}}-\frac{a \cos \left(f x +e \right)}{\left(a -b \right)^{2} f}+\frac{a b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \left(a -b \right)^{2} \sqrt{\left(a -b \right) b}}"," ",0,"1/3/f/(a-b)^2*a*cos(f*x+e)^3-1/3/f/(a-b)^2*b*cos(f*x+e)^3-a*cos(f*x+e)/(a-b)^2/f+1/f*a*b/(a-b)^2/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))","A"
57,1,63,52,0.382000," ","int(sin(f*x+e)/(a+b*tan(f*x+e)^2),x)","-\frac{\cos \left(f x +e \right)}{\left(a -b \right) f}+\frac{b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \left(a -b \right) \sqrt{\left(a -b \right) b}}"," ",0,"-cos(f*x+e)/(a-b)/f+1/f*b/(a-b)/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))","A"
58,1,75,52,0.565000," ","int(csc(f*x+e)/(a+b*tan(f*x+e)^2),x)","\frac{b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f a \sqrt{\left(a -b \right) b}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f a}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f a}"," ",0,"1/f/a*b/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+1/2/f/a*ln(-1+cos(f*x+e))-1/2/f/a*ln(1+cos(f*x+e))","A"
59,1,189,77,0.694000," ","int(csc(f*x+e)^3/(a+b*tan(f*x+e)^2),x)","\frac{b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f a \sqrt{\left(a -b \right) b}}-\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{2} \sqrt{\left(a -b \right) b}}+\frac{1}{4 f a \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{4 f a}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b}{2 f \,a^{2}}+\frac{1}{4 f a \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{4 f a}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) b}{2 f \,a^{2}}"," ",0,"1/f/a*b/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-1/f*b^2/a^2/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+1/4/f/a/(-1+cos(f*x+e))+1/4/f/a*ln(-1+cos(f*x+e))-1/2/f/a^2*ln(-1+cos(f*x+e))*b+1/4/f/a/(1+cos(f*x+e))-1/4/f/a*ln(1+cos(f*x+e))+1/2/f/a^2*ln(1+cos(f*x+e))*b","B"
60,1,344,116,0.597000," ","int(csc(f*x+e)^5/(a+b*tan(f*x+e)^2),x)","\frac{b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f a \sqrt{\left(a -b \right) b}}-\frac{2 b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{2} \sqrt{\left(a -b \right) b}}+\frac{b^{3} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{3} \sqrt{\left(a -b \right) b}}-\frac{1}{16 f a \left(-1+\cos \left(f x +e \right)\right)^{2}}+\frac{3}{16 f a \left(-1+\cos \left(f x +e \right)\right)}-\frac{b}{4 f \,a^{2} \left(-1+\cos \left(f x +e \right)\right)}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right)}{16 f a}-\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b}{4 f \,a^{2}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{2 f \,a^{3}}+\frac{1}{16 f a \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{3}{16 f a \left(1+\cos \left(f x +e \right)\right)}-\frac{b}{4 f \,a^{2} \left(1+\cos \left(f x +e \right)\right)}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right)}{16 f a}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b}{4 f \,a^{2}}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{2 f \,a^{3}}"," ",0,"1/f/a*b/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-2/f*b^2/a^2/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+1/f*b^3/a^3/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-1/16/f/a/(-1+cos(f*x+e))^2+3/16/f/a/(-1+cos(f*x+e))-1/4/f/a^2/(-1+cos(f*x+e))*b+3/16/f/a*ln(-1+cos(f*x+e))-3/4/f/a^2*ln(-1+cos(f*x+e))*b+1/2/f/a^3*ln(-1+cos(f*x+e))*b^2+1/16/f/a/(1+cos(f*x+e))^2+3/16/f/a/(1+cos(f*x+e))-1/4/f/a^2/(1+cos(f*x+e))*b-3/16/f/a*ln(1+cos(f*x+e))+3/4/f/a^2*ln(1+cos(f*x+e))*b-1/2/f/a^3*ln(1+cos(f*x+e))*b^2","B"
61,1,545,162,0.524000," ","int(sin(f*x+e)^6/(a+b*tan(f*x+e)^2),x)","-\frac{b \,a^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \left(a -b \right)^{4} \sqrt{a b}}-\frac{11 \left(\tan^{5}\left(f x +e \right)\right) a^{3}}{16 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{15 \left(\tan^{5}\left(f x +e \right)\right) a^{2} b}{16 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \left(\tan^{5}\left(f x +e \right)\right) b^{2} a}{16 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{\left(\tan^{5}\left(f x +e \right)\right) b^{3}}{16 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right) a^{3}}{6 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{\left(\tan^{3}\left(f x +e \right)\right) a^{2} b}{2 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{\left(\tan^{3}\left(f x +e \right)\right) b^{2} a}{2 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b^{3}}{6 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \tan \left(f x +e \right) a^{3}}{16 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{\tan \left(f x +e \right) a^{2} b}{16 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{5 \tan \left(f x +e \right) b^{2} a}{16 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{\tan \left(f x +e \right) b^{3}}{16 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{5 \arctan \left(\tan \left(f x +e \right)\right) a^{3}}{16 f \left(a -b \right)^{4}}+\frac{15 \arctan \left(\tan \left(f x +e \right)\right) a^{2} b}{16 f \left(a -b \right)^{4}}-\frac{5 \arctan \left(\tan \left(f x +e \right)\right) b^{2} a}{16 f \left(a -b \right)^{4}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3}}{16 f \left(a -b \right)^{4}}"," ",0,"-1/f*b*a^3/(a-b)^4/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-11/16/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)^5*a^3+15/16/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)^5*a^2*b-5/16/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)^5*b^2*a+1/16/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)^5*b^3-5/6/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)^3*a^3+1/2/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)^3*a^2*b+1/2/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)^3*b^2*a-1/6/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)^3*b^3-5/16/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)*a^3+1/16/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)*a^2*b+5/16/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)*b^2*a-1/16/f/(a-b)^4/(1+tan(f*x+e)^2)^3*tan(f*x+e)*b^3+5/16/f/(a-b)^4*arctan(tan(f*x+e))*a^3+15/16/f/(a-b)^4*arctan(tan(f*x+e))*a^2*b-5/16/f/(a-b)^4*arctan(tan(f*x+e))*b^2*a+1/16/f/(a-b)^4*arctan(tan(f*x+e))*b^3","B"
62,1,304,115,0.623000," ","int(sin(f*x+e)^4/(a+b*tan(f*x+e)^2),x)","-\frac{b \,a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \left(a -b \right)^{3} \sqrt{a b}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right) a^{2}}{8 f \left(a -b \right)^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{3 \left(\tan^{3}\left(f x +e \right)\right) a b}{4 f \left(a -b \right)^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b^{2}}{8 f \left(a -b \right)^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \tan \left(f x +e \right) a^{2}}{8 f \left(a -b \right)^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{\tan \left(f x +e \right) a b}{4 f \left(a -b \right)^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{\tan \left(f x +e \right) b^{2}}{8 f \left(a -b \right)^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2}}{8 f \left(a -b \right)^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a b}{4 f \left(a -b \right)^{3}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2}}{8 f \left(a -b \right)^{3}}"," ",0,"-1/f*b*a^2/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-5/8/f/(a-b)^3/(1+tan(f*x+e)^2)^2*tan(f*x+e)^3*a^2+3/4/f/(a-b)^3/(1+tan(f*x+e)^2)^2*tan(f*x+e)^3*a*b-1/8/f/(a-b)^3/(1+tan(f*x+e)^2)^2*tan(f*x+e)^3*b^2-3/8/f/(a-b)^3/(1+tan(f*x+e)^2)^2*tan(f*x+e)*a^2+1/4/f/(a-b)^3/(1+tan(f*x+e)^2)^2*tan(f*x+e)*a*b+1/8/f/(a-b)^3/(1+tan(f*x+e)^2)^2*tan(f*x+e)*b^2+3/8/f/(a-b)^3*arctan(tan(f*x+e))*a^2+3/4/f/(a-b)^3*arctan(tan(f*x+e))*a*b-1/8/f/(a-b)^3*arctan(tan(f*x+e))*b^2","B"
63,1,137,70,0.515000," ","int(sin(f*x+e)^2/(a+b*tan(f*x+e)^2),x)","-\frac{b a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \left(a -b \right)^{2} \sqrt{a b}}-\frac{\tan \left(f x +e \right) a}{2 f \left(a -b \right)^{2} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\tan \left(f x +e \right) b}{2 f \left(a -b \right)^{2} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a}{2 f \left(a -b \right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b}{2 f \left(a -b \right)^{2}}"," ",0,"-1/f*b*a/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/2/f/(a-b)^2*tan(f*x+e)/(1+tan(f*x+e)^2)*a+1/2/f/(a-b)^2*tan(f*x+e)/(1+tan(f*x+e)^2)*b+1/2/f/(a-b)^2*arctan(tan(f*x+e))*a+1/2/f/(a-b)^2*arctan(tan(f*x+e))*b","A"
64,1,52,42,0.219000," ","int(1/(a+b*tan(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \left(a -b \right) \sqrt{a b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)}"," ",0,"-1/f*b/(a-b)/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f/(a-b)*arctan(tan(f*x+e))","A"
65,1,46,40,0.579000," ","int(csc(f*x+e)^2/(a+b*tan(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f a \sqrt{a b}}-\frac{1}{f a \tan \left(f x +e \right)}"," ",0,"-1/f/a*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/a/tan(f*x+e)","A"
66,1,107,66,0.581000," ","int(csc(f*x+e)^4/(a+b*tan(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f a \sqrt{a b}}+\frac{b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \,a^{2} \sqrt{a b}}-\frac{1}{3 f a \tan \left(f x +e \right)^{3}}-\frac{1}{f a \tan \left(f x +e \right)}+\frac{b}{f \,a^{2} \tan \left(f x +e \right)}"," ",0,"-1/f/a*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f*b^2/a^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/3/f/a/tan(f*x+e)^3-1/f/a/tan(f*x+e)+1/f/a^2/tan(f*x+e)*b","A"
67,1,191,93,0.552000," ","int(csc(f*x+e)^6/(a+b*tan(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f a \sqrt{a b}}+\frac{2 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \,a^{2} \sqrt{a b}}-\frac{b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \,a^{3} \sqrt{a b}}-\frac{1}{5 f a \tan \left(f x +e \right)^{5}}-\frac{2}{3 f a \tan \left(f x +e \right)^{3}}+\frac{b}{3 f \,a^{2} \tan \left(f x +e \right)^{3}}-\frac{1}{f a \tan \left(f x +e \right)}+\frac{2 b}{f \,a^{2} \tan \left(f x +e \right)}-\frac{b^{2}}{f \,a^{3} \tan \left(f x +e \right)}"," ",0,"-1/f/a*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+2/f*b^2/a^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f*b^3/a^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/5/f/a/tan(f*x+e)^5-2/3/f/a/tan(f*x+e)^3+1/3/f/a^2/tan(f*x+e)^3*b-1/f/a/tan(f*x+e)+2/f/a^2/tan(f*x+e)*b-1/f/a^3/tan(f*x+e)*b^2","B"
68,1,388,186,0.576000," ","int(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x)","-\frac{\left(\cos^{5}\left(f x +e \right)\right) a^{2}}{5 f \left(a -b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 \left(\cos^{5}\left(f x +e \right)\right) a b}{5 f \left(a -b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(\cos^{5}\left(f x +e \right)\right) b^{2}}{5 f \left(a -b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 \left(\cos^{3}\left(f x +e \right)\right) a^{2}}{3 f \left(a -b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 \left(\cos^{3}\left(f x +e \right)\right) a b}{3 f \left(a -b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{\cos \left(f x +e \right) a^{2}}{f \left(a -b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 \cos \left(f x +e \right) a b}{f \left(a -b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{a^{2} b \cos \left(f x +e \right)}{2 f \left(a -b \right)^{4} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{3 a^{2} b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{2 f \left(a -b \right)^{4} \sqrt{\left(a -b \right) b}}+\frac{2 a \,b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \left(a -b \right)^{4} \sqrt{\left(a -b \right) b}}"," ",0,"-1/5/f/(a-b)^2/(a^2-2*a*b+b^2)*cos(f*x+e)^5*a^2+2/5/f/(a-b)^2/(a^2-2*a*b+b^2)*cos(f*x+e)^5*a*b-1/5/f/(a-b)^2/(a^2-2*a*b+b^2)*cos(f*x+e)^5*b^2+2/3/f/(a-b)^2/(a^2-2*a*b+b^2)*cos(f*x+e)^3*a^2-2/3/f/(a-b)^2/(a^2-2*a*b+b^2)*cos(f*x+e)^3*a*b-1/f/(a-b)^2/(a^2-2*a*b+b^2)*cos(f*x+e)*a^2-2/f/(a-b)^2/(a^2-2*a*b+b^2)*cos(f*x+e)*a*b-1/2/f*a^2*b/(a-b)^4*cos(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+3/2/f*a^2*b/(a-b)^4/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+2/f*a*b^2/(a-b)^4/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))","B"
69,1,269,119,0.560000," ","int(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x)","\frac{a \left(\cos^{3}\left(f x +e \right)\right)}{3 f \left(a -b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{b \left(\cos^{3}\left(f x +e \right)\right)}{3 f \left(a -b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{a \cos \left(f x +e \right)}{f \left(a -b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\cos \left(f x +e \right) b}{f \left(a -b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{b a \cos \left(f x +e \right)}{2 f \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{3 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right) a}{2 f \left(a -b \right)^{3} \sqrt{\left(a -b \right) b}}+\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \left(a -b \right)^{3} \sqrt{\left(a -b \right) b}}"," ",0,"1/3/f/(a-b)/(a^2-2*a*b+b^2)*a*cos(f*x+e)^3-1/3/f/(a-b)/(a^2-2*a*b+b^2)*b*cos(f*x+e)^3-1/f/(a-b)/(a^2-2*a*b+b^2)*a*cos(f*x+e)-1/f/(a-b)/(a^2-2*a*b+b^2)*cos(f*x+e)*b-1/2/f*b/(a-b)^3*a*cos(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+3/2/f*b/(a-b)^3/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))*a+1/f*b^2/(a-b)^3/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))","B"
70,1,114,87,0.419000," ","int(sin(f*x+e)/(a+b*tan(f*x+e)^2)^2,x)","-\frac{\cos \left(f x +e \right)}{f \left(a^{2}-2 a b +b^{2}\right)}-\frac{b \cos \left(f x +e \right)}{2 f \left(a -b \right)^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{3 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{2 f \left(a -b \right)^{2} \sqrt{\left(a -b \right) b}}"," ",0,"-1/f/(a^2-2*a*b+b^2)*cos(f*x+e)-1/2/f*b/(a-b)^2*cos(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+3/2/f*b/(a-b)^2/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))","A"
71,1,179,98,0.644000," ","int(csc(f*x+e)/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b \cos \left(f x +e \right)}{2 f a \left(a -b \right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{3 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{2 f a \left(a -b \right) \sqrt{\left(a -b \right) b}}-\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{2} \left(a -b \right) \sqrt{\left(a -b \right) b}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \,a^{2}}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \,a^{2}}"," ",0,"-1/2/f*b/a/(a-b)*cos(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+3/2/f*b/a/(a-b)/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-1/f*b^2/a^2/(a-b)/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+1/2/f/a^2*ln(-1+cos(f*x+e))-1/2/f/a^2*ln(1+cos(f*x+e))","A"
72,1,229,133,0.652000," ","int(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b \cos \left(f x +e \right)}{2 f \,a^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{3 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{2 f \,a^{2} \sqrt{\left(a -b \right) b}}-\frac{2 b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{3} \sqrt{\left(a -b \right) b}}+\frac{1}{4 f \,a^{2} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{4 f \,a^{2}}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b}{f \,a^{3}}+\frac{1}{4 f \,a^{2} \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{4 f \,a^{2}}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) b}{f \,a^{3}}"," ",0,"-1/2/f*b/a^2*cos(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+3/2/f*b/a^2/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-2/f*b^2/a^3/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+1/4/f/a^2/(-1+cos(f*x+e))+1/4/f/a^2*ln(-1+cos(f*x+e))-1/f/a^3*ln(-1+cos(f*x+e))*b+1/4/f/a^2/(1+cos(f*x+e))-1/4/f/a^2*ln(1+cos(f*x+e))+1/f/a^3*ln(1+cos(f*x+e))*b","A"
73,1,428,192,0.568000," ","int(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b \cos \left(f x +e \right)}{2 f \,a^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{b^{2} \cos \left(f x +e \right)}{2 f \,a^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{3 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{2 f \,a^{2} \sqrt{\left(a -b \right) b}}-\frac{9 b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{2 f \,a^{3} \sqrt{\left(a -b \right) b}}+\frac{3 b^{3} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{4} \sqrt{\left(a -b \right) b}}-\frac{1}{16 f \,a^{2} \left(-1+\cos \left(f x +e \right)\right)^{2}}+\frac{3}{16 f \,a^{2} \left(-1+\cos \left(f x +e \right)\right)}-\frac{b}{2 f \,a^{3} \left(-1+\cos \left(f x +e \right)\right)}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right)}{16 f \,a^{2}}-\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b}{2 f \,a^{3}}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{2 f \,a^{4}}+\frac{1}{16 f \,a^{2} \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{3}{16 f \,a^{2} \left(1+\cos \left(f x +e \right)\right)}-\frac{b}{2 f \,a^{3} \left(1+\cos \left(f x +e \right)\right)}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right)}{16 f \,a^{2}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b}{2 f \,a^{3}}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{2 f \,a^{4}}"," ",0,"-1/2/f*b/a^2*cos(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/2/f*b^2/a^3*cos(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+3/2/f*b/a^2/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-9/2/f*b^2/a^3/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+3/f*b^3/a^4/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-1/16/f/a^2/(-1+cos(f*x+e))^2+3/16/f/a^2/(-1+cos(f*x+e))-1/2/f/a^3/(-1+cos(f*x+e))*b+3/16/f/a^2*ln(-1+cos(f*x+e))-3/2/f/a^3*ln(-1+cos(f*x+e))*b+3/2/f/a^4*ln(-1+cos(f*x+e))*b^2+1/16/f/a^2/(1+cos(f*x+e))^2+3/16/f/a^2/(1+cos(f*x+e))-1/2/f/a^3/(1+cos(f*x+e))*b-3/16/f/a^2*ln(1+cos(f*x+e))+3/2/f/a^3*ln(1+cos(f*x+e))*b-3/2/f/a^4*ln(1+cos(f*x+e))*b^2","B"
74,1,411,178,0.586000," ","int(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x)","-\frac{a^{2} b \tan \left(f x +e \right)}{2 f \left(a -b \right)^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{a \,b^{2} \tan \left(f x +e \right)}{2 f \left(a -b \right)^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 a^{2} b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \left(a -b \right)^{4} \sqrt{a b}}-\frac{3 a \,b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \left(a -b \right)^{4} \sqrt{a b}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right) a^{2}}{8 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{\left(\tan^{3}\left(f x +e \right)\right) a b}{4 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{3 \left(\tan^{3}\left(f x +e \right)\right) b^{2}}{8 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \tan \left(f x +e \right) a^{2}}{8 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{5 \tan \left(f x +e \right) b^{2}}{8 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{\tan \left(f x +e \right) a b}{4 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{9 \arctan \left(\tan \left(f x +e \right)\right) a b}{4 f \left(a -b \right)^{4}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{8 f \left(a -b \right)^{4}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2}}{8 f \left(a -b \right)^{4}}"," ",0,"-1/2/f*a^2*b/(a-b)^4*tan(f*x+e)/(a+b*tan(f*x+e)^2)+1/2/f*a*b^2/(a-b)^4*tan(f*x+e)/(a+b*tan(f*x+e)^2)-3/2/f*a^2*b/(a-b)^4/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-3/2/f*a*b^2/(a-b)^4/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-5/8/f/(a-b)^4/(1+tan(f*x+e)^2)^2*tan(f*x+e)^3*a^2+1/4/f/(a-b)^4/(1+tan(f*x+e)^2)^2*tan(f*x+e)^3*a*b+3/8/f/(a-b)^4/(1+tan(f*x+e)^2)^2*tan(f*x+e)^3*b^2-3/8/f/(a-b)^4/(1+tan(f*x+e)^2)^2*tan(f*x+e)*a^2+5/8/f/(a-b)^4/(1+tan(f*x+e)^2)^2*tan(f*x+e)*b^2-1/4/f/(a-b)^4/(1+tan(f*x+e)^2)^2*tan(f*x+e)*a*b+9/4/f/(a-b)^4*arctan(tan(f*x+e))*a*b+3/8/f/(a-b)^4*arctan(tan(f*x+e))*b^2+3/8/f/(a-b)^4*arctan(tan(f*x+e))*a^2","B"
75,1,240,124,0.513000," ","int(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right) a}{2 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{b^{2} \tan \left(f x +e \right)}{2 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right) a}{2 f \left(a -b \right)^{3} \sqrt{a b}}-\frac{b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \left(a -b \right)^{3} \sqrt{a b}}-\frac{\tan \left(f x +e \right) a}{2 f \left(a -b \right)^{3} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\tan \left(f x +e \right) b}{2 f \left(a -b \right)^{3} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a}{2 f \left(a -b \right)^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b}{2 f \left(a -b \right)^{3}}"," ",0,"-1/2/f/(a-b)^3*b*tan(f*x+e)/(a+b*tan(f*x+e)^2)*a+1/2/f/(a-b)^3*b^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)-3/2/f/(a-b)^3*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))*a-1/2/f/(a-b)^3*b^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/2/f/(a-b)^3*tan(f*x+e)/(1+tan(f*x+e)^2)*a+1/2/f/(a-b)^3*tan(f*x+e)/(1+tan(f*x+e)^2)*b+1/2/f/(a-b)^3*arctan(tan(f*x+e))*a+3/2/f/(a-b)^3*arctan(tan(f*x+e))*b","A"
76,1,160,85,0.181000," ","int(1/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 \left(a -b \right)^{2} f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{b^{2} \tan \left(f x +e \right)}{2 f \left(a -b \right)^{2} a \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \left(a -b \right)^{2} \sqrt{a b}}+\frac{b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \left(a -b \right)^{2} a \sqrt{a b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{2}}"," ",0,"-1/2*b*tan(f*x+e)/(a-b)^2/f/(a+b*tan(f*x+e)^2)+1/2/f*b^2/(a-b)^2/a*tan(f*x+e)/(a+b*tan(f*x+e)^2)-3/2/f*b/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/2/f*b^2/(a-b)^2/a/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f/(a-b)^2*arctan(tan(f*x+e))","A"
77,1,75,68,0.585000," ","int(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 f \,a^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{2} \sqrt{a b}}-\frac{1}{f \,a^{2} \tan \left(f x +e \right)}"," ",0,"-1/2/f*b/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)-3/2/f*b/a^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/a^2/tan(f*x+e)","A"
78,1,169,102,0.623000," ","int(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 f \,a^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{b^{2} \tan \left(f x +e \right)}{2 f \,a^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{2} \sqrt{a b}}+\frac{5 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{3} \sqrt{a b}}-\frac{1}{3 f \,a^{2} \tan \left(f x +e \right)^{3}}-\frac{1}{f \,a^{2} \tan \left(f x +e \right)}+\frac{2 b}{f \,a^{3} \tan \left(f x +e \right)}"," ",0,"-1/2/f*b/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)+1/2/f/a^3*b^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)-3/2/f*b/a^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+5/2/f/a^3*b^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/3/f/a^2/tan(f*x+e)^3-1/f/a^2/tan(f*x+e)+2/f/a^3/tan(f*x+e)*b","A"
79,1,281,164,0.578000," ","int(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 f \,a^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{b^{2} \tan \left(f x +e \right)}{f \,a^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{b^{3} \tan \left(f x +e \right)}{2 f \,a^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{2} \sqrt{a b}}+\frac{5 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \,a^{3} \sqrt{a b}}-\frac{7 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{4} \sqrt{a b}}-\frac{1}{5 f \,a^{2} \tan \left(f x +e \right)^{5}}-\frac{2}{3 f \,a^{2} \tan \left(f x +e \right)^{3}}+\frac{2 b}{3 f \,a^{3} \tan \left(f x +e \right)^{3}}-\frac{1}{f \,a^{2} \tan \left(f x +e \right)}+\frac{4 b}{f \,a^{3} \tan \left(f x +e \right)}-\frac{3 b^{2}}{f \,a^{4} \tan \left(f x +e \right)}"," ",0,"-1/2/f*b/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)+1/f/a^3*b^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)-1/2/f*b^3/a^4*tan(f*x+e)/(a+b*tan(f*x+e)^2)-3/2/f*b/a^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+5/f/a^3*b^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-7/2/f*b^3/a^4/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/5/f/a^2/tan(f*x+e)^5-2/3/f/a^2/tan(f*x+e)^3+2/3/f/a^3/tan(f*x+e)^3*b-1/f/a^2/tan(f*x+e)+4/f/a^3/tan(f*x+e)*b-3/f/a^4/tan(f*x+e)*b^2","A"
80,1,844,244,0.642000," ","int(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x)","-\frac{\left(\cos^{5}\left(f x +e \right)\right) a^{2}}{5 f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 \left(\cos^{5}\left(f x +e \right)\right) a b}{5 f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(\cos^{5}\left(f x +e \right)\right) b^{2}}{5 f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 a^{2} \left(\cos^{3}\left(f x +e \right)\right)}{3 f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(\cos^{3}\left(f x +e \right)\right) a b}{3 f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(\cos^{3}\left(f x +e \right)\right) b^{2}}{3 f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{a^{2} \cos \left(f x +e \right)}{f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{4 a \cos \left(f x +e \right) b}{f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\cos \left(f x +e \right) b^{2}}{f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{9 b \left(\cos^{3}\left(f x +e \right)\right) a^{3}}{8 f \left(a -b \right)^{5} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{b^{2} \left(\cos^{3}\left(f x +e \right)\right) a^{2}}{8 f \left(a -b \right)^{5} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{b^{3} \left(\cos^{3}\left(f x +e \right)\right) a}{f \left(a -b \right)^{5} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}-\frac{7 b^{2} \cos \left(f x +e \right) a^{2}}{8 f \left(a -b \right)^{5} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}-\frac{b^{3} \cos \left(f x +e \right) a}{f \left(a -b \right)^{5} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{15 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right) a^{2}}{8 f \left(a -b \right)^{5} \sqrt{\left(a -b \right) b}}+\frac{5 b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right) a}{f \left(a -b \right)^{5} \sqrt{\left(a -b \right) b}}+\frac{b^{3} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \left(a -b \right)^{5} \sqrt{\left(a -b \right) b}}"," ",0,"-1/5/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a^2-2*a*b+b^2)*cos(f*x+e)^5*a^2+2/5/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a^2-2*a*b+b^2)*cos(f*x+e)^5*a*b-1/5/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a^2-2*a*b+b^2)*cos(f*x+e)^5*b^2+2/3/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a^2-2*a*b+b^2)*a^2*cos(f*x+e)^3-1/3/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a^2-2*a*b+b^2)*cos(f*x+e)^3*a*b-1/3/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a^2-2*a*b+b^2)*cos(f*x+e)^3*b^2-1/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a^2-2*a*b+b^2)*a^2*cos(f*x+e)-4/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a^2-2*a*b+b^2)*a*cos(f*x+e)*b-1/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a^2-2*a*b+b^2)*cos(f*x+e)*b^2-9/8/f*b/(a-b)^5/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3*a^3+1/8/f*b^2/(a-b)^5/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3*a^2+1/f*b^3/(a-b)^5/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3*a-7/8/f*b^2/(a-b)^5/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)*a^2-1/f*b^3/(a-b)^5/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)*a+15/8/f*b/(a-b)^5/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))*a^2+5/f*b^2/(a-b)^5/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))*a+1/f*b^3/(a-b)^5/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))","B"
81,1,504,164,0.592000," ","int(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x)","\frac{a \left(\cos^{3}\left(f x +e \right)\right)}{3 f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a -b \right)}-\frac{b \left(\cos^{3}\left(f x +e \right)\right)}{3 f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a -b \right)}-\frac{a \cos \left(f x +e \right)}{f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a -b \right)}-\frac{2 \cos \left(f x +e \right) b}{f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a -b \right)}-\frac{9 b \,a^{2} \left(\cos^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{4} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{5 b^{2} \left(\cos^{3}\left(f x +e \right)\right) a}{8 f \left(a -b \right)^{4} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{b^{3} \left(\cos^{3}\left(f x +e \right)\right)}{2 f \left(a -b \right)^{4} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}-\frac{7 b^{2} a \cos \left(f x +e \right)}{8 f \left(a -b \right)^{4} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}-\frac{b^{3} \cos \left(f x +e \right)}{2 f \left(a -b \right)^{4} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{15 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right) a}{8 f \left(a -b \right)^{4} \sqrt{\left(a -b \right) b}}+\frac{5 b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{2 f \left(a -b \right)^{4} \sqrt{\left(a -b \right) b}}"," ",0,"1/3/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a-b)*a*cos(f*x+e)^3-1/3/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a-b)*b*cos(f*x+e)^3-1/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a-b)*a*cos(f*x+e)-2/f/(a^3-3*a^2*b+3*a*b^2-b^3)/(a-b)*cos(f*x+e)*b-9/8/f*b/(a-b)^4/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*a^2*cos(f*x+e)^3+5/8/f*b^2/(a-b)^4/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3*a+1/2/f*b^3/(a-b)^4/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3-7/8/f*b^2/(a-b)^4/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*a*cos(f*x+e)-1/2/f*b^3/(a-b)^4/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)+15/8/f*b/(a-b)^4/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))*a+5/2/f*b^2/(a-b)^4/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))","B"
82,1,221,122,0.474000," ","int(sin(f*x+e)/(a+b*tan(f*x+e)^2)^3,x)","-\frac{\cos \left(f x +e \right)}{f \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{9 b a \left(\cos^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{9 b^{2} \left(\cos^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}-\frac{7 b^{2} \cos \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{15 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{8 f \left(a -b \right)^{3} \sqrt{\left(a -b \right) b}}"," ",0,"-1/f/(a^3-3*a^2*b+3*a*b^2-b^3)*cos(f*x+e)-9/8/f*b/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*a*cos(f*x+e)^3+9/8/f*b^2/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3-7/8/f*b^2/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)+15/8/f*b/(a-b)^3/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))","A"
83,1,408,152,0.789000," ","int(csc(f*x+e)/(a+b*tan(f*x+e)^2)^3,x)","-\frac{9 b \left(\cos^{3}\left(f x +e \right)\right)}{8 f a \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \left(a -b \right)}+\frac{b^{2} \left(\cos^{3}\left(f x +e \right)\right)}{2 f \,a^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \left(a -b \right)}-\frac{7 b^{2} \cos \left(f x +e \right)}{8 f a \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{b^{3} \cos \left(f x +e \right)}{2 f \,a^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{15 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{8 f a \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(a -b \right) b}}-\frac{5 b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{2 f \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(a -b \right) b}}+\frac{b^{3} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{3} \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(a -b \right) b}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \,a^{3}}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \,a^{3}}"," ",0,"-9/8/f*b/a/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/(a-b)*cos(f*x+e)^3+1/2/f*b^2/a^2/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/(a-b)*cos(f*x+e)^3-7/8/f*b^2/a/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/(a^2-2*a*b+b^2)*cos(f*x+e)+1/2/f*b^3/a^2/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/(a^2-2*a*b+b^2)*cos(f*x+e)+15/8/f*b/a/(a^2-2*a*b+b^2)/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-5/2/f*b^2/a^2/(a^2-2*a*b+b^2)/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+1/f*b^3/a^3/(a^2-2*a*b+b^2)/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+1/2/f/a^3*ln(-1+cos(f*x+e))-1/2/f/a^3*ln(1+cos(f*x+e))","B"
84,1,435,187,0.815000," ","int(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x)","-\frac{9 b \left(\cos^{3}\left(f x +e \right)\right)}{8 f \,a^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{b^{2} \left(\cos^{3}\left(f x +e \right)\right)}{f \,a^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}-\frac{7 b^{2} \cos \left(f x +e \right)}{8 f \,a^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \left(a -b \right)}+\frac{b^{3} \cos \left(f x +e \right)}{f \,a^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \left(a -b \right)}+\frac{15 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{8 f \,a^{2} \left(a -b \right) \sqrt{\left(a -b \right) b}}-\frac{5 b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{3} \left(a -b \right) \sqrt{\left(a -b \right) b}}+\frac{3 b^{3} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{4} \left(a -b \right) \sqrt{\left(a -b \right) b}}+\frac{1}{4 f \,a^{3} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{4 f \,a^{3}}-\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b}{2 f \,a^{4}}+\frac{1}{4 f \,a^{3} \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{4 f \,a^{3}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b}{2 f \,a^{4}}"," ",0,"-9/8/f*b/a^2/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3+1/f*b^2/a^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3-7/8/f*b^2/a^2/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/(a-b)*cos(f*x+e)+1/f*b^3/a^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/(a-b)*cos(f*x+e)+15/8/f*b/a^2/(a-b)/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-5/f*b^2/a^3/(a-b)/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+3/f*b^3/a^4/(a-b)/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+1/4/f/a^3/(-1+cos(f*x+e))+1/4/f/a^3*ln(-1+cos(f*x+e))-3/2/f/a^4*ln(-1+cos(f*x+e))*b+1/4/f/a^3/(1+cos(f*x+e))-1/4/f/a^3*ln(1+cos(f*x+e))+3/2/f/a^4*ln(1+cos(f*x+e))*b","B"
85,1,560,239,0.674000," ","int(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x)","-\frac{9 b \left(\cos^{3}\left(f x +e \right)\right)}{8 f \,a^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{21 b^{2} \left(\cos^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}-\frac{3 b^{3} \left(\cos^{3}\left(f x +e \right)\right)}{2 f \,a^{4} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}-\frac{7 b^{2} \cos \left(f x +e \right)}{8 f \,a^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{3 b^{3} \cos \left(f x +e \right)}{2 f \,a^{4} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{15 b \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{8 f \,a^{3} \sqrt{\left(a -b \right) b}}-\frac{15 b^{2} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{2 f \,a^{4} \sqrt{\left(a -b \right) b}}+\frac{6 b^{3} \arctan \left(\frac{\left(a -b \right) \cos \left(f x +e \right)}{\sqrt{\left(a -b \right) b}}\right)}{f \,a^{5} \sqrt{\left(a -b \right) b}}-\frac{1}{16 f \,a^{3} \left(-1+\cos \left(f x +e \right)\right)^{2}}+\frac{3}{16 f \,a^{3} \left(-1+\cos \left(f x +e \right)\right)}-\frac{3 b}{4 f \,a^{4} \left(-1+\cos \left(f x +e \right)\right)}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right)}{16 f \,a^{3}}-\frac{9 \ln \left(-1+\cos \left(f x +e \right)\right) b}{4 f \,a^{4}}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{f \,a^{5}}+\frac{1}{16 f \,a^{3} \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{3}{16 f \,a^{3} \left(1+\cos \left(f x +e \right)\right)}-\frac{3 b}{4 f \,a^{4} \left(1+\cos \left(f x +e \right)\right)}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right)}{16 f \,a^{3}}+\frac{9 \ln \left(1+\cos \left(f x +e \right)\right) b}{4 f \,a^{4}}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{f \,a^{5}}"," ",0,"-9/8/f*b/a^2/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3+21/8/f*b^2/a^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3-3/2/f*b^3/a^4/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)^3-7/8/f*b^2/a^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)+3/2/f*b^3/a^4/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*cos(f*x+e)+15/8/f*b/a^3/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-15/2/f*b^2/a^4/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))+6/f*b^3/a^5/((a-b)*b)^(1/2)*arctan((a-b)*cos(f*x+e)/((a-b)*b)^(1/2))-1/16/f/a^3/(-1+cos(f*x+e))^2+3/16/f/a^3/(-1+cos(f*x+e))-3/4/f/a^4/(-1+cos(f*x+e))*b+3/16/f/a^3*ln(-1+cos(f*x+e))-9/4/f/a^4*ln(-1+cos(f*x+e))*b+3/f/a^5*ln(-1+cos(f*x+e))*b^2+1/16/f/a^3/(1+cos(f*x+e))^2+3/16/f/a^3/(1+cos(f*x+e))-3/4/f/a^4/(1+cos(f*x+e))*b-3/16/f/a^3*ln(1+cos(f*x+e))+9/4/f/a^4*ln(1+cos(f*x+e))*b-3/f/a^5*ln(1+cos(f*x+e))*b^2","B"
86,1,598,230,0.627000," ","int(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right) a^{2}}{8 f \left(a -b \right)^{5} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{3} \left(\tan^{3}\left(f x +e \right)\right) a}{4 f \left(a -b \right)^{5} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{5 b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{5} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 b \tan \left(f x +e \right) a^{3}}{8 f \left(a -b \right)^{5} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 b^{2} \tan \left(f x +e \right) a^{2}}{4 f \left(a -b \right)^{5} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 b^{3} \tan \left(f x +e \right) a}{8 f \left(a -b \right)^{5} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{15 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right) a^{2}}{8 f \left(a -b \right)^{5} \sqrt{a b}}-\frac{15 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right) a}{4 f \left(a -b \right)^{5} \sqrt{a b}}-\frac{3 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{5} \sqrt{a b}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) a b}{4 f \left(a -b \right)^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{7 \left(\tan^{3}\left(f x +e \right)\right) b^{2}}{8 f \left(a -b \right)^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right) a^{2}}{8 f \left(a -b \right)^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \tan \left(f x +e \right) a^{2}}{8 f \left(a -b \right)^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \tan \left(f x +e \right) a b}{4 f \left(a -b \right)^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{9 \tan \left(f x +e \right) b^{2}}{8 f \left(a -b \right)^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{15 \arctan \left(\tan \left(f x +e \right)\right) a b}{4 f \left(a -b \right)^{5}}+\frac{15 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{8 f \left(a -b \right)^{5}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) a^{2}}{8 f \left(a -b \right)^{5}}"," ",0,"-7/8/f*b^2/(a-b)^5/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3*a^2+1/4/f*b^3/(a-b)^5/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3*a+5/8/f*b^4/(a-b)^5/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-9/8/f*b/(a-b)^5/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)*a^3+3/4/f*b^2/(a-b)^5/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)*a^2+3/8/f*b^3/(a-b)^5/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)*a-15/8/f*b/(a-b)^5/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))*a^2-15/4/f*b^2/(a-b)^5/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))*a-3/8/f*b^3/(a-b)^5/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/4/f/(a-b)^5/(1+tan(f*x+e)^2)^2*tan(f*x+e)^3*a*b+7/8/f/(a-b)^5/(1+tan(f*x+e)^2)^2*tan(f*x+e)^3*b^2-5/8/f/(a-b)^5/(1+tan(f*x+e)^2)^2*tan(f*x+e)^3*a^2-3/8/f/(a-b)^5/(1+tan(f*x+e)^2)^2*tan(f*x+e)*a^2-3/4/f/(a-b)^5/(1+tan(f*x+e)^2)^2*tan(f*x+e)*a*b+9/8/f/(a-b)^5/(1+tan(f*x+e)^2)^2*tan(f*x+e)*b^2+15/4/f/(a-b)^5*arctan(tan(f*x+e))*a*b+15/8/f/(a-b)^5*arctan(tan(f*x+e))*b^2+3/8/f/(a-b)^5*arctan(tan(f*x+e))*a^2","B"
87,1,430,175,0.560000," ","int(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x)","-\frac{7 b^{2} a \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{4 f \left(a -b \right)^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a}-\frac{9 b \tan \left(f x +e \right) a^{2}}{8 f \left(a -b \right)^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{5 b^{2} \tan \left(f x +e \right) a}{4 f \left(a -b \right)^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{3} \tan \left(f x +e \right)}{8 f \left(a -b \right)^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{15 b a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{4} \sqrt{a b}}-\frac{5 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{4 f \left(a -b \right)^{4} \sqrt{a b}}+\frac{b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{4} a \sqrt{a b}}-\frac{\tan \left(f x +e \right) a}{2 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\tan \left(f x +e \right) b}{2 f \left(a -b \right)^{4} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a}{2 f \left(a -b \right)^{4}}+\frac{5 \arctan \left(\tan \left(f x +e \right)\right) b}{2 f \left(a -b \right)^{4}}"," ",0,"-7/8/f/(a-b)^4*b^2/(a+b*tan(f*x+e)^2)^2*a*tan(f*x+e)^3+3/4/f/(a-b)^4*b^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+1/8/f/(a-b)^4*b^4/(a+b*tan(f*x+e)^2)^2/a*tan(f*x+e)^3-9/8/f/(a-b)^4*b/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)*a^2+5/4/f/(a-b)^4*b^2/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)*a-1/8/f/(a-b)^4*b^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-15/8/f/(a-b)^4*b*a/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-5/4/f/(a-b)^4*b^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/8/f/(a-b)^4*b^3/a/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/2/f/(a-b)^4*tan(f*x+e)/(1+tan(f*x+e)^2)*a+1/2/f/(a-b)^4*tan(f*x+e)/(1+tan(f*x+e)^2)*b+1/2/f/(a-b)^4*arctan(tan(f*x+e))*a+5/2/f/(a-b)^4*arctan(tan(f*x+e))*b","B"
88,1,350,136,0.266000," ","int(1/(a+b*tan(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{5 b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a}-\frac{3 b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a^{2}}-\frac{9 b a \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{7 b^{2} \tan \left(f x +e \right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{5 b^{3} \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a}-\frac{15 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} \sqrt{a b}}+\frac{5 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{4 f \left(a -b \right)^{3} a \sqrt{a b}}-\frac{3 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} a^{2} \sqrt{a b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{3}}"," ",0,"-7/8/f*b^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+5/4/f*b^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2/a*tan(f*x+e)^3-3/8/f*b^4/(a-b)^3/(a+b*tan(f*x+e)^2)^2/a^2*tan(f*x+e)^3-9/8/f*b/(a-b)^3/(a+b*tan(f*x+e)^2)^2*a*tan(f*x+e)+7/4/f*b^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-5/8/f*b^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2/a*tan(f*x+e)-15/8/f*b/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+5/4/f*b^2/(a-b)^3/a/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-3/8/f*b^3/(a-b)^3/a^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f/(a-b)^3*arctan(tan(f*x+e))","B"
89,1,108,96,0.751000," ","int(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 b \tan \left(f x +e \right)}{8 f \,a^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{15 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{3} \sqrt{a b}}-\frac{1}{f \,a^{3} \tan \left(f x +e \right)}"," ",0,"-7/8/f/a^3*b^2/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-9/8/f/a^2*b/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-15/8/f/a^3*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/a^3/tan(f*x+e)","A"
90,1,235,138,0.793000," ","int(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{11 b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 b \tan \left(f x +e \right)}{8 f \,a^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{13 b^{2} \tan \left(f x +e \right)}{8 f \,a^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{15 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{3} \sqrt{a b}}+\frac{35 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{4} \sqrt{a b}}-\frac{1}{3 f \,a^{3} \tan \left(f x +e \right)^{3}}-\frac{1}{f \,a^{3} \tan \left(f x +e \right)}+\frac{3 b}{f \,a^{4} \tan \left(f x +e \right)}"," ",0,"-7/8/f/a^3*b^2/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+11/8/f/a^4*b^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-9/8/f/a^2*b/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)+13/8/f/a^3*b^2/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-15/8/f/a^3*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+35/8/f/a^4*b^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/3/f/a^3/tan(f*x+e)^3-1/f/a^3/tan(f*x+e)+3/f/a^4/tan(f*x+e)*b","A"
91,1,380,211,0.727000," ","int(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{11 b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{4 f \,a^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{15 b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{5} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 b \tan \left(f x +e \right)}{8 f \,a^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{13 b^{2} \tan \left(f x +e \right)}{4 f \,a^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{17 b^{3} \tan \left(f x +e \right)}{8 f \,a^{4} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{15 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{3} \sqrt{a b}}+\frac{35 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{4 f \,a^{4} \sqrt{a b}}-\frac{63 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{5} \sqrt{a b}}-\frac{1}{5 f \,a^{3} \tan \left(f x +e \right)^{5}}+\frac{b}{f \,a^{4} \tan \left(f x +e \right)^{3}}-\frac{2}{3 f \,a^{3} \tan \left(f x +e \right)^{3}}-\frac{1}{f \,a^{3} \tan \left(f x +e \right)}+\frac{6 b}{f \,a^{4} \tan \left(f x +e \right)}-\frac{6 b^{2}}{f \,a^{5} \tan \left(f x +e \right)}"," ",0,"-7/8/f/a^3*b^2/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+11/4/f/a^4*b^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-15/8/f*b^4/a^5/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-9/8/f/a^2*b/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)+13/4/f/a^3*b^2/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-17/8/f*b^3/a^4/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-15/8/f/a^3*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+35/4/f/a^4*b^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-63/8/f*b^3/a^5/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/5/f/a^3/tan(f*x+e)^5+1/f/a^4/tan(f*x+e)^3*b-2/3/f/a^3/tan(f*x+e)^3-1/f/a^3/tan(f*x+e)+6/f/a^4/tan(f*x+e)*b-6/f/a^5/tan(f*x+e)*b^2","A"
92,1,7044,145,5.177000," ","int(sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
93,1,4296,101,1.015000," ","int(sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"1/6/f*(-1+cos(f*x+e))^2*(-3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(9/2)*4^(1/2)+3*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(9/2)*4^(1/2)-4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(5/2)*a^(1/2)+8*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(3/2)*a^(3/2)-4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(1/2)*a^(5/2)+9*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*4^(1/2)*a^2-9*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a^(5/2)*4^(1/2)*b^2+3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(3/2)*4^(1/2)*a^3-3*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(3/2)*4^(1/2)*a^3+9*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a^(3/2)*4^(1/2)*b^3-3*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a^(1/2)*4^(1/2)*b^4-15*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2)*a^(3/2)*4^(1/2)+12*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)*a^(5/2)*4^(1/2)-3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*a^(7/2)*4^(1/2)+2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(5/2)*cos(f*x+e)^4*a^(1/2)-4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(3/2)*cos(f*x+e)^4*a^(3/2)+2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(1/2)*cos(f*x+e)^4*a^(5/2)+8*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(5/2)*cos(f*x+e)^3*a^(1/2)-16*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(3/2)*cos(f*x+e)^3*a^(3/2)+8*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(1/2)*cos(f*x+e)^3*a^(5/2)-3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(9/2)*cos(f*x+e)*4^(1/2)+3*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(9/2)*cos(f*x+e)*4^(1/2)+6*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(5/2)*cos(f*x+e)^2*a^(1/2)-12*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(3/2)*cos(f*x+e)^2*a^(3/2)+6*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(1/2)*cos(f*x+e)^2*a^(5/2)-4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(5/2)*cos(f*x+e)*a^(1/2)+8*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(3/2)*cos(f*x+e)*a^(3/2)-4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(1/2)*cos(f*x+e)*a^(5/2)+6*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(7/2)*a^(1/2)*4^(1/2)+9*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*4^(1/2)*a-9*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*4^(1/2)*a+3*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a^(7/2)*4^(1/2)*b-9*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*4^(1/2)*a^2+6*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(7/2)*cos(f*x+e)*a^(1/2)*4^(1/2)+9*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*cos(f*x+e)*4^(1/2)*a-9*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*cos(f*x+e)*4^(1/2)*a+3*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*cos(f*x+e)*a^(7/2)*4^(1/2)*b-9*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*cos(f*x+e)*4^(1/2)*a^2+9*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*cos(f*x+e)*4^(1/2)*a^2-9*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*cos(f*x+e)*a^(5/2)*4^(1/2)*b^2+3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(3/2)*cos(f*x+e)*4^(1/2)*a^3-3*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(3/2)*cos(f*x+e)*4^(1/2)*a^3+9*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*cos(f*x+e)*a^(3/2)*4^(1/2)*b^3-3*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*cos(f*x+e)*a^(1/2)*4^(1/2)*b^4-18*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2)*cos(f*x+e)*a^(3/2)*4^(1/2)+18*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)*cos(f*x+e)*a^(5/2)*4^(1/2)-6*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*cos(f*x+e)*a^(7/2)*4^(1/2))*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)/sin(f*x+e)^4/(a-b)^3/a^(1/2)/b^(1/2)","B"
94,1,144,64,0.394000," ","int(sin(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(\sqrt{b}\, \ln \left(\frac{2 \sqrt{b}\, \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}+2 b}{\cos \left(f x +e \right)}\right)-\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}\right)}{f \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}}"," ",0,"1/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)*(b^(1/2)*ln(2*(b^(1/2)*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(1/2)+b)/cos(f*x+e))-(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(1/2))/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(1/2)","B"
95,1,721,72,1.191000," ","int(csc(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \sqrt{4}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \left(2 \sqrt{a}\, \arctanh \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{4}\, \cos \left(f x +e \right)-\sqrt{4}-2 \cos \left(f x +e \right)-2\right) \sqrt{b}\, \sqrt{4}}{8 \sin \left(f x +e \right)^{2} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right) b +2 \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) b^{\frac{3}{2}}-2 b^{\frac{3}{2}} \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right)-\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) a \sqrt{b}-a \ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right) \sqrt{b}\right)}{4 f \sin \left(f x +e \right)^{2} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}\, \sqrt{b}}"," ",0,"-1/4/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)*4^(1/2)*cos(f*x+e)*(-1+cos(f*x+e))*(2*a^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b+2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(3/2)-2*b^(3/2)*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))-ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*a*b^(1/2)-a*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b^(1/2))/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)/a^(1/2)/b^(1/2)","B"
96,1,2075,109,1.235000," ","int(csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/8/f*(-1+cos(f*x+e))*(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2*b^(3/2)*a^(1/2)*4^(1/2)-4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2*b^(1/2)*a^(3/2)*4^(1/2)+3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^2*b^(3/2)*4^(1/2)*a-ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*b^(3/2)*4^(1/2)*a-4*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^2*b^(3/2)*4^(1/2)*a+4*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*cos(f*x+e)^2*a^(3/2)*4^(1/2)*b+8*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^2*b^(1/2)*a^(1/2)+2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*b^(1/2)*a^(3/2)*4^(1/2)-ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^2*b^(1/2)*4^(1/2)*a^2-ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*b^(1/2)*4^(1/2)*a^2+16*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)*b^(1/2)*a^(1/2)-4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)*a^(1/2)*4^(1/2)+2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*a^(3/2)*4^(1/2)-3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(3/2)*4^(1/2)*a+ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b^(3/2)*4^(1/2)*a+4*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(3/2)*4^(1/2)*a-4*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a^(3/2)*4^(1/2)*b+8*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)*b^(1/2)*a^(1/2)+ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(1/2)*4^(1/2)*a^2+ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b^(1/2)*4^(1/2)*a^2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)/sin(f*x+e)^4/a^(3/2)/b^(1/2)","B"
97,1,5378,165,1.343000," ","int(csc(f*x+e)^5*(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
98,1,2498,167,1.987000," ","int(sin(f*x+e)^4*(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\left(2 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}-4 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +2 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+6 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a^{2} \sin \left(f x +e \right)-24 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a b \sin \left(f x +e \right)+16 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b^{2} \sin \left(f x +e \right)+16 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a b \sin \left(f x +e \right)-16 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b^{2} \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a^{2} \sin \left(f x +e \right)+4 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a b \sin \left(f x +e \right)-2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}+4 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-5 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}+13 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -8 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+5 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}-13 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +8 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-5 \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +6 \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+5 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -6 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(a -b \right)}"," ",0,"1/8/f*(2*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2-4*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+2*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^2*sin(f*x+e)-24*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*b*sin(f*x+e)+16*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2*sin(f*x+e)+16*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*b*sin(f*x+e)-16*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2*sin(f*x+e)-3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^2*sin(f*x+e)+4*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a*b*sin(f*x+e)-2*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2+4*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-2*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-5*cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2+13*cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-8*cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+5*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2-13*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+8*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-5*cos(f*x+e)*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+6*cos(f*x+e)*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2)*cos(f*x+e)*sin(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/(-1+cos(f*x+e))/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/(a-b)","C"
99,1,1342,110,0.779000," ","int(sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\left(-4 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a \sin \left(f x +e \right)+4 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a \sin \left(f x +e \right)+\left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a -\left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a +\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b +\cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b -\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b \right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}"," ",0,"-1/2/f*(-4*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b*sin(f*x+e)-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*sin(f*x+e)+4*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b*sin(f*x+e)+2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a*sin(f*x+e)+cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a-cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b-cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a+cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b+cos(f*x+e)*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b-((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b)*cos(f*x+e)*sin(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/(-1+cos(f*x+e))/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
100,1,169,73,0.249000," ","int((a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{b}\, \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}+\frac{a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/f*b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*(b^4*(a-b))^(1/2)/b/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))+1/f*a*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
101,1,1215,58,4.516000," ","int(csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) b \sin \left(f x +e \right) \cos \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b \sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right) \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, b +2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b \sin \left(f x +e \right)+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b +\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b \right)}{f \sin \left(f x +e \right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}"," ",0,"-1/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)*(-2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*b*sin(f*x+e)*cos(f*x+e)+2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b*sin(f*x+e)*cos(f*x+e)-sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*b+2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b*sin(f*x+e)+cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a-cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b+((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b)/sin(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
102,1,2444,88,1.710000," ","int(csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\left(6 \sin \left(f x +e \right) \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -3 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a b +6 \sin \left(f x +e \right) \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -3 \sin \left(f x +e \right) \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -6 \sin \left(f x +e \right) \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \cos \left(f x +e \right) a b +3 \sin \left(f x +e \right) \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \cos \left(f x +e \right) a b -6 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a b \sin \left(f x +e \right)+3 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a b \sin \left(f x +e \right)+2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}-\left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -\left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}+4 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-3 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}\right) \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}}{3 f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \sin \left(f x +e \right)^{3} a \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}"," ",0,"1/3/f*(6*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^3*a*b-3*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a*b+6*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b-3*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b-6*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)*a*b+3*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)*a*b-6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*b*sin(f*x+e)+3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a*b*sin(f*x+e)+2*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2-cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-3*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2+4*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+2*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/sin(f*x+e)^3/a/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
103,1,3769,125,1.327000," ","int(csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/15/f*(-15*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^5*a^2*b-15*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^2*b*sin(f*x+e)+30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^2*b*sin(f*x+e)+15*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b+10*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^2-2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^3+30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)*cos(f*x+e)^4*a^2*b-15*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^4*a^2*b-60*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)*cos(f*x+e)^3*a^2*b+30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^3*a^2*b-60*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^2*b+30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^2*b+30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)*cos(f*x+e)*a^2*b-15*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*cos(f*x+e)*a^2*b+30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)*cos(f*x+e)^5*a^2*b-6*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^3+6*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^3+8*cos(f*x+e)^6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^3-20*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^3+15*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^3+2*cos(f*x+e)^6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^3+cos(f*x+e)^6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b-11*cos(f*x+e)^6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^2+9*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b+32*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^2-25*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b-31*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/sin(f*x+e)^5/a^2/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
104,1,2399,203,1.179000," ","int(sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/60/f*(-1+cos(f*x+e))^3*(-32*cos(f*x+e)^4*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2)+30*cos(f*x+e)^3*a^(9/2)*b^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)-140*cos(f*x+e)^3*a^(7/2)*b^(3/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+116*cos(f*x+e)^3*a^(5/2)*b^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+30*a^(9/2)*b^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-140*a^(7/2)*b^(3/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2+116*a^(5/2)*b^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-15*cos(f*x+e)*a^(7/2)*b^(3/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+15*cos(f*x+e)*a^(5/2)*b^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)-30*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a^2+30*cos(f*x+e)^2*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a^2+45*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*a^3-45*cos(f*x+e)^2*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*a^3+6*cos(f*x+e)^7*a^(9/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)-12*cos(f*x+e)^7*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)+6*cos(f*x+e)^7*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2)+6*cos(f*x+e)^6*a^(9/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)-12*cos(f*x+e)^6*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)+6*cos(f*x+e)^6*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2)-20*cos(f*x+e)^5*a^(9/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)+52*cos(f*x+e)^5*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)-32*cos(f*x+e)^5*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2)-15*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(9/2)*a+15*cos(f*x+e)^2*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(9/2)*a+150*cos(f*x+e)^2*a^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^2-105*cos(f*x+e)^2*a^(5/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^3-45*cos(f*x+e)^2*a^(9/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b-20*cos(f*x+e)^4*a^(9/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)+52*cos(f*x+e)^4*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)-15*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)+15*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2))*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)*4^(1/2)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)/sin(f*x+e)^6/(a-b)/a^(5/2)/b^(1/2)","B"
105,1,1104,166,0.800000," ","int(sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{3} \left(2 \left(\cos^{5}\left(f x +e \right)\right) a^{\frac{7}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{b}-2 \left(\cos^{5}\left(f x +e \right)\right) a^{\frac{5}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{\frac{3}{2}}+2 \left(\cos^{4}\left(f x +e \right)\right) a^{\frac{7}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{b}-2 \left(\cos^{4}\left(f x +e \right)\right) a^{\frac{5}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{\frac{3}{2}}-6 \left(\cos^{3}\left(f x +e \right)\right) a^{\frac{7}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{b}+14 \left(\cos^{3}\left(f x +e \right)\right) a^{\frac{5}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{\frac{3}{2}}+9 \left(\cos^{2}\left(f x +e \right)\right) a^{\frac{7}{2}} \arctanh \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{4}\, \cos \left(f x +e \right)-\sqrt{4}-2 \cos \left(f x +e \right)-2\right) \sqrt{b}\, \sqrt{4}}{8 \sin \left(f x +e \right)^{2} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right) b -6 \left(\cos^{2}\left(f x +e \right)\right) a^{\frac{7}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{b}+14 \left(\cos^{2}\left(f x +e \right)\right) a^{\frac{5}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{\frac{3}{2}}-6 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) b^{\frac{7}{2}} a +6 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) b^{\frac{7}{2}} a -15 \left(\cos^{2}\left(f x +e \right)\right) a^{\frac{5}{2}} \arctanh \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{4}\, \cos \left(f x +e \right)-\sqrt{4}-2 \cos \left(f x +e \right)-2\right) \sqrt{b}\, \sqrt{4}}{8 \sin \left(f x +e \right)^{2} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right) b^{2}+3 \cos \left(f x +e \right) a^{\frac{5}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{\frac{3}{2}}+3 a^{\frac{5}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{\frac{3}{2}}\right) \cos \left(f x +e \right) \sqrt{4}\, \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{12 f \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{6} a^{\frac{5}{2}} \sqrt{b}}"," ",0,"-1/12/f*(-1+cos(f*x+e))^3*(2*cos(f*x+e)^5*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)-2*cos(f*x+e)^5*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)+2*cos(f*x+e)^4*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)-2*cos(f*x+e)^4*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)-6*cos(f*x+e)^3*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)+14*cos(f*x+e)^3*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)+9*cos(f*x+e)^2*a^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b-6*cos(f*x+e)^2*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)+14*cos(f*x+e)^2*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)-6*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a+6*cos(f*x+e)^2*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a-15*cos(f*x+e)^2*a^(5/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^2+3*cos(f*x+e)*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)+3*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2))*cos(f*x+e)*4^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)/sin(f*x+e)^6/a^(5/2)/b^(1/2)","B"
106,1,357,99,0.322000," ","int(sin(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \cos \left(f x +e \right) \left(-\left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right) a +\left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right) b +3 b^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{b}\, \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}+2 b}{\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) a -3 b^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{b}\, \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}+2 b}{\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+\left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{\frac{5}{2}}-3 \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}\, \left(\cos^{2}\left(f x +e \right)\right) a b +3 \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}\, \left(\cos^{2}\left(f x +e \right)\right) b^{2}\right)}{2 f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{\frac{3}{2}} b}"," ",0,"1/2/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)*(-(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(3/2)*cos(f*x+e)^2*a+(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(3/2)*cos(f*x+e)^2*b+3*b^(3/2)*ln(2*(b^(1/2)*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(1/2)+b)/cos(f*x+e))*cos(f*x+e)^2*a-3*b^(5/2)*ln(2*(b^(1/2)*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(1/2)+b)/cos(f*x+e))*cos(f*x+e)^2+(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(5/2)-3*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(1/2)*cos(f*x+e)^2*a*b+3*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(1/2)*cos(f*x+e)^2*b^2)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^(3/2)/b","B"
107,1,1249,109,0.973000," ","int(csc(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sqrt{4}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{3} \left(4 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) b^{\frac{7}{2}} a -4 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) b^{\frac{7}{2}} a +3 \left(\cos^{2}\left(f x +e \right)\right) a^{\frac{7}{2}} \arctanh \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{4}\, \cos \left(f x +e \right)-\sqrt{4}-2 \cos \left(f x +e \right)-2\right) \sqrt{b}\, \sqrt{4}}{8 \sin \left(f x +e \right)^{2} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right) b +\cos \left(f x +e \right) a^{\frac{5}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{\frac{3}{2}}-6 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) b^{\frac{5}{2}} a^{2}+6 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) b^{\frac{5}{2}} a^{2}-\left(\cos^{2}\left(f x +e \right)\right) a^{\frac{5}{2}} \arctanh \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{4}\, \cos \left(f x +e \right)-\sqrt{4}-2 \cos \left(f x +e \right)-2\right) \sqrt{b}\, \sqrt{4}}{8 \sin \left(f x +e \right)^{2} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right) b^{2}+a^{\frac{5}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{\frac{3}{2}}-\left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \sqrt{b}\, a^{4}-\left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right) \sqrt{b}\, a^{4}\right)}{4 f \sin \left(f x +e \right)^{6} \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}} a^{\frac{5}{2}} \sqrt{b}}"," ",0,"-1/4/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)*4^(1/2)*cos(f*x+e)*(-1+cos(f*x+e))^3*(4*cos(f*x+e)^2*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a-4*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a+3*cos(f*x+e)^2*a^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b+cos(f*x+e)*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)-6*cos(f*x+e)^2*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*a^2+6*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*a^2-cos(f*x+e)^2*a^(5/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^2+a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)-cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(1/2)*a^4-cos(f*x+e)^2*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b^(1/2)*a^4)/sin(f*x+e)^6/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)/a^(5/2)/b^(1/2)","B"
108,1,2904,145,0.991000," ","int(csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"-1/8/f*(-1+cos(f*x+e))^2*(6*cos(f*x+e)^3*a^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b+10*cos(f*x+e)^3*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a-10*cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a+2*cos(f*x+e)^3*a^(5/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^2-18*cos(f*x+e)^3*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*a^2+18*cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*a^2-6*cos(f*x+e)^2*a^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b+2*cos(f*x+e)^2*a^(7/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)+2*cos(f*x+e)^2*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)-10*cos(f*x+e)^2*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a+10*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(7/2)*a-3*cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(3/2)*a^3-3*cos(f*x+e)^3*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b^(3/2)*a^3-2*cos(f*x+e)^2*a^(5/2)*arctanh(1/8*(-1+cos(f*x+e))*(4^(1/2)*cos(f*x+e)-4^(1/2)-2*cos(f*x+e)-2)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^2+18*cos(f*x+e)^2*ln(-4*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*a^2-18*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(5/2)*a^2-cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(1/2)*a^4-cos(f*x+e)^3*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b^(1/2)*a^4+3*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(3/2)*a^3+3*cos(f*x+e)^2*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b^(3/2)*a^3-2*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)+cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b^(1/2)*a^4+cos(f*x+e)^2*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b^(1/2)*a^4)*cos(f*x+e)*4^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)/sin(f*x+e)^6/a^(5/2)/b^(1/2)","B"
109,1,6194,195,1.337000," ","int(csc(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
110,1,2630,194,1.166000," ","int(sin(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\left(6 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+24 \sin \left(f x +e \right) \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +12 \sin \left(f x +e \right) \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -12 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-5 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}-4 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-4 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{7}\left(f x +e \right)\right) a b +4 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{6}\left(f x +e \right)\right) a b +17 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +4 \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+12 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+5 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}+2 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{7}\left(f x +e \right)\right) a^{2}-2 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{6}\left(f x +e \right)\right) a^{2}+2 b^{2} \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{7}\left(f x +e \right)\right)-2 b^{2} \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{6}\left(f x +e \right)\right)-17 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -\left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-48 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a b -3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a^{2}+6 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a^{2}+48 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b^{2}-48 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b^{2}\right) \cos \left(f x +e \right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}"," ",0,"1/8/f*(-5*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2+24*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b+12*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b-4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-12*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^7*a*b+4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6*a*b+17*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-17*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+5*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2+12*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+6*cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-6*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+4*cos(f*x+e)*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^7*a^2-2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6*a^2+2*b^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^7-2*b^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6-3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^2+6*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^2+48*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2-48*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2-48*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*b)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)*sin(f*x+e)/(-1+cos(f*x+e))/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
111,1,2261,143,0.774000," ","int(sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a^{2}-2 \sin \left(f x +e \right) \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -2 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a^{2}+10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a b -8 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b^{2}-6 \sin \left(f x +e \right) \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +8 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) b^{2}+\left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}-2 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +\left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-\left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}+2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -\left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-\cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}"," ",0,"-1/2/f*(cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^2-2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b-2*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^2+10*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*b-8*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2-6*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b+8*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2+cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2-2*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2+2*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-cos(f*x+e)*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2)*cos(f*x+e)*sin(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/(-1+cos(f*x+e))/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
112,1,297,107,0.257000," ","int((a+b*tan(f*x+e)^2)^(3/2),x)","\frac{b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 f}+\frac{3 \sqrt{b}\, a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f}-\frac{b^{\frac{3}{2}} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)}-\frac{2 a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}+\frac{a^{2} \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/2*b*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/f+3/2/f*b^(1/2)*a*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*b^(3/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))-2/f*a/b*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))+1/f*a^2*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
113,1,1355,86,0.986000," ","int(csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \cos \left(f x +e \right) \left(-3 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a b +6 \sin \left(f x +e \right) \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -3 \sin \left(f x +e \right) \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +6 \sin \left(f x +e \right) \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}-\left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -\left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}\right)}{2 f \sin \left(f x +e \right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}"," ",0,"-1/2/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)*(-3*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a*b+6*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^3*a*b-3*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b+6*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b+2*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2-cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+2*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2)/sin(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
114,1,4594,142,1.310000," ","int(csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"1/6/f*(-18*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^3*a*b-9*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^4*a*b+18*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^5*a*b-9*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^5*a*b+18*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^4*a*b+9*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a*b-18*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b+9*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b+3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+7*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6*a*b+12*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^5*b^2-6*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^5*b^2+12*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^4*b^2-6*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^4*b^2-12*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^3*b^2+6*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^3*b^2+6*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^2*b^2-4*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-3*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-6*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2+25*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-17*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6*a^2-11*b^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6-12*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/sin(f*x+e)^3/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
115,1,6988,172,1.834000," ","int(csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
116,1,169,132,1.086000," ","int(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \left(3 \left(\cos^{4}\left(f x +e \right)\right) a^{2}-6 \left(\cos^{4}\left(f x +e \right)\right) a b +3 \left(\cos^{4}\left(f x +e \right)\right) b^{2}-10 a^{2} \left(\cos^{2}\left(f x +e \right)\right)+16 \left(\cos^{2}\left(f x +e \right)\right) a b -6 b^{2} \left(\cos^{2}\left(f x +e \right)\right)+15 a^{2}-10 a b +3 b^{2}\right)}{15 f \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(a -b \right)^{3}}"," ",0,"-1/15/f*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)*(3*cos(f*x+e)^4*a^2-6*cos(f*x+e)^4*a*b+3*cos(f*x+e)^4*b^2-10*a^2*cos(f*x+e)^2+16*cos(f*x+e)^2*a*b-6*b^2*cos(f*x+e)^2+15*a^2-10*a*b+3*b^2)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(a-b)^3","A"
117,1,104,80,0.874000," ","int(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b -3 a +b \right)}{3 f \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(a -b \right)^{2}}"," ",0,"1/3/f*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)*(a*cos(f*x+e)^2-cos(f*x+e)^2*b-3*a+b)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(a-b)^2","A"
118,1,78,35,0.373000," ","int(sin(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{f \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(a -b \right)}"," ",0,"-1/f/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(a-b)","B"
119,1,351,36,1.216000," ","int(csc(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right)+\ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right)\right) \left(\sin^{2}\left(f x +e \right)\right)}{2 f \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{a}}"," ",0,"1/2/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*(ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))+ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e))))*sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/a^(1/2)","B"
120,1,2801,79,1.200000," ","int(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"1/4/f*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^3*a^2-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^3*a*b+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^3*a^2-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^3*a*b-2*cos(f*x+e)^2*a^(5/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^2*a^2-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^2*a*b+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*a^2-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*a*b+2*cos(f*x+e)^2*a^(3/2)*b-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*a^2+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*a*b-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a^2+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a*b-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*a^2+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*a*b-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a^2+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a*b-2*a^(3/2)*b)*sin(f*x+e)^2/(-1+cos(f*x+e))^2/cos(f*x+e)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/(1+cos(f*x+e))^2/a^(5/2)","B"
121,1,6334,127,1.424000," ","int(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
122,1,1169,130,1.080000," ","int(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \left(2 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}-4 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +2 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}+4 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-3 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a^{2} \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a^{2} \sin \left(f x +e \right)-5 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}+9 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -4 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+5 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}-9 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +4 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}-5 \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +2 \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+5 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -2 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}\right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(a -b \right)^{2}}"," ",0,"1/8/f*sin(f*x+e)*(2*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2-4*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+2*cos(f*x+e)^5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-2*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2+4*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-2*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^2*sin(f*x+e)+6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^2*sin(f*x+e)-5*cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2+9*cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-4*cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+5*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2-9*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+4*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-5*cos(f*x+e)*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+2*cos(f*x+e)*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2)/(-1+cos(f*x+e))/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/(a-b)^2","C"
123,1,795,81,0.844000," ","int(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\sin \left(f x +e \right) \left(\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a \sin \left(f x +e \right)+\left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a -\left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a +\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b +\cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b -\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(a -b \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}"," ",0,"-1/2/f*sin(f*x+e)*(2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a*sin(f*x+e)-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*sin(f*x+e)+cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a-cos(f*x+e)^3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b-cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a+cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b+cos(f*x+e)*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b-((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b)/(-1+cos(f*x+e))/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(a-b)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
124,1,67,40,0.353000," ","int(1/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/f*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
125,1,57,28,1.044000," ","int(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right)}{f \sin \left(f x +e \right) a}"," ",0,"-1/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)/sin(f*x+e)/a","A"
126,1,86,66,1.082000," ","int(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\left(2 a \left(\cos^{2}\left(f x +e \right)\right)-2 \left(\cos^{2}\left(f x +e \right)\right) b -3 a +2 b \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right)}{3 f \sin \left(f x +e \right)^{3} a^{2}}"," ",0,"1/3/f*(2*a*cos(f*x+e)^2-2*cos(f*x+e)^2*b-3*a+2*b)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)/sin(f*x+e)^3/a^2","A"
127,1,148,111,1.329000," ","int(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\left(8 \left(\cos^{4}\left(f x +e \right)\right) a^{2}-16 \left(\cos^{4}\left(f x +e \right)\right) a b +8 \left(\cos^{4}\left(f x +e \right)\right) b^{2}-20 a^{2} \left(\cos^{2}\left(f x +e \right)\right)+36 \left(\cos^{2}\left(f x +e \right)\right) a b -16 b^{2} \left(\cos^{2}\left(f x +e \right)\right)+15 a^{2}-20 a b +8 b^{2}\right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right)}{15 f \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"-1/15/f*(8*cos(f*x+e)^4*a^2-16*cos(f*x+e)^4*a*b+8*cos(f*x+e)^4*b^2-20*a^2*cos(f*x+e)^2+36*cos(f*x+e)^2*a*b-16*b^2*cos(f*x+e)^2+15*a^2-20*a*b+8*b^2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)/sin(f*x+e)^5/a^3","A"
128,1,67748,183,7.052000," ","int(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
129,1,14991,119,1.990000," ","int(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
130,1,103,72,0.349000," ","int(sin(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +2 b \right)}{f \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{3} \left(a -b \right)^{2}}"," ",0,"-1/f*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+2*b)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/cos(f*x+e)^3/(a-b)^2","A"
131,1,3491,76,1.191000," ","int(csc(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"-1/2/f*(2*a^(5/2)*cos(f*x+e)^2*b+cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^3-2*cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^2*b+cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a*b^2+cos(f*x+e)^3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a^3-2*cos(f*x+e)^3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a^2*b+cos(f*x+e)^3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a*b^2-2*a^(3/2)*cos(f*x+e)^2*b^2+cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^3-2*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^2*b+cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a*b^2+cos(f*x+e)^2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a^3-2*cos(f*x+e)^2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a^2*b+cos(f*x+e)^2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a*b^2+cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^2*b-cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a*b^2+cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a^2*b-cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a*b^2+2*b^2*a^(3/2)+ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^2*b-ln(-2*(-1+cos(f*x+e))*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a*b^2+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a^2*b-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(a^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*a*b^2)/cos(f*x+e)^3/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/a^(5/2)/(a-b)","B"
132,1,5633,111,1.191000," ","int(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
133,1,10582,167,1.246000," ","int(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
134,1,6027,167,16.158000," ","int(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
135,1,1614,118,5.316000," ","int(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \left(\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a \sin \left(f x +e \right)+\cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b -\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b \right) \sin \left(f x +e \right)}{f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{3} a \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(a -b \right)}+\frac{\left(\cos^{2}\left(2 f x +2 e \right)\right) \left(a -b \right)^{\frac{3}{2}} a^{3} b -2 \left(a -b \right)^{\frac{3}{2}} \left(\cos^{2}\left(2 f x +2 e \right)\right) a^{2} b^{2}+\left(a -b \right)^{\frac{3}{2}} \left(\cos^{2}\left(2 f x +2 e \right)\right) a \,b^{3}+2 \left(a -b \right)^{\frac{3}{2}} \cos \left(2 f x +2 e \right) a^{2} b^{2}+2 \left(a -b \right)^{\frac{3}{2}} \cos \left(2 f x +2 e \right) a \,b^{3}-4 \left(a -b \right)^{\frac{3}{2}} \cos \left(2 f x +2 e \right) b^{4}-4 \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(-1+\cos \left(2 f x +2 e \right)\right) \left(a -b \right) b^{2}}{\sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \sin \left(2 f x +2 e \right) \sqrt{b^{4} \left(a -b \right)}}\right) \sin \left(2 f x +2 e \right) \sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, a \left(a -b \right)^{\frac{3}{2}}+2 \sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \arctan \left(\frac{\left(-1+\cos \left(2 f x +2 e \right)\right) \sqrt{a -b}}{\sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \sin \left(2 f x +2 e \right)}\right) \sin \left(2 f x +2 e \right) a^{4} b -8 \sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \arctan \left(\frac{\left(-1+\cos \left(2 f x +2 e \right)\right) \sqrt{a -b}}{\sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \sin \left(2 f x +2 e \right)}\right) \sin \left(2 f x +2 e \right) a^{3} b^{2}+10 \sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \arctan \left(\frac{\left(-1+\cos \left(2 f x +2 e \right)\right) \sqrt{a -b}}{\sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \sin \left(2 f x +2 e \right)}\right) \sin \left(2 f x +2 e \right) a^{2} b^{3}-4 \sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \arctan \left(\frac{\left(-1+\cos \left(2 f x +2 e \right)\right) \sqrt{a -b}}{\sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \sin \left(2 f x +2 e \right)}\right) \sin \left(2 f x +2 e \right) a \,b^{4}-\left(a -b \right)^{\frac{3}{2}} a^{3} b -3 \left(a -b \right)^{\frac{3}{2}} a \,b^{3}+4 \left(a -b \right)^{\frac{3}{2}} b^{4}}{4 f \sin \left(2 f x +2 e \right) \sqrt{\frac{a \cos \left(2 f x +2 e \right)-b \cos \left(2 f x +2 e \right)+a +b}{\cos \left(2 f x +2 e \right)+1}}\, \left(a -b \right)^{\frac{9}{2}} a b}"," ",0,"-1/f*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)*(2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a*sin(f*x+e)-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*sin(f*x+e)+cos(f*x+e)*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b-((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b)*sin(f*x+e)/(-1+cos(f*x+e))/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/cos(f*x+e)^3/a/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/(a-b)+1/4/f*(cos(2*f*x+2*e)^2*(a-b)^(3/2)*a^3*b-2*(a-b)^(3/2)*cos(2*f*x+2*e)^2*a^2*b^2+(a-b)^(3/2)*cos(2*f*x+2*e)^2*a*b^3+2*(a-b)^(3/2)*cos(2*f*x+2*e)*a^2*b^2+2*(a-b)^(3/2)*cos(2*f*x+2*e)*a*b^3-4*(a-b)^(3/2)*cos(2*f*x+2*e)*b^4-4*(b^4*(a-b))^(1/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)*b^2/(b^4*(a-b))^(1/2))*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)*a*(a-b)^(3/2)+2*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*sin(2*f*x+2*e)*a^4*b-8*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*sin(2*f*x+2*e)*a^3*b^2+10*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*sin(2*f*x+2*e)*a^2*b^3-4*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*sin(2*f*x+2*e)*a*b^4-(a-b)^(3/2)*a^3*b-3*(a-b)^(3/2)*a*b^3+4*(a-b)^(3/2)*b^4)/sin(2*f*x+2*e)/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/(a-b)^(9/2)/a/b","C"
136,1,104,77,0.293000," ","int(1/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{b \tan \left(f x +e \right)}{a \left(a -b \right) f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{2} b^{2}}"," ",0,"-b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)^2*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
137,1,109,58,0.941000," ","int(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(a \left(\cos^{2}\left(f x +e \right)\right)-2 \left(\cos^{2}\left(f x +e \right)\right) b +2 b \right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(f x +e \right)\right)}{f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \sin \left(f x +e \right) a^{2}}"," ",0,"-1/f/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*(a*cos(f*x+e)^2-2*cos(f*x+e)^2*b+2*b)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^3/sin(f*x+e)/a^2","A"
138,1,170,102,1.077000," ","int(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\left(2 \left(\cos^{4}\left(f x +e \right)\right) a^{2}-10 \left(\cos^{4}\left(f x +e \right)\right) a b +8 \left(\cos^{4}\left(f x +e \right)\right) b^{2}-3 a^{2} \left(\cos^{2}\left(f x +e \right)\right)+16 \left(\cos^{2}\left(f x +e \right)\right) a b -16 b^{2} \left(\cos^{2}\left(f x +e \right)\right)-6 a b +8 b^{2}\right) \left(\cos^{3}\left(f x +e \right)\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{3 f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \sin \left(f x +e \right)^{3} a^{3}}"," ",0,"1/3/f/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*(2*cos(f*x+e)^4*a^2-10*cos(f*x+e)^4*a*b+8*cos(f*x+e)^4*b^2-3*a^2*cos(f*x+e)^2+16*cos(f*x+e)^2*a*b-16*b^2*cos(f*x+e)^2-6*a*b+8*b^2)*cos(f*x+e)^3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/sin(f*x+e)^3/a^3","A"
139,1,264,155,1.095000," ","int(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(8 \left(\cos^{6}\left(f x +e \right)\right) a^{3}-64 \left(\cos^{6}\left(f x +e \right)\right) a^{2} b +104 \left(\cos^{6}\left(f x +e \right)\right) a \,b^{2}-48 \left(\cos^{6}\left(f x +e \right)\right) b^{3}-20 \left(\cos^{4}\left(f x +e \right)\right) a^{3}+164 \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -288 \left(\cos^{4}\left(f x +e \right)\right) a \,b^{2}+144 \left(\cos^{4}\left(f x +e \right)\right) b^{3}+15 \left(\cos^{2}\left(f x +e \right)\right) a^{3}-130 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b +264 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-144 \left(\cos^{2}\left(f x +e \right)\right) b^{3}+30 a^{2} b -80 b^{2} a +48 b^{3}\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(f x +e \right)\right)}{15 f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \sin \left(f x +e \right)^{5} a^{4}}"," ",0,"-1/15/f/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*(8*cos(f*x+e)^6*a^3-64*cos(f*x+e)^6*a^2*b+104*cos(f*x+e)^6*a*b^2-48*cos(f*x+e)^6*b^3-20*cos(f*x+e)^4*a^3+164*cos(f*x+e)^4*a^2*b-288*cos(f*x+e)^4*a*b^2+144*cos(f*x+e)^4*b^3+15*cos(f*x+e)^2*a^3-130*a^2*cos(f*x+e)^2*b+264*cos(f*x+e)^2*a*b^2-144*cos(f*x+e)^2*b^3+30*a^2*b-80*b^2*a+48*b^3)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^3/sin(f*x+e)^5/a^4","A"
140,1,391,228,4.522000," ","int(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x)","\frac{\left(a -b \right)^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \left(3 \left(\cos^{8}\left(f x +e \right)\right) a^{4}-12 \left(\cos^{8}\left(f x +e \right)\right) a^{3} b +18 \left(\cos^{8}\left(f x +e \right)\right) a^{2} b^{2}-12 \left(\cos^{8}\left(f x +e \right)\right) a \,b^{3}+3 \left(\cos^{8}\left(f x +e \right)\right) b^{4}-10 \left(\cos^{6}\left(f x +e \right)\right) a^{4}+32 \left(\cos^{6}\left(f x +e \right)\right) a^{3} b -36 \left(\cos^{6}\left(f x +e \right)\right) a^{2} b^{2}+16 \left(\cos^{6}\left(f x +e \right)\right) a \,b^{3}-2 \left(\cos^{6}\left(f x +e \right)\right) b^{4}+15 \left(\cos^{4}\left(f x +e \right)\right) a^{4}-42 a^{2} b^{2} \left(\cos^{4}\left(f x +e \right)\right)+24 \left(\cos^{4}\left(f x +e \right)\right) a \,b^{3}+3 \left(\cos^{4}\left(f x +e \right)\right) b^{4}+60 \left(\cos^{2}\left(f x +e \right)\right) a^{3} b +60 \left(\cos^{2}\left(f x +e \right)\right) a^{2} b^{2}-108 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{3}-12 \left(\cos^{2}\left(f x +e \right)\right) b^{4}+40 a^{2} b^{2}+80 a \,b^{3}+8 b^{4}\right) \sqrt{4}\, a^{7}}{30 f \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{5} \left(\sqrt{-\left(a -b \right) b}+a -b \right)^{7} \left(\sqrt{-\left(a -b \right) b}-a +b \right)^{7}}"," ",0,"1/30/f*(a-b)^2*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)*(3*cos(f*x+e)^8*a^4-12*cos(f*x+e)^8*a^3*b+18*cos(f*x+e)^8*a^2*b^2-12*cos(f*x+e)^8*a*b^3+3*cos(f*x+e)^8*b^4-10*cos(f*x+e)^6*a^4+32*cos(f*x+e)^6*a^3*b-36*cos(f*x+e)^6*a^2*b^2+16*cos(f*x+e)^6*a*b^3-2*cos(f*x+e)^6*b^4+15*cos(f*x+e)^4*a^4-42*a^2*b^2*cos(f*x+e)^4+24*cos(f*x+e)^4*a*b^3+3*cos(f*x+e)^4*b^4+60*cos(f*x+e)^2*a^3*b+60*cos(f*x+e)^2*a^2*b^2-108*cos(f*x+e)^2*a*b^3-12*cos(f*x+e)^2*b^4+40*a^2*b^2+80*a*b^3+8*b^4)*4^(1/2)*a^7/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5/((-(a-b)*b)^(1/2)+a-b)^7/((-(a-b)*b)^(1/2)-a+b)^7","A"
141,1,262,154,1.505000," ","int(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{\left(a -b \right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \left(\left(\cos^{6}\left(f x +e \right)\right) a^{3}-3 \left(\cos^{6}\left(f x +e \right)\right) a^{2} b +3 \left(\cos^{6}\left(f x +e \right)\right) a \,b^{2}-\left(\cos^{6}\left(f x +e \right)\right) b^{3}-3 \left(\cos^{4}\left(f x +e \right)\right) a^{3}+3 \left(\cos^{4}\left(f x +e \right)\right) a^{2} b +3 \left(\cos^{4}\left(f x +e \right)\right) a \,b^{2}-3 \left(\cos^{4}\left(f x +e \right)\right) b^{3}-12 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b +12 \left(\cos^{2}\left(f x +e \right)\right) b^{3}-8 b^{2} a -8 b^{3}\right) \sqrt{4}\, a^{5}}{6 f \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{5} \left(\sqrt{-\left(a -b \right) b}+a -b \right)^{5} \left(\sqrt{-\left(a -b \right) b}-a +b \right)^{5}}"," ",0,"-1/6/f*(a-b)*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)*(cos(f*x+e)^6*a^3-3*cos(f*x+e)^6*a^2*b+3*cos(f*x+e)^6*a*b^2-cos(f*x+e)^6*b^3-3*cos(f*x+e)^4*a^3+3*cos(f*x+e)^4*a^2*b+3*cos(f*x+e)^4*a*b^2-3*cos(f*x+e)^4*b^3-12*a^2*cos(f*x+e)^2*b+12*cos(f*x+e)^2*b^3-8*b^2*a-8*b^3)*4^(1/2)*a^5/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5/((-(a-b)*b)^(1/2)+a-b)^5/((-(a-b)*b)^(1/2)-a+b)^5","A"
142,1,147,108,0.335000," ","int(sin(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{\left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \left(3 \left(\cos^{4}\left(f x +e \right)\right) a^{2}-6 \left(\cos^{4}\left(f x +e \right)\right) a b +3 \left(\cos^{4}\left(f x +e \right)\right) b^{2}+12 \left(\cos^{2}\left(f x +e \right)\right) a b -12 b^{2} \left(\cos^{2}\left(f x +e \right)\right)+8 b^{2}\right)}{3 f \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{5} \left(a -b \right)^{3}}"," ",0,"-1/3/f*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)*(3*cos(f*x+e)^4*a^2-6*cos(f*x+e)^4*a*b+3*cos(f*x+e)^4*b^2+12*cos(f*x+e)^2*a*b-12*b^2*cos(f*x+e)^2+8*b^2)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5/(a-b)^3","A"
143,1,27448,122,2.457000," ","int(csc(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
144,1,38486,157,3.841000," ","int(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
145,1,49917,213,7.125000," ","int(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
146,1,7943,222,15.659000," ","int(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
147,1,2511,161,6.091000," ","int(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x)","\text{Expression too large to display}"," ",0,"1/3/f*(-1+cos(2*f*x+2*e))*(3*(b^4*(a-b))^(1/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)*b^2/(b^4*(a-b))^(1/2))*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*sin(2*f*x+2*e)*cos(2*f*x+2*e)*a^2+3*(b^4*(a-b))^(1/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)*b^2/(b^4*(a-b))^(1/2))*sin(2*f*x+2*e)*a^2*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)-6*cos(2*f*x+2*e)^2*a^3*b^3+14*cos(2*f*x+2*e)^2*a^2*b^4-10*cos(2*f*x+2*e)^2*a*b^5+2*cos(2*f*x+2*e)^2*b^6-10*cos(2*f*x+2*e)*a^2*b^4+14*cos(2*f*x+2*e)*a*b^5-4*cos(2*f*x+2*e)*b^6+6*a^3*b^3-4*b^4*a^2-4*a*b^5+2*b^6)/sin(2*f*x+2*e)^3/(a-b)^3/a^2/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)/b^2+1/12/f*(-1+cos(2*f*x+2*e))*(-52*(a-b)^(3/2)*cos(2*f*x+2*e)^2*a*b^5-3*(a-b)^(3/2)*cos(2*f*x+2*e)^3*a^5*b+9*(a-b)^(3/2)*cos(2*f*x+2*e)^3*a^4*b^2-3*(a-b)^(3/2)*cos(2*f*x+2*e)^2*a^5*b-3*(a-b)^(3/2)*cos(2*f*x+2*e)^2*a^4*b^2+24*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*(a-b)^(3/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)*b^2/(b^4*(a-b))^(1/2))*cos(2*f*x+2*e)*(b^4*(a-b))^(1/2)*a^2+33*(a-b)^(3/2)*a^3*b^3-19*(a-b)^(3/2)*a^2*b^4-28*(a-b)^(3/2)*a*b^5-3*(a-b)^(3/2)*cos(2*f*x+2*e)*a^3*b^3-55*(a-b)^(3/2)*cos(2*f*x+2*e)*a^2*b^4+80*(a-b)^(3/2)*cos(2*f*x+2*e)*a*b^5-9*(a-b)^(3/2)*a^4*b^2*cos(2*f*x+2*e)+3*(a-b)^(3/2)*a^5*b*cos(2*f*x+2*e)-9*(a-b)^(3/2)*cos(2*f*x+2*e)^3*a^3*b^3+3*(a-b)^(3/2)*cos(2*f*x+2*e)^3*a^2*b^4-21*(a-b)^(3/2)*cos(2*f*x+2*e)^2*a^3*b^3+71*(a-b)^(3/2)*cos(2*f*x+2*e)^2*a^2*b^4-16*(a-b)^(3/2)*cos(2*f*x+2*e)*b^6+8*(a-b)^(3/2)*cos(2*f*x+2*e)^2*b^6-6*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*a^5*b+24*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*a^4*b^2-30*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*a^3*b^3+12*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*a^2*b^4+3*(a-b)^(3/2)*a^5*b+3*(a-b)^(3/2)*a^4*b^2+8*(a-b)^(3/2)*b^6-6*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*cos(2*f*x+2*e)*a^5*b+24*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*cos(2*f*x+2*e)*a^4*b^2-30*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*cos(2*f*x+2*e)*a^3*b^3+12*sin(2*f*x+2*e)*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)^(1/2))*cos(2*f*x+2*e)*a^2*b^4+24*(b^4*(a-b))^(1/2)*arctan((-1+cos(2*f*x+2*e))/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(1/2)/sin(2*f*x+2*e)*(a-b)*b^2/(b^4*(a-b))^(1/2))*sin(2*f*x+2*e)*a^2*((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)*(a-b)^(3/2))/(a-b)^(11/2)/sin(2*f*x+2*e)^3/((a*cos(2*f*x+2*e)-b*cos(2*f*x+2*e)+a+b)/(cos(2*f*x+2*e)+1))^(3/2)/a^2/b","B"
148,1,176,120,0.327000," ","int(1/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{b \tan \left(f x +e \right)}{3 a \left(a -b \right) f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{2 b \tan \left(f x +e \right)}{3 f \left(a -b \right) a^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{b \tan \left(f x +e \right)}{f \left(a -b \right)^{2} a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{3} b^{2}}"," ",0,"-1/3*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-2/3/f*b/(a-b)/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)-1/f*b/(a-b)^2*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)^3*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
149,1,153,87,1.123000," ","int(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{\left(3 \left(\cos^{4}\left(f x +e \right)\right) a^{2}-12 \left(\cos^{4}\left(f x +e \right)\right) a b +8 \left(\cos^{4}\left(f x +e \right)\right) b^{2}+12 \left(\cos^{2}\left(f x +e \right)\right) a b -16 b^{2} \left(\cos^{2}\left(f x +e \right)\right)+8 b^{2}\right) \left(\cos^{5}\left(f x +e \right)\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}}}{3 f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{4} \sin \left(f x +e \right) a^{3}}"," ",0,"-1/3/f/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^4*(3*cos(f*x+e)^4*a^2-12*cos(f*x+e)^4*a*b+8*cos(f*x+e)^4*b^2+12*cos(f*x+e)^2*a*b-16*b^2*cos(f*x+e)^2+8*b^2)*cos(f*x+e)^5*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(5/2)/sin(f*x+e)/a^3","A"
150,1,245,132,1.314000," ","int(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x)","\frac{\left(2 \left(\cos^{6}\left(f x +e \right)\right) a^{3}-18 \left(\cos^{6}\left(f x +e \right)\right) a^{2} b +32 \left(\cos^{6}\left(f x +e \right)\right) a \,b^{2}-16 \left(\cos^{6}\left(f x +e \right)\right) b^{3}-3 \left(\cos^{4}\left(f x +e \right)\right) a^{3}+30 \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -72 \left(\cos^{4}\left(f x +e \right)\right) a \,b^{2}+48 \left(\cos^{4}\left(f x +e \right)\right) b^{3}-12 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b +48 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-48 \left(\cos^{2}\left(f x +e \right)\right) b^{3}-8 b^{2} a +16 b^{3}\right) \left(\cos^{5}\left(f x +e \right)\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}}}{3 f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{4} \sin \left(f x +e \right)^{3} a^{4}}"," ",0,"1/3/f/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^4*(2*cos(f*x+e)^6*a^3-18*cos(f*x+e)^6*a^2*b+32*cos(f*x+e)^6*a*b^2-16*cos(f*x+e)^6*b^3-3*cos(f*x+e)^4*a^3+30*cos(f*x+e)^4*a^2*b-72*cos(f*x+e)^4*a*b^2+48*cos(f*x+e)^4*b^3-12*a^2*cos(f*x+e)^2*b+48*cos(f*x+e)^2*a*b^2-48*cos(f*x+e)^2*b^3-8*b^2*a+16*b^3)*cos(f*x+e)^5*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(5/2)/sin(f*x+e)^3/a^4","A"
151,1,371,199,1.098000," ","int(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{\left(8 \left(\cos^{8}\left(f x +e \right)\right) a^{4}-112 \left(\cos^{8}\left(f x +e \right)\right) a^{3} b +328 \left(\cos^{8}\left(f x +e \right)\right) a^{2} b^{2}-352 \left(\cos^{8}\left(f x +e \right)\right) a \,b^{3}+128 \left(\cos^{8}\left(f x +e \right)\right) b^{4}-20 \left(\cos^{6}\left(f x +e \right)\right) a^{4}+292 \left(\cos^{6}\left(f x +e \right)\right) a^{3} b -976 \left(\cos^{6}\left(f x +e \right)\right) a^{2} b^{2}+1216 \left(\cos^{6}\left(f x +e \right)\right) a \,b^{3}-512 \left(\cos^{6}\left(f x +e \right)\right) b^{4}+15 \left(\cos^{4}\left(f x +e \right)\right) a^{4}-240 \left(\cos^{4}\left(f x +e \right)\right) a^{3} b +1008 a^{2} b^{2} \left(\cos^{4}\left(f x +e \right)\right)-1536 \left(\cos^{4}\left(f x +e \right)\right) a \,b^{3}+768 \left(\cos^{4}\left(f x +e \right)\right) b^{4}+60 \left(\cos^{2}\left(f x +e \right)\right) a^{3} b -400 \left(\cos^{2}\left(f x +e \right)\right) a^{2} b^{2}+832 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{3}-512 \left(\cos^{2}\left(f x +e \right)\right) b^{4}+40 a^{2} b^{2}-160 a \,b^{3}+128 b^{4}\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \left(\cos^{5}\left(f x +e \right)\right)}{15 f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{4} \sin \left(f x +e \right)^{5} a^{5}}"," ",0,"-1/15/f/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^4*(8*cos(f*x+e)^8*a^4-112*cos(f*x+e)^8*a^3*b+328*cos(f*x+e)^8*a^2*b^2-352*cos(f*x+e)^8*a*b^3+128*cos(f*x+e)^8*b^4-20*cos(f*x+e)^6*a^4+292*cos(f*x+e)^6*a^3*b-976*cos(f*x+e)^6*a^2*b^2+1216*cos(f*x+e)^6*a*b^3-512*cos(f*x+e)^6*b^4+15*cos(f*x+e)^4*a^4-240*cos(f*x+e)^4*a^3*b+1008*a^2*b^2*cos(f*x+e)^4-1536*cos(f*x+e)^4*a*b^3+768*cos(f*x+e)^4*b^4+60*cos(f*x+e)^2*a^3*b-400*cos(f*x+e)^2*a^2*b^2+832*cos(f*x+e)^2*a*b^3-512*cos(f*x+e)^2*b^4+40*a^2*b^2-160*a*b^3+128*b^4)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(5/2)*cos(f*x+e)^5/sin(f*x+e)^5/a^5","A"
152,0,0,78,4.956000," ","int((d*sin(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","\int \left(d \sin \left(f x +e \right)\right)^{m} \left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*sin(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","F"
153,0,0,113,2.144000," ","int((d*sin(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","\int \left(d \sin \left(f x +e \right)\right)^{m} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*sin(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","F"
154,0,0,200,5.199000," ","int(sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\sin^{5}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x)","F"
155,0,0,134,4.457000," ","int(sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\sin^{3}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x)","F"
156,0,0,77,0.911000," ","int(sin(f*x+e)*(a+b*tan(f*x+e)^2)^p,x)","\int \sin \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sin(f*x+e)*(a+b*tan(f*x+e)^2)^p,x)","F"
157,0,0,84,1.108000," ","int(csc(f*x+e)*(a+b*tan(f*x+e)^2)^p,x)","\int \csc \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)*(a+b*tan(f*x+e)^2)^p,x)","F"
158,0,0,86,1.117000," ","int(csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\csc^{3}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x)","F"
159,0,0,77,4.824000," ","int(sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\sin^{2}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x)","F"
160,0,0,74,0.734000," ","int((a+b*tan(f*x+e)^2)^p,x)","\int \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*tan(f*x+e)^2)^p,x)","F"
161,0,0,66,1.053000," ","int(csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\csc^{2}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x)","F"
162,0,0,114,1.079000," ","int(csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\csc^{4}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x)","F"
163,0,0,172,1.051000," ","int(csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\csc^{6}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x)","F"
164,0,0,92,7.974000," ","int((d*sin(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \sin \left(f x +e \right)\right)^{m} \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*sin(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","F"
165,-1,0,59,180.000000," ","int(sin(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sin^{2}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sin(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","F"
166,-1,0,57,180.000000," ","int((b*(c*tan(f*x+e))^n)^p,x)","\int \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((b*(c*tan(f*x+e))^n)^p,x)","F"
167,-1,0,33,180.000000," ","int(csc(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\csc^{2}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","F"
168,-1,0,69,180.000000," ","int(csc(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\csc^{4}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x)","F"
169,1,171293,104,26.464000," ","int(csc(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x)","\text{output too large to display}"," ",0,"result too large to display","C"
170,0,0,83,33.920000," ","int(sin(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sin^{3}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sin(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","F"
171,0,0,81,21.642000," ","int(sin(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","\int \sin \left(f x +e \right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sin(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","F"
172,0,0,72,25.659000," ","int(csc(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","\int \csc \left(f x +e \right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(csc(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","F"
173,0,0,83,21.941000," ","int(csc(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\csc^{3}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","F"
174,0,0,27,7.662000," ","int((d*sin(f*x+e))^m*(a+b*tan(f*x+e)^n)^p,x)","\int \left(d \sin \left(f x +e \right)\right)^{m} \left(a +b \left(\tan^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*sin(f*x+e))^m*(a+b*tan(f*x+e)^n)^p,x)","F"
175,0,0,77,4.901000," ","int((d*cos(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","\int \left(d \cos \left(f x +e \right)\right)^{m} \left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*cos(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","F"
176,0,0,100,2.810000," ","int((d*cos(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","\int \left(d \cos \left(f x +e \right)\right)^{m} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*cos(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","F"
177,0,0,91,1.404000," ","int((d*cos(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \cos \left(f x +e \right)\right)^{m} \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*cos(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","F"
178,0,0,56,7.982000," ","int((d*cos(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \cos \left(f x +e \right)\right)^{m} \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*cos(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
179,1,43,61,0.024000," ","int((a+a*tan(d*x+c)^2)^4,x)","\frac{a^{4} \left(\frac{\left(\tan^{7}\left(d x +c \right)\right)}{7}+\frac{3 \left(\tan^{5}\left(d x +c \right)\right)}{5}+\tan^{3}\left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^4*(1/7*tan(d*x+c)^7+3/5*tan(d*x+c)^5+tan(d*x+c)^3+tan(d*x+c))","A"
180,1,35,46,0.028000," ","int((a+a*tan(d*x+c)^2)^3,x)","\frac{a^{3} \left(\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}+\frac{2 \left(\tan^{3}\left(d x +c \right)\right)}{3}+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^3*(1/5*tan(d*x+c)^5+2/3*tan(d*x+c)^3+tan(d*x+c))","A"
181,1,25,30,0.024000," ","int((a+a*tan(d*x+c)^2)^2,x)","\frac{a^{2} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^2*(1/3*tan(d*x+c)^3+tan(d*x+c))","A"
182,1,43,27,0.173000," ","int(1/(a+a*tan(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)}{2 a d \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{2 a d}"," ",0,"1/2/a/d*tan(d*x+c)/(1+tan(d*x+c)^2)+1/2/a/d*arctan(tan(d*x+c))","A"
183,1,69,49,0.354000," ","int(1/(a+a*tan(d*x+c)^2)^2,x)","\frac{\tan \left(d x +c \right)}{4 d \,a^{2} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 \tan \left(d x +c \right)}{8 d \,a^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right)}{8 d \,a^{2}}"," ",0,"1/4/d/a^2*tan(d*x+c)/(1+tan(d*x+c)^2)^2+3/8/d/a^2*tan(d*x+c)/(1+tan(d*x+c)^2)+3/8/d/a^2*arctan(tan(d*x+c))","A"
184,1,95,71,0.339000," ","int(1/(a+a*tan(d*x+c)^2)^3,x)","\frac{\tan \left(d x +c \right)}{6 d \,a^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{5 \tan \left(d x +c \right)}{24 d \,a^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \tan \left(d x +c \right)}{16 d \,a^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{5 \arctan \left(\tan \left(d x +c \right)\right)}{16 d \,a^{3}}"," ",0,"1/6/d/a^3*tan(d*x+c)/(1+tan(d*x+c)^2)^3+5/24/d/a^3*tan(d*x+c)/(1+tan(d*x+c)^2)^2+5/16/d/a^3*tan(d*x+c)/(1+tan(d*x+c)^2)+5/16/d/a^3*arctan(tan(d*x+c))","A"
185,1,106,68,0.035000," ","int(tan(f*x+e)^5*(a+b*tan(f*x+e)^2),x)","\frac{b \left(\tan^{6}\left(f x +e \right)\right)}{6 f}+\frac{\left(\tan^{4}\left(f x +e \right)\right) a}{4 f}-\frac{b \left(\tan^{4}\left(f x +e \right)\right)}{4 f}-\frac{a \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{b \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b}{2 f}"," ",0,"1/6*b*tan(f*x+e)^6/f+1/4/f*tan(f*x+e)^4*a-1/4*b*tan(f*x+e)^4/f-1/2/f*a*tan(f*x+e)^2+1/2*b*tan(f*x+e)^2/f+1/2/f*ln(1+tan(f*x+e)^2)*a-1/2/f*ln(1+tan(f*x+e)^2)*b","A"
186,1,78,49,0.029000," ","int(tan(f*x+e)^3*(a+b*tan(f*x+e)^2),x)","\frac{b \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{a \left(\tan^{2}\left(f x +e \right)\right)}{2 f}-\frac{b \left(\tan^{2}\left(f x +e \right)\right)}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b}{2 f}"," ",0,"1/4*b*tan(f*x+e)^4/f+1/2/f*a*tan(f*x+e)^2-1/2*b*tan(f*x+e)^2/f-1/2/f*ln(1+tan(f*x+e)^2)*a+1/2/f*ln(1+tan(f*x+e)^2)*b","A"
187,1,50,32,0.031000," ","int(tan(f*x+e)*(a+b*tan(f*x+e)^2),x)","\frac{b \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b}{2 f}"," ",0,"1/2*b*tan(f*x+e)^2/f+1/2/f*ln(1+tan(f*x+e)^2)*a-1/2/f*ln(1+tan(f*x+e)^2)*b","A"
188,1,27,26,0.569000," ","int(cot(f*x+e)*(a+b*tan(f*x+e)^2),x)","-\frac{b \ln \left(\cos \left(f x +e \right)\right)}{f}+\frac{a \ln \left(\sin \left(f x +e \right)\right)}{f}"," ",0,"-b*ln(cos(f*x+e))/f+a*ln(sin(f*x+e))/f","A"
189,1,41,32,0.662000," ","int(cot(f*x+e)^3*(a+b*tan(f*x+e)^2),x)","\frac{b \ln \left(\sin \left(f x +e \right)\right)}{f}-\frac{a \left(\cot^{2}\left(f x +e \right)\right)}{2 f}-\frac{a \ln \left(\sin \left(f x +e \right)\right)}{f}"," ",0,"1/f*b*ln(sin(f*x+e))-1/2*a*cot(f*x+e)^2/f-a*ln(sin(f*x+e))/f","A"
190,1,69,49,0.534000," ","int(cot(f*x+e)^5*(a+b*tan(f*x+e)^2),x)","-\frac{b \left(\cot^{2}\left(f x +e \right)\right)}{2 f}-\frac{b \ln \left(\sin \left(f x +e \right)\right)}{f}-\frac{a \left(\cot^{4}\left(f x +e \right)\right)}{4 f}+\frac{a \left(\cot^{2}\left(f x +e \right)\right)}{2 f}+\frac{a \ln \left(\sin \left(f x +e \right)\right)}{f}"," ",0,"-1/2/f*b*cot(f*x+e)^2-1/f*b*ln(sin(f*x+e))-1/4*a*cot(f*x+e)^4/f+1/2*a*cot(f*x+e)^2/f+a*ln(sin(f*x+e))/f","A"
191,1,120,74,0.028000," ","int(tan(f*x+e)^6*(a+b*tan(f*x+e)^2),x)","\frac{b \left(\tan^{7}\left(f x +e \right)\right)}{7 f}+\frac{a \left(\tan^{5}\left(f x +e \right)\right)}{5 f}-\frac{b \left(\tan^{5}\left(f x +e \right)\right)}{5 f}-\frac{a \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{b \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{a \tan \left(f x +e \right)}{f}-\frac{b \tan \left(f x +e \right)}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b}{f}"," ",0,"1/7*b*tan(f*x+e)^7/f+1/5/f*a*tan(f*x+e)^5-1/5*b*tan(f*x+e)^5/f-1/3/f*a*tan(f*x+e)^3+1/3*b*tan(f*x+e)^3/f+1/f*a*tan(f*x+e)-b*tan(f*x+e)/f-1/f*arctan(tan(f*x+e))*a+1/f*arctan(tan(f*x+e))*b","A"
192,1,92,56,0.035000," ","int(tan(f*x+e)^4*(a+b*tan(f*x+e)^2),x)","\frac{b \left(\tan^{5}\left(f x +e \right)\right)}{5 f}+\frac{a \left(\tan^{3}\left(f x +e \right)\right)}{3 f}-\frac{b \left(\tan^{3}\left(f x +e \right)\right)}{3 f}-\frac{a \tan \left(f x +e \right)}{f}+\frac{b \tan \left(f x +e \right)}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b}{f}"," ",0,"1/5*b*tan(f*x+e)^5/f+1/3/f*a*tan(f*x+e)^3-1/3*b*tan(f*x+e)^3/f-1/f*a*tan(f*x+e)+b*tan(f*x+e)/f+1/f*arctan(tan(f*x+e))*a-1/f*arctan(tan(f*x+e))*b","A"
193,1,64,38,0.035000," ","int(tan(f*x+e)^2*(a+b*tan(f*x+e)^2),x)","\frac{b \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{a \tan \left(f x +e \right)}{f}-\frac{b \tan \left(f x +e \right)}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b}{f}"," ",0,"1/3*b*tan(f*x+e)^3/f+1/f*a*tan(f*x+e)-b*tan(f*x+e)/f-1/f*arctan(tan(f*x+e))*a+1/f*arctan(tan(f*x+e))*b","A"
194,1,29,19,0.031000," ","int(a+b*tan(f*x+e)^2,x)","a x +\frac{b \tan \left(f x +e \right)}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b}{f}"," ",0,"a*x+b*tan(f*x+e)/f-1/f*arctan(tan(f*x+e))*b","A"
195,1,31,21,0.512000," ","int(cot(f*x+e)^2*(a+b*tan(f*x+e)^2),x)","\frac{\left(f x +e \right) b +a \left(-\cot \left(f x +e \right)-f x -e \right)}{f}"," ",0,"1/f*((f*x+e)*b+a*(-cot(f*x+e)-f*x-e))","A"
196,1,47,37,0.586000," ","int(cot(f*x+e)^4*(a+b*tan(f*x+e)^2),x)","\frac{b \left(-\cot \left(f x +e \right)-f x -e \right)+a \left(-\frac{\left(\cot^{3}\left(f x +e \right)\right)}{3}+\cot \left(f x +e \right)+f x +e \right)}{f}"," ",0,"1/f*(b*(-cot(f*x+e)-f*x-e)+a*(-1/3*cot(f*x+e)^3+cot(f*x+e)+f*x+e))","A"
197,1,67,57,0.445000," ","int(cot(f*x+e)^6*(a+b*tan(f*x+e)^2),x)","\frac{b \left(-\frac{\left(\cot^{3}\left(f x +e \right)\right)}{3}+\cot \left(f x +e \right)+f x +e \right)+a \left(-\frac{\left(\cot^{5}\left(f x +e \right)\right)}{5}+\frac{\left(\cot^{3}\left(f x +e \right)\right)}{3}-\cot \left(f x +e \right)-f x -e \right)}{f}"," ",0,"1/f*(b*(-1/3*cot(f*x+e)^3+cot(f*x+e)+f*x+e)+a*(-1/5*cot(f*x+e)^5+1/3*cot(f*x+e)^3-cot(f*x+e)-f*x-e))","A"
198,1,198,97,0.030000," ","int(tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan^{8}\left(f x +e \right)\right)}{8 f}+\frac{a b \left(\tan^{6}\left(f x +e \right)\right)}{3 f}-\frac{b^{2} \left(\tan^{6}\left(f x +e \right)\right)}{6 f}+\frac{\left(\tan^{4}\left(f x +e \right)\right) a^{2}}{4 f}-\frac{\left(\tan^{4}\left(f x +e \right)\right) a b}{2 f}+\frac{b^{2} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}-\frac{\left(\tan^{2}\left(f x +e \right)\right) a^{2}}{2 f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) a b}{f}-\frac{b^{2} \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2}}{2 f}"," ",0,"1/8*b^2*tan(f*x+e)^8/f+1/3/f*a*b*tan(f*x+e)^6-1/6*b^2*tan(f*x+e)^6/f+1/4/f*tan(f*x+e)^4*a^2-1/2/f*tan(f*x+e)^4*a*b+1/4/f*b^2*tan(f*x+e)^4-1/2/f*tan(f*x+e)^2*a^2+1/f*tan(f*x+e)^2*a*b-1/2*b^2*tan(f*x+e)^2/f+1/2/f*ln(1+tan(f*x+e)^2)*a^2-1/f*ln(1+tan(f*x+e)^2)*a*b+1/2/f*ln(1+tan(f*x+e)^2)*b^2","B"
199,1,151,76,0.042000," ","int(tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan^{6}\left(f x +e \right)\right)}{6 f}+\frac{\left(\tan^{4}\left(f x +e \right)\right) a b}{2 f}-\frac{b^{2} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) a^{2}}{2 f}-\frac{\left(\tan^{2}\left(f x +e \right)\right) a b}{f}+\frac{b^{2} \left(\tan^{2}\left(f x +e \right)\right)}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2}}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b}{f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2}}{2 f}"," ",0,"1/6*b^2*tan(f*x+e)^6/f+1/2/f*tan(f*x+e)^4*a*b-1/4/f*b^2*tan(f*x+e)^4+1/2/f*tan(f*x+e)^2*a^2-1/f*tan(f*x+e)^2*a*b+1/2*b^2*tan(f*x+e)^2/f-1/2/f*ln(1+tan(f*x+e)^2)*a^2+1/f*ln(1+tan(f*x+e)^2)*a*b-1/2/f*ln(1+tan(f*x+e)^2)*b^2","A"
200,1,104,58,0.029000," ","int(tan(f*x+e)*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan^{4}\left(f x +e \right)\right)}{4 f}+\frac{\left(\tan^{2}\left(f x +e \right)\right) a b}{f}-\frac{b^{2} \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a^{2}}{2 f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) a b}{f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right) b^{2}}{2 f}"," ",0,"1/4/f*b^2*tan(f*x+e)^4+1/f*tan(f*x+e)^2*a*b-1/2*b^2*tan(f*x+e)^2/f+1/2/f*ln(1+tan(f*x+e)^2)*a^2-1/f*ln(1+tan(f*x+e)^2)*a*b+1/2/f*ln(1+tan(f*x+e)^2)*b^2","A"
201,1,60,49,0.640000," ","int(cot(f*x+e)*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{b^{2} \ln \left(\cos \left(f x +e \right)\right)}{f}-\frac{2 a b \ln \left(\cos \left(f x +e \right)\right)}{f}+\frac{a^{2} \ln \left(\sin \left(f x +e \right)\right)}{f}"," ",0,"1/2*b^2*tan(f*x+e)^2/f+1/f*b^2*ln(cos(f*x+e))-2/f*a*b*ln(cos(f*x+e))+1/f*a^2*ln(sin(f*x+e))","A"
202,1,62,54,0.736000," ","int(cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x)","-\frac{b^{2} \ln \left(\cos \left(f x +e \right)\right)}{f}+\frac{2 a b \ln \left(\sin \left(f x +e \right)\right)}{f}-\frac{a^{2} \left(\cot^{2}\left(f x +e \right)\right)}{2 f}-\frac{a^{2} \ln \left(\sin \left(f x +e \right)\right)}{f}"," ",0,"-1/f*b^2*ln(cos(f*x+e))+2/f*a*b*ln(sin(f*x+e))-1/2*a^2*cot(f*x+e)^2/f-1/f*a^2*ln(sin(f*x+e))","A"
203,1,91,72,0.543000," ","int(cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \ln \left(\sin \left(f x +e \right)\right)}{f}-\frac{a b \left(\cot^{2}\left(f x +e \right)\right)}{f}-\frac{2 a b \ln \left(\sin \left(f x +e \right)\right)}{f}-\frac{a^{2} \left(\cot^{4}\left(f x +e \right)\right)}{4 f}+\frac{a^{2} \left(\cot^{2}\left(f x +e \right)\right)}{2 f}+\frac{a^{2} \ln \left(\sin \left(f x +e \right)\right)}{f}"," ",0,"1/f*b^2*ln(sin(f*x+e))-1/f*a*b*cot(f*x+e)^2-2/f*a*b*ln(sin(f*x+e))-1/4*a^2*cot(f*x+e)^4/f+1/2*a^2*cot(f*x+e)^2/f+1/f*a^2*ln(sin(f*x+e))","A"
204,1,226,105,0.032000," ","int(tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan^{9}\left(f x +e \right)\right)}{9 f}+\frac{2 \left(\tan^{7}\left(f x +e \right)\right) a b}{7 f}-\frac{b^{2} \left(\tan^{7}\left(f x +e \right)\right)}{7 f}+\frac{\left(\tan^{5}\left(f x +e \right)\right) a^{2}}{5 f}-\frac{2 \left(\tan^{5}\left(f x +e \right)\right) a b}{5 f}+\frac{b^{2} \left(\tan^{5}\left(f x +e \right)\right)}{5 f}-\frac{\left(\tan^{3}\left(f x +e \right)\right) a^{2}}{3 f}+\frac{2 \left(\tan^{3}\left(f x +e \right)\right) a b}{3 f}-\frac{b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{a^{2} \tan \left(f x +e \right)}{f}-\frac{2 a b \tan \left(f x +e \right)}{f}+\frac{b^{2} \tan \left(f x +e \right)}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2}}{f}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f}"," ",0,"1/9*b^2*tan(f*x+e)^9/f+2/7/f*tan(f*x+e)^7*a*b-1/7*b^2*tan(f*x+e)^7/f+1/5/f*tan(f*x+e)^5*a^2-2/5/f*tan(f*x+e)^5*a*b+1/5*b^2*tan(f*x+e)^5/f-1/3/f*tan(f*x+e)^3*a^2+2/3/f*tan(f*x+e)^3*a*b-1/3*b^2*tan(f*x+e)^3/f+1/f*a^2*tan(f*x+e)-2*a*b*tan(f*x+e)/f+b^2*tan(f*x+e)/f-1/f*arctan(tan(f*x+e))*a^2+2/f*arctan(tan(f*x+e))*a*b-1/f*arctan(tan(f*x+e))*b^2","B"
205,1,179,85,0.034000," ","int(tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan^{7}\left(f x +e \right)\right)}{7 f}+\frac{2 \left(\tan^{5}\left(f x +e \right)\right) a b}{5 f}-\frac{b^{2} \left(\tan^{5}\left(f x +e \right)\right)}{5 f}+\frac{\left(\tan^{3}\left(f x +e \right)\right) a^{2}}{3 f}-\frac{2 \left(\tan^{3}\left(f x +e \right)\right) a b}{3 f}+\frac{b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}-\frac{a^{2} \tan \left(f x +e \right)}{f}+\frac{2 a b \tan \left(f x +e \right)}{f}-\frac{b^{2} \tan \left(f x +e \right)}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2}}{f}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f}"," ",0,"1/7*b^2*tan(f*x+e)^7/f+2/5/f*tan(f*x+e)^5*a*b-1/5*b^2*tan(f*x+e)^5/f+1/3/f*tan(f*x+e)^3*a^2-2/3/f*tan(f*x+e)^3*a*b+1/3*b^2*tan(f*x+e)^3/f-1/f*a^2*tan(f*x+e)+2*a*b*tan(f*x+e)/f-b^2*tan(f*x+e)/f+1/f*arctan(tan(f*x+e))*a^2-2/f*arctan(tan(f*x+e))*a*b+1/f*arctan(tan(f*x+e))*b^2","B"
206,1,132,65,0.029000," ","int(tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan^{5}\left(f x +e \right)\right)}{5 f}+\frac{2 \left(\tan^{3}\left(f x +e \right)\right) a b}{3 f}-\frac{b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{a^{2} \tan \left(f x +e \right)}{f}-\frac{2 a b \tan \left(f x +e \right)}{f}+\frac{b^{2} \tan \left(f x +e \right)}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2}}{f}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b}{f}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f}"," ",0,"1/5*b^2*tan(f*x+e)^5/f+2/3/f*tan(f*x+e)^3*a*b-1/3*b^2*tan(f*x+e)^3/f+1/f*a^2*tan(f*x+e)-2*a*b*tan(f*x+e)/f+b^2*tan(f*x+e)/f-1/f*arctan(tan(f*x+e))*a^2+2/f*arctan(tan(f*x+e))*a*b-1/f*arctan(tan(f*x+e))*b^2","B"
207,1,87,44,0.030000," ","int((a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{3 f}+\frac{2 a b \tan \left(f x +e \right)}{f}-\frac{b^{2} \tan \left(f x +e \right)}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) a^{2}}{f}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) a b}{f}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f}"," ",0,"1/3*b^2*tan(f*x+e)^3/f+2*a*b*tan(f*x+e)/f-b^2*tan(f*x+e)/f+1/f*arctan(tan(f*x+e))*a^2-2/f*arctan(tan(f*x+e))*a*b+1/f*arctan(tan(f*x+e))*b^2","A"
208,1,53,38,0.480000," ","int(cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(\tan \left(f x +e \right)-f x -e \right)+2 a b \left(f x +e \right)+a^{2} \left(-\cot \left(f x +e \right)-f x -e \right)}{f}"," ",0,"1/f*(b^2*(tan(f*x+e)-f*x-e)+2*a*b*(f*x+e)+a^2*(-cot(f*x+e)-f*x-e))","A"
209,1,60,42,0.534000," ","int(cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(f x +e \right)+2 a b \left(-\cot \left(f x +e \right)-f x -e \right)+a^{2} \left(-\frac{\left(\cot^{3}\left(f x +e \right)\right)}{3}+\cot \left(f x +e \right)+f x +e \right)}{f}"," ",0,"1/f*(b^2*(f*x+e)+2*a*b*(-cot(f*x+e)-f*x-e)+a^2*(-1/3*cot(f*x+e)^3+cot(f*x+e)+f*x+e))","A"
210,1,91,64,0.694000," ","int(cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \left(-\cot \left(f x +e \right)-f x -e \right)+2 a b \left(-\frac{\left(\cot^{3}\left(f x +e \right)\right)}{3}+\cot \left(f x +e \right)+f x +e \right)+a^{2} \left(-\frac{\left(\cot^{5}\left(f x +e \right)\right)}{5}+\frac{\left(\cot^{3}\left(f x +e \right)\right)}{3}-\cot \left(f x +e \right)-f x -e \right)}{f}"," ",0,"1/f*(b^2*(-cot(f*x+e)-f*x-e)+2*a*b*(-1/3*cot(f*x+e)^3+cot(f*x+e)+f*x+e)+a^2*(-1/5*cot(f*x+e)^5+1/3*cot(f*x+e)^3-cot(f*x+e)-f*x-e))","A"
211,1,72,67,0.182000," ","int(tan(f*x+e)^5/(a+b*tan(f*x+e)^2),x)","\frac{\tan^{2}\left(f x +e \right)}{2 b f}-\frac{a^{2} \ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{2 \left(a -b \right) b^{2} f}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \left(a -b \right)}"," ",0,"1/2*tan(f*x+e)^2/b/f-1/2*a^2*ln(a+b*tan(f*x+e)^2)/(a-b)/b^2/f+1/2/f/(a-b)*ln(1+tan(f*x+e)^2)","A"
212,1,54,48,0.143000," ","int(tan(f*x+e)^3/(a+b*tan(f*x+e)^2),x)","\frac{a \ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{2 \left(a -b \right) b f}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \left(a -b \right)}"," ",0,"1/2*a*ln(a+b*tan(f*x+e)^2)/(a-b)/b/f-1/2/f/(a-b)*ln(1+tan(f*x+e)^2)","A"
213,1,50,34,0.188000," ","int(tan(f*x+e)/(a+b*tan(f*x+e)^2),x)","-\frac{\ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{2 f \left(a -b \right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \left(a -b \right)}"," ",0,"-1/2/f/(a-b)*ln(a+b*tan(f*x+e)^2)+1/2/f/(a-b)*ln(1+tan(f*x+e)^2)","A"
214,1,76,62,0.726000," ","int(cot(f*x+e)/(a+b*tan(f*x+e)^2),x)","\frac{b \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f a \left(a -b \right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f a}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f a}"," ",0,"1/2/f/a*b/(a-b)*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/2/f/a*ln(-1+cos(f*x+e))+1/2/f/a*ln(1+cos(f*x+e))","A"
215,1,150,85,0.779000," ","int(cot(f*x+e)^3/(a+b*tan(f*x+e)^2),x)","-\frac{b^{2} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f \,a^{2} \left(a -b \right)}+\frac{1}{4 f a \left(-1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f a}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b}{2 f \,a^{2}}-\frac{1}{4 f a \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f a}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) b}{2 f \,a^{2}}"," ",0,"-1/2/f*b^2/a^2/(a-b)*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/4/f/a/(-1+cos(f*x+e))-1/2/f/a*ln(-1+cos(f*x+e))-1/2/f/a^2*ln(-1+cos(f*x+e))*b-1/4/f/a/(1+cos(f*x+e))-1/2/f/a*ln(1+cos(f*x+e))-1/2/f/a^2*ln(1+cos(f*x+e))*b","A"
216,1,264,109,0.923000," ","int(cot(f*x+e)^5/(a+b*tan(f*x+e)^2),x)","\frac{b^{3} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f \,a^{3} \left(a -b \right)}-\frac{1}{16 f a \left(-1+\cos \left(f x +e \right)\right)^{2}}-\frac{7}{16 f a \left(-1+\cos \left(f x +e \right)\right)}-\frac{b}{4 f \,a^{2} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f a}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b}{2 f \,a^{2}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{2 f \,a^{3}}-\frac{1}{16 f a \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{7}{16 f a \left(1+\cos \left(f x +e \right)\right)}+\frac{b}{4 f \,a^{2} \left(1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f a}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) b}{2 f \,a^{2}}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{2 f \,a^{3}}"," ",0,"1/2/f*b^3/a^3/(a-b)*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-1/16/f/a/(-1+cos(f*x+e))^2-7/16/f/a/(-1+cos(f*x+e))-1/4/f/a^2/(-1+cos(f*x+e))*b+1/2/f/a*ln(-1+cos(f*x+e))+1/2/f/a^2*ln(-1+cos(f*x+e))*b+1/2/f/a^3*ln(-1+cos(f*x+e))*b^2-1/16/f/a/(1+cos(f*x+e))^2+7/16/f/a/(1+cos(f*x+e))+1/4/f/a^2/(1+cos(f*x+e))*b+1/2/f/a*ln(1+cos(f*x+e))+1/2/f/a^2*ln(1+cos(f*x+e))*b+1/2/f/a^3*ln(1+cos(f*x+e))*b^2","B"
217,1,102,75,0.176000," ","int(tan(f*x+e)^6/(a+b*tan(f*x+e)^2),x)","\frac{\tan^{3}\left(f x +e \right)}{3 b f}-\frac{a \tan \left(f x +e \right)}{f \,b^{2}}-\frac{\tan \left(f x +e \right)}{b f}+\frac{a^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \,b^{2} \left(a -b \right) \sqrt{a b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)}"," ",0,"1/3*tan(f*x+e)^3/b/f-1/f/b^2*a*tan(f*x+e)-tan(f*x+e)/b/f+1/f/b^2*a^3/(a-b)/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/(a-b)*arctan(tan(f*x+e))","A"
218,1,70,55,0.130000," ","int(tan(f*x+e)^4/(a+b*tan(f*x+e)^2),x)","\frac{\tan \left(f x +e \right)}{b f}-\frac{a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f b \left(a -b \right) \sqrt{a b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)}"," ",0,"tan(f*x+e)/b/f-1/f/b*a^2/(a-b)/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f/(a-b)*arctan(tan(f*x+e))","A"
219,1,52,42,0.158000," ","int(tan(f*x+e)^2/(a+b*tan(f*x+e)^2),x)","\frac{a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \left(a -b \right) \sqrt{a b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)}"," ",0,"1/f*a/(a-b)/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/(a-b)*arctan(tan(f*x+e))","A"
220,1,52,42,0.255000," ","int(1/(a+b*tan(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \left(a -b \right) \sqrt{a b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)}"," ",0,"-1/f*b/(a-b)/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f/(a-b)*arctan(tan(f*x+e))","A"
221,1,73,56,0.610000," ","int(cot(f*x+e)^2/(a+b*tan(f*x+e)^2),x)","\frac{b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f a \left(a -b \right) \sqrt{a b}}-\frac{1}{f a \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)}"," ",0,"1/f/a*b^2/(a-b)/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/a/tan(f*x+e)-1/f/(a-b)*arctan(tan(f*x+e))","A"
222,1,104,74,0.845000," ","int(cot(f*x+e)^4/(a+b*tan(f*x+e)^2),x)","-\frac{b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \,a^{2} \left(a -b \right) \sqrt{a b}}-\frac{1}{3 f a \tan \left(f x +e \right)^{3}}+\frac{1}{f a \tan \left(f x +e \right)}+\frac{b}{f \,a^{2} \tan \left(f x +e \right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)}"," ",0,"-1/f/a^2*b^3/(a-b)/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/3/f/a/tan(f*x+e)^3+1/f/a/tan(f*x+e)+1/f/a^2/tan(f*x+e)*b+1/f/(a-b)*arctan(tan(f*x+e))","A"
223,1,158,101,0.889000," ","int(cot(f*x+e)^6/(a+b*tan(f*x+e)^2),x)","\frac{b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{f \,a^{3} \left(a -b \right) \sqrt{a b}}-\frac{1}{5 f a \tan \left(f x +e \right)^{5}}+\frac{1}{3 f a \tan \left(f x +e \right)^{3}}+\frac{b}{3 f \,a^{2} \tan \left(f x +e \right)^{3}}-\frac{1}{f a \tan \left(f x +e \right)}-\frac{b}{f \,a^{2} \tan \left(f x +e \right)}-\frac{b^{2}}{f \,a^{3} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)}"," ",0,"1/f/a^3*b^4/(a-b)/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/5/f/a/tan(f*x+e)^5+1/3/f/a/tan(f*x+e)^3+1/3/f/a^2/tan(f*x+e)^3*b-1/f/a/tan(f*x+e)-1/f/a^2/tan(f*x+e)*b-1/f/a^3/tan(f*x+e)*b^2-1/f/(a-b)*arctan(tan(f*x+e))","A"
224,1,149,86,0.179000," ","int(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x)","\frac{a^{2} \ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{2 f \left(a -b \right)^{2} b^{2}}-\frac{a \ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{f \left(a -b \right)^{2} b}+\frac{a^{3}}{2 f \left(a -b \right)^{2} b^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{a^{2}}{2 f \left(a -b \right)^{2} b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \left(a -b \right)^{2}}"," ",0,"1/2/f*a^2/(a-b)^2/b^2*ln(a+b*tan(f*x+e)^2)-1/f*a/(a-b)^2/b*ln(a+b*tan(f*x+e)^2)+1/2/f*a^3/(a-b)^2/b^2/(a+b*tan(f*x+e)^2)-1/2/f*a^2/(a-b)^2/b/(a+b*tan(f*x+e)^2)+1/2/f/(a-b)^2*ln(1+tan(f*x+e)^2)","A"
225,1,109,65,0.268000," ","int(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x)","\frac{\ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{2 f \left(a -b \right)^{2}}-\frac{a^{2}}{2 f \left(a -b \right)^{2} b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{a}{2 f \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \left(a -b \right)^{2}}"," ",0,"1/2/f/(a-b)^2*ln(a+b*tan(f*x+e)^2)-1/2/f*a^2/(a-b)^2/b/(a+b*tan(f*x+e)^2)+1/2/f/(a-b)^2*a/(a+b*tan(f*x+e)^2)-1/2/f/(a-b)^2*ln(1+tan(f*x+e)^2)","A"
226,1,104,61,0.210000," ","int(tan(f*x+e)/(a+b*tan(f*x+e)^2)^2,x)","-\frac{\ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{2 f \left(a -b \right)^{2}}+\frac{a}{2 f \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{b}{2 f \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \left(a -b \right)^{2}}"," ",0,"-1/2/f/(a-b)^2*ln(a+b*tan(f*x+e)^2)+1/2/f/(a-b)^2*a/(a+b*tan(f*x+e)^2)-1/2/f*b/(a-b)^2/(a+b*tan(f*x+e)^2)+1/2/f/(a-b)^2*ln(1+tan(f*x+e)^2)","A"
227,1,160,99,0.984000," ","int(cot(f*x+e)/(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2}}{2 f a \left(a -b \right)^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{b \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{f a \left(a -b \right)^{2}}-\frac{b^{2} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f \,a^{2} \left(a -b \right)^{2}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \,a^{2}}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \,a^{2}}"," ",0,"1/2/f*b^2/a/(a-b)^2/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/f*b/a/(a-b)^2*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-1/2/f*b^2/a^2/(a-b)^2*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/2/f/a^2*ln(-1+cos(f*x+e))+1/2/f/a^2*ln(1+cos(f*x+e))","A"
228,1,234,126,0.999000," ","int(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b^{3}}{2 f \,a^{2} \left(a -b \right)^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}-\frac{3 b^{2} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f \,a^{2} \left(a -b \right)^{2}}+\frac{b^{3} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{f \,a^{3} \left(a -b \right)^{2}}+\frac{1}{4 f \,a^{2} \left(-1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \,a^{2}}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b}{f \,a^{3}}-\frac{1}{4 f \,a^{2} \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \,a^{2}}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) b}{f \,a^{3}}"," ",0,"-1/2/f*b^3/a^2/(a-b)^2/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-3/2/f*b^2/a^2/(a-b)^2*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/f*b^3/a^3/(a-b)^2*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/4/f/a^2/(-1+cos(f*x+e))-1/2/f/a^2*ln(-1+cos(f*x+e))-1/f/a^3*ln(-1+cos(f*x+e))*b-1/4/f/a^2/(1+cos(f*x+e))-1/2/f/a^2*ln(1+cos(f*x+e))-1/f/a^3*ln(1+cos(f*x+e))*b","A"
229,1,347,153,0.988000," ","int(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{4}}{2 f \,a^{3} \left(a -b \right)^{2} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{2 b^{3} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{f \,a^{3} \left(a -b \right)^{2}}-\frac{3 b^{4} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f \,a^{4} \left(a -b \right)^{2}}-\frac{1}{16 f \,a^{2} \left(-1+\cos \left(f x +e \right)\right)^{2}}-\frac{7}{16 f \,a^{2} \left(-1+\cos \left(f x +e \right)\right)}-\frac{b}{2 f \,a^{3} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \,a^{2}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b}{f \,a^{3}}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{2 f \,a^{4}}-\frac{1}{16 f \,a^{2} \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{7}{16 f \,a^{2} \left(1+\cos \left(f x +e \right)\right)}+\frac{b}{2 f \,a^{3} \left(1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \,a^{2}}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) b}{f \,a^{3}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{2 f \,a^{4}}"," ",0,"1/2/f*b^4/a^3/(a-b)^2/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+2/f*b^3/a^3/(a-b)^2*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-3/2/f*b^4/a^4/(a-b)^2*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-1/16/f/a^2/(-1+cos(f*x+e))^2-7/16/f/a^2/(-1+cos(f*x+e))-1/2/f/a^3/(-1+cos(f*x+e))*b+1/2/f/a^2*ln(-1+cos(f*x+e))+1/f/a^3*ln(-1+cos(f*x+e))*b+3/2/f/a^4*ln(-1+cos(f*x+e))*b^2-1/16/f/a^2/(1+cos(f*x+e))^2+7/16/f/a^2/(1+cos(f*x+e))+1/2/f/a^3/(1+cos(f*x+e))*b+1/2/f/a^2*ln(1+cos(f*x+e))+1/f/a^3*ln(1+cos(f*x+e))*b+3/2/f/a^4*ln(1+cos(f*x+e))*b^2","B"
230,1,184,116,0.201000," ","int(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^2,x)","\frac{\tan \left(f x +e \right)}{f \,b^{2}}+\frac{a^{3} \tan \left(f x +e \right)}{2 f \,b^{2} \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{a^{2} \tan \left(f x +e \right)}{2 f b \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 a^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,b^{2} \left(a -b \right)^{2} \sqrt{a b}}+\frac{5 a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f b \left(a -b \right)^{2} \sqrt{a b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{2}}"," ",0,"1/f/b^2*tan(f*x+e)+1/2/f*a^3/b^2/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)-1/2/f*a^2/b/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)-3/2/f*a^3/b^2/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+5/2/f*a^2/b/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/(a-b)^2*arctan(tan(f*x+e))","A"
231,1,160,83,0.204000," ","int(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x)","-\frac{a^{2} \tan \left(f x +e \right)}{2 f b \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{a \tan \left(f x +e \right)}{2 f \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f b \left(a -b \right)^{2} \sqrt{a b}}-\frac{3 a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \left(a -b \right)^{2} \sqrt{a b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{2}}"," ",0,"-1/2/f*a^2/b/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)+1/2/f*a/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)+1/2/f*a^2/b/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-3/2/f*a/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f/(a-b)^2*arctan(tan(f*x+e))","A"
232,1,151,78,0.216000," ","int(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x)","\frac{a \tan \left(f x +e \right)}{2 f \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{b \tan \left(f x +e \right)}{2 \left(a -b \right)^{2} f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \left(a -b \right)^{2} \sqrt{a b}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right) b}{2 f \left(a -b \right)^{2} \sqrt{a b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{2}}"," ",0,"1/2/f*a/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)-1/2*b*tan(f*x+e)/(a-b)^2/f/(a+b*tan(f*x+e)^2)+1/2/f*a/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/2/f/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))*b-1/f/(a-b)^2*arctan(tan(f*x+e))","A"
233,1,160,85,0.291000," ","int(1/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 \left(a -b \right)^{2} f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{b^{2} \tan \left(f x +e \right)}{2 f \left(a -b \right)^{2} a \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right) b}{2 f \left(a -b \right)^{2} \sqrt{a b}}+\frac{b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \left(a -b \right)^{2} a \sqrt{a b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{2}}"," ",0,"-1/2*b*tan(f*x+e)/(a-b)^2/f/(a+b*tan(f*x+e)^2)+1/2/f*b^2/(a-b)^2/a*tan(f*x+e)/(a+b*tan(f*x+e)^2)-3/2/f/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))*b+1/2/f*b^2/(a-b)^2/a/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f/(a-b)^2*arctan(tan(f*x+e))","A"
234,1,187,114,0.834000," ","int(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{2} \tan \left(f x +e \right)}{2 f \left(a -b \right)^{2} a \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{b^{3} \tan \left(f x +e \right)}{2 f \,a^{2} \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{5 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \left(a -b \right)^{2} a \sqrt{a b}}-\frac{3 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{2} \left(a -b \right)^{2} \sqrt{a b}}-\frac{1}{f \,a^{2} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{2}}"," ",0,"1/2/f*b^2/(a-b)^2/a*tan(f*x+e)/(a+b*tan(f*x+e)^2)-1/2/f*b^3/a^2/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)+5/2/f*b^2/(a-b)^2/a/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-3/2/f*b^3/a^2/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/a^2/tan(f*x+e)-1/f/(a-b)^2*arctan(tan(f*x+e))","A"
235,1,218,153,0.944000," ","int(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x)","-\frac{b^{3} \tan \left(f x +e \right)}{2 f \,a^{2} \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{b^{4} \tan \left(f x +e \right)}{2 f \,a^{3} \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{7 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{2} \left(a -b \right)^{2} \sqrt{a b}}+\frac{5 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{3} \left(a -b \right)^{2} \sqrt{a b}}-\frac{1}{3 f \,a^{2} \tan \left(f x +e \right)^{3}}+\frac{1}{f \,a^{2} \tan \left(f x +e \right)}+\frac{2 b}{f \,a^{3} \tan \left(f x +e \right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{2}}"," ",0,"-1/2/f*b^3/a^2/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)+1/2/f*b^4/a^3/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)-7/2/f*b^3/a^2/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+5/2/f*b^4/a^3/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/3/f/a^2/tan(f*x+e)^3+1/f/a^2/tan(f*x+e)+2/f/a^3/tan(f*x+e)*b+1/f/(a-b)^2*arctan(tan(f*x+e))","A"
236,1,272,200,0.936000," ","int(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^2,x)","\frac{b^{4} \tan \left(f x +e \right)}{2 f \,a^{3} \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{b^{5} \tan \left(f x +e \right)}{2 f \,a^{4} \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{9 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{3} \left(a -b \right)^{2} \sqrt{a b}}-\frac{7 b^{5} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{4} \left(a -b \right)^{2} \sqrt{a b}}-\frac{1}{5 f \,a^{2} \tan \left(f x +e \right)^{5}}+\frac{1}{3 f \,a^{2} \tan \left(f x +e \right)^{3}}+\frac{2 b}{3 f \,a^{3} \tan \left(f x +e \right)^{3}}-\frac{1}{f \,a^{2} \tan \left(f x +e \right)}-\frac{2 b}{f \,a^{3} \tan \left(f x +e \right)}-\frac{3 b^{2}}{f \,a^{4} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{2}}"," ",0,"1/2/f*b^4/a^3/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)-1/2/f*b^5/a^4/(a-b)^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)+9/2/f*b^4/a^3/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-7/2/f*b^5/a^4/(a-b)^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/5/f/a^2/tan(f*x+e)^5+1/3/f/a^2/tan(f*x+e)^3+2/3/f/a^3/tan(f*x+e)^3*b-1/f/a^2/tan(f*x+e)-2/f/a^3/tan(f*x+e)*b-3/f/a^4/tan(f*x+e)*b^2-1/f/(a-b)^2*arctan(tan(f*x+e))","A"
237,1,234,102,0.197000," ","int(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x)","-\frac{\ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{2 f \left(a -b \right)^{3}}-\frac{a^{3}}{2 f \left(a -b \right)^{3} b^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{3 a^{2}}{2 f \left(a -b \right)^{3} b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{a}{f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{a^{4}}{4 f \left(a -b \right)^{3} b^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{a^{3}}{2 f \left(a -b \right)^{3} b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{a^{2}}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \left(a -b \right)^{3}}"," ",0,"-1/2/f/(a-b)^3*ln(a+b*tan(f*x+e)^2)-1/2/f/(a-b)^3*a^3/b^2/(a+b*tan(f*x+e)^2)+3/2/f/(a-b)^3*a^2/b/(a+b*tan(f*x+e)^2)-1/f/(a-b)^3*a/(a+b*tan(f*x+e)^2)+1/4/f/(a-b)^3*a^4/b^2/(a+b*tan(f*x+e)^2)^2-1/2/f/(a-b)^3*a^3/b/(a+b*tan(f*x+e)^2)^2+1/4/f/(a-b)^3*a^2/(a+b*tan(f*x+e)^2)^2+1/2/f/(a-b)^3*ln(1+tan(f*x+e)^2)","B"
238,1,193,91,0.204000," ","int(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x)","\frac{\ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{2 f \left(a -b \right)^{3}}-\frac{a}{2 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{b}{2 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{a^{3}}{4 f \left(a -b \right)^{3} b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{a^{2}}{2 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{a b}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \left(a -b \right)^{3}}"," ",0,"1/2/f/(a-b)^3*ln(a+b*tan(f*x+e)^2)-1/2/f/(a-b)^3*a/(a+b*tan(f*x+e)^2)+1/2/f/(a-b)^3/(a+b*tan(f*x+e)^2)*b-1/4/f/(a-b)^3*a^3/b/(a+b*tan(f*x+e)^2)^2+1/2/f/(a-b)^3*a^2/(a+b*tan(f*x+e)^2)^2-1/4/f/(a-b)^3*a*b/(a+b*tan(f*x+e)^2)^2-1/2/f/(a-b)^3*ln(1+tan(f*x+e)^2)","B"
239,1,190,87,0.243000," ","int(tan(f*x+e)/(a+b*tan(f*x+e)^2)^3,x)","-\frac{\ln \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}{2 f \left(a -b \right)^{3}}+\frac{a}{2 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{b}{2 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{a^{2}}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{a b}{2 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{2}}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(f x +e \right)\right)}{2 f \left(a -b \right)^{3}}"," ",0,"-1/2/f/(a-b)^3*ln(a+b*tan(f*x+e)^2)+1/2/f/(a-b)^3*a/(a+b*tan(f*x+e)^2)-1/2/f/(a-b)^3/(a+b*tan(f*x+e)^2)*b+1/4/f/(a-b)^3*a^2/(a+b*tan(f*x+e)^2)^2-1/2/f/(a-b)^3*a*b/(a+b*tan(f*x+e)^2)^2+1/4/f*b^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2+1/2/f/(a-b)^3*ln(1+tan(f*x+e)^2)","B"
240,1,289,142,0.865000," ","int(cot(f*x+e)/(a+b*tan(f*x+e)^2)^3,x)","\frac{3 b^{2}}{2 f a \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}-\frac{b^{3}}{2 f \,a^{2} \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{3 b \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f a \left(a -b \right)^{3}}-\frac{3 b^{2} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f \,a^{2} \left(a -b \right)^{3}}+\frac{b^{3} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f \,a^{3} \left(a -b \right)^{3}}-\frac{b^{3}}{4 f a \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \,a^{3}}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \,a^{3}}"," ",0,"3/2/f*b^2/a/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-1/2/f*b^3/a^2/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+3/2/f*b/a/(a-b)^3*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-3/2/f*b^2/a^2/(a-b)^3*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/2/f*b^3/a^3/(a-b)^3*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-1/4/f*b^3/a/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2+1/2/f/a^3*ln(-1+cos(f*x+e))+1/2/f/a^3*ln(1+cos(f*x+e))","B"
241,1,362,173,0.997000," ","int(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x)","-\frac{2 b^{3}}{f \,a^{2} \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{b^{4}}{f \,a^{3} \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}-\frac{3 b^{2} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{f \,a^{2} \left(a -b \right)^{3}}+\frac{4 b^{3} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{f \,a^{3} \left(a -b \right)^{3}}-\frac{3 b^{4} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f \,a^{4} \left(a -b \right)^{3}}+\frac{b^{4}}{4 f \,a^{2} \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}+\frac{1}{4 f \,a^{3} \left(-1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \,a^{3}}-\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b}{2 f \,a^{4}}-\frac{1}{4 f \,a^{3} \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \,a^{3}}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b}{2 f \,a^{4}}"," ",0,"-2/f*b^3/a^2/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/f*b^4/a^3/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-3/f*b^2/a^2/(a-b)^3*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+4/f*b^3/a^3/(a-b)^3*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-3/2/f*b^4/a^4/(a-b)^3*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+1/4/f*b^4/a^2/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2+1/4/f/a^3/(-1+cos(f*x+e))-1/2/f/a^3*ln(-1+cos(f*x+e))-3/2/f/a^4*ln(-1+cos(f*x+e))*b-1/4/f/a^3/(1+cos(f*x+e))-1/2/f/a^3*ln(1+cos(f*x+e))-3/2/f/a^4*ln(1+cos(f*x+e))*b","B"
242,1,477,200,0.921000," ","int(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x)","\frac{5 b^{4}}{2 f \,a^{3} \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}-\frac{3 b^{5}}{2 f \,a^{4} \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}+\frac{5 b^{3} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{f \,a^{3} \left(a -b \right)^{3}}-\frac{15 b^{4} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{2 f \,a^{4} \left(a -b \right)^{3}}+\frac{3 b^{5} \ln \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)}{f \,a^{5} \left(a -b \right)^{3}}-\frac{b^{5}}{4 f \,a^{3} \left(a -b \right)^{3} \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2}}-\frac{1}{16 f \,a^{3} \left(-1+\cos \left(f x +e \right)\right)^{2}}-\frac{7}{16 f \,a^{3} \left(-1+\cos \left(f x +e \right)\right)}-\frac{3 b}{4 f \,a^{4} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \,a^{3}}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b}{2 f \,a^{4}}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{f \,a^{5}}-\frac{1}{16 f \,a^{3} \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{7}{16 f \,a^{3} \left(1+\cos \left(f x +e \right)\right)}+\frac{3 b}{4 f \,a^{4} \left(1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \,a^{3}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b}{2 f \,a^{4}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{f \,a^{5}}"," ",0,"5/2/f*b^4/a^3/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-3/2/f*b^5/a^4/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+5/f*b^3/a^3/(a-b)^3*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-15/2/f*b^4/a^4/(a-b)^3*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)+3/f*b^5/a^5/(a-b)^3*ln(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)-1/4/f*b^5/a^3/(a-b)^3/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2-1/16/f/a^3/(-1+cos(f*x+e))^2-7/16/f/a^3/(-1+cos(f*x+e))-3/4/f/a^4/(-1+cos(f*x+e))*b+1/2/f/a^3*ln(-1+cos(f*x+e))+3/2/f/a^4*ln(-1+cos(f*x+e))*b+3/f/a^5*ln(-1+cos(f*x+e))*b^2-1/16/f/a^3/(1+cos(f*x+e))^2+7/16/f/a^3/(1+cos(f*x+e))+3/4/f/a^4/(1+cos(f*x+e))*b+1/2/f/a^3*ln(1+cos(f*x+e))+3/2/f/a^4*ln(1+cos(f*x+e))*b+3/f/a^5*ln(1+cos(f*x+e))*b^2","B"
243,1,351,139,0.240000," ","int(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^3,x)","-\frac{5 a^{3} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b}+\frac{7 a^{2} \left(\tan^{3}\left(f x +e \right)\right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 a b \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{3 a^{4} \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b^{2}}+\frac{5 a^{3} \tan \left(f x +e \right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b}-\frac{7 a^{2} \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 a^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} b^{2} \sqrt{a b}}-\frac{5 a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{4 f \left(a -b \right)^{3} b \sqrt{a b}}+\frac{15 a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} \sqrt{a b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{3}}"," ",0,"-5/8/f*a^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2/b*tan(f*x+e)^3+7/4/f*a^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-9/8/f*a/(a-b)^3/(a+b*tan(f*x+e)^2)^2*b*tan(f*x+e)^3-3/8/f*a^4/(a-b)^3/(a+b*tan(f*x+e)^2)^2/b^2*tan(f*x+e)+5/4/f*a^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2/b*tan(f*x+e)-7/8/f*a^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)+3/8/f*a^3/(a-b)^3/b^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-5/4/f*a^2/(a-b)^3/b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+15/8/f*a/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/(a-b)^3*arctan(tan(f*x+e))","B"
244,1,338,131,0.214000," ","int(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x)","\frac{a^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{3 a b \left(\tan^{3}\left(f x +e \right)\right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{5 \left(\tan^{3}\left(f x +e \right)\right) b^{2}}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{a^{3} \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b}-\frac{a^{2} \tan \left(f x +e \right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 a b \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} b \sqrt{a b}}-\frac{3 a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{4 f \left(a -b \right)^{3} \sqrt{a b}}-\frac{3 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} \sqrt{a b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{3}}"," ",0,"1/8/f*a^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-3/4/f*a/(a-b)^3/(a+b*tan(f*x+e)^2)^2*b*tan(f*x+e)^3+5/8/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3*b^2-1/8/f*a^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2/b*tan(f*x+e)-1/4/f*a^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)+3/8/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*a*b*tan(f*x+e)+1/8/f*a^2/(a-b)^3/b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-3/4/f*a/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-3/8/f/(a-b)^3*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f/(a-b)^3*arctan(tan(f*x+e))","B"
245,1,339,130,0.237000," ","int(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x)","\frac{3 a b \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b^{2}}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a}+\frac{5 a^{2} \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{3 a b \tan \left(f x +e \right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{\tan \left(f x +e \right) b^{2}}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} \sqrt{a b}}+\frac{3 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{4 f \left(a -b \right)^{3} \sqrt{a b}}-\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right) b^{2}}{8 f \left(a -b \right)^{3} a \sqrt{a b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{3}}"," ",0,"3/8/f*a/(a-b)^3/(a+b*tan(f*x+e)^2)^2*b*tan(f*x+e)^3-1/4/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3*b^2-1/8/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*b^3/a*tan(f*x+e)^3+5/8/f*a^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-3/4/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*a*b*tan(f*x+e)+1/8/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)*b^2+3/8/f*a/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+3/4/f/(a-b)^3*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/8/f/(a-b)^3/a/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))*b^2-1/f/(a-b)^3*arctan(tan(f*x+e))","B"
246,1,350,136,0.350000," ","int(1/(a+b*tan(f*x+e)^2)^3,x)","-\frac{7 \left(\tan^{3}\left(f x +e \right)\right) b^{2}}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{5 b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a}-\frac{3 b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a^{2}}-\frac{9 a b \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{7 \tan \left(f x +e \right) b^{2}}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{5 b^{3} \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a}-\frac{15 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} \sqrt{a b}}+\frac{5 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right) b^{2}}{4 f \left(a -b \right)^{3} a \sqrt{a b}}-\frac{3 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} a^{2} \sqrt{a b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{3}}"," ",0,"-7/8/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3*b^2+5/4/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*b^3/a*tan(f*x+e)^3-3/8/f*b^4/(a-b)^3/(a+b*tan(f*x+e)^2)^2/a^2*tan(f*x+e)^3-9/8/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*a*b*tan(f*x+e)+7/4/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)*b^2-5/8/f*b^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2/a*tan(f*x+e)-15/8/f/(a-b)^3*b/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+5/4/f/(a-b)^3/a/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))*b^2-3/8/f*b^3/(a-b)^3/a^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+1/f/(a-b)^3*arctan(tan(f*x+e))","B"
247,1,379,173,0.980000," ","int(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x)","\frac{11 b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a}-\frac{9 b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a^{2}}+\frac{7 b^{5} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{13 \tan \left(f x +e \right) b^{2}}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{11 b^{3} \tan \left(f x +e \right)}{4 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a}+\frac{9 b^{4} \tan \left(f x +e \right)}{8 f \,a^{2} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{35 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right) b^{2}}{8 f \left(a -b \right)^{3} a \sqrt{a b}}-\frac{21 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{4 f \left(a -b \right)^{3} a^{2} \sqrt{a b}}+\frac{15 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{3} \left(a -b \right)^{3} \sqrt{a b}}-\frac{1}{f \,a^{3} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{3}}"," ",0,"11/8/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*b^3/a*tan(f*x+e)^3-9/4/f*b^4/(a-b)^3/(a+b*tan(f*x+e)^2)^2/a^2*tan(f*x+e)^3+7/8/f*b^5/a^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+13/8/f/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)*b^2-11/4/f*b^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2/a*tan(f*x+e)+9/8/f*b^4/a^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)+35/8/f/(a-b)^3/a/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))*b^2-21/4/f*b^3/(a-b)^3/a^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+15/8/f*b^4/a^3/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/f/a^3/tan(f*x+e)-1/f/(a-b)^3*arctan(tan(f*x+e))","B"
248,1,413,222,0.808000," ","int(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x)","-\frac{15 b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a^{2}}+\frac{13 b^{5} \left(\tan^{3}\left(f x +e \right)\right)}{4 f \,a^{3} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{11 b^{6} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{4} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{17 b^{3} \tan \left(f x +e \right)}{8 f \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} a}+\frac{15 b^{4} \tan \left(f x +e \right)}{4 f \,a^{2} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{13 b^{5} \tan \left(f x +e \right)}{8 f \,a^{3} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{63 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \left(a -b \right)^{3} a^{2} \sqrt{a b}}+\frac{45 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{4 f \,a^{3} \left(a -b \right)^{3} \sqrt{a b}}-\frac{35 b^{5} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{4} \left(a -b \right)^{3} \sqrt{a b}}-\frac{1}{3 f \,a^{3} \tan \left(f x +e \right)^{3}}+\frac{1}{f \,a^{3} \tan \left(f x +e \right)}+\frac{3 b}{f \,a^{4} \tan \left(f x +e \right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{3}}"," ",0,"-15/8/f*b^4/(a-b)^3/(a+b*tan(f*x+e)^2)^2/a^2*tan(f*x+e)^3+13/4/f*b^5/a^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-11/8/f*b^6/a^4/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-17/8/f*b^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2/a*tan(f*x+e)+15/4/f*b^4/a^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-13/8/f*b^5/a^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-63/8/f*b^3/(a-b)^3/a^2/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+45/4/f*b^4/a^3/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-35/8/f*b^5/a^4/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/3/f/a^3/tan(f*x+e)^3+1/f/a^3/tan(f*x+e)+3/f/a^4/tan(f*x+e)*b+1/f/(a-b)^3*arctan(tan(f*x+e))","A"
249,1,466,277,1.085000," ","int(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^3,x)","\frac{19 b^{5} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{17 b^{6} \left(\tan^{3}\left(f x +e \right)\right)}{4 f \,a^{4} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{15 b^{7} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{5} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{21 b^{4} \tan \left(f x +e \right)}{8 f \,a^{2} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{19 b^{5} \tan \left(f x +e \right)}{4 f \,a^{3} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{17 b^{6} \tan \left(f x +e \right)}{8 f \,a^{4} \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{99 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{3} \left(a -b \right)^{3} \sqrt{a b}}-\frac{77 b^{5} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{4 f \,a^{4} \left(a -b \right)^{3} \sqrt{a b}}+\frac{63 b^{6} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{5} \left(a -b \right)^{3} \sqrt{a b}}-\frac{1}{5 f \,a^{3} \tan \left(f x +e \right)^{5}}+\frac{1}{3 f \,a^{3} \tan \left(f x +e \right)^{3}}+\frac{b}{f \,a^{4} \tan \left(f x +e \right)^{3}}-\frac{1}{f \,a^{3} \tan \left(f x +e \right)}-\frac{3 b}{f \,a^{4} \tan \left(f x +e \right)}-\frac{6 b^{2}}{f \,a^{5} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \left(a -b \right)^{3}}"," ",0,"19/8/f*b^5/a^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-17/4/f*b^6/a^4/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+15/8/f*b^7/a^5/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+21/8/f*b^4/a^2/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)-19/4/f*b^5/a^3/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)+17/8/f*b^6/a^4/(a-b)^3/(a+b*tan(f*x+e)^2)^2*tan(f*x+e)+99/8/f*b^4/a^3/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-77/4/f*b^5/a^4/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))+63/8/f*b^6/a^5/(a-b)^3/(a*b)^(1/2)*arctan(tan(f*x+e)*b/(a*b)^(1/2))-1/5/f/a^3/tan(f*x+e)^5+1/3/f/a^3/tan(f*x+e)^3+1/f/a^4/tan(f*x+e)^3*b-1/f/a^3/tan(f*x+e)-3/f/a^4/tan(f*x+e)*b-6/f/a^5/tan(f*x+e)*b^2-1/f/(a-b)^3*arctan(tan(f*x+e))","A"
250,1,242,109,0.037000," ","int((a+b*tan(d*x+c)^2)^4,x)","\frac{b^{4} \left(\tan^{7}\left(d x +c \right)\right)}{7 d}+\frac{4 \left(\tan^{5}\left(d x +c \right)\right) a \,b^{3}}{5 d}-\frac{\left(\tan^{5}\left(d x +c \right)\right) b^{4}}{5 d}+\frac{2 \left(\tan^{3}\left(d x +c \right)\right) a^{2} b^{2}}{d}-\frac{4 \left(\tan^{3}\left(d x +c \right)\right) a \,b^{3}}{3 d}+\frac{b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{4 a^{3} b \tan \left(d x +c \right)}{d}-\frac{6 a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{4 a \,b^{3} \tan \left(d x +c \right)}{d}-\frac{b^{4} \tan \left(d x +c \right)}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d}-\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d}+\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d}-\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d}"," ",0,"1/7*b^4*tan(d*x+c)^7/d+4/5/d*tan(d*x+c)^5*a*b^3-1/5/d*tan(d*x+c)^5*b^4+2/d*tan(d*x+c)^3*a^2*b^2-4/3/d*tan(d*x+c)^3*a*b^3+1/3*b^4*tan(d*x+c)^3/d+4/d*a^3*b*tan(d*x+c)-6*a^2*b^2*tan(d*x+c)/d+4*a*b^3*tan(d*x+c)/d-1/d*b^4*tan(d*x+c)+1/d*arctan(tan(d*x+c))*a^4-4/d*arctan(tan(d*x+c))*a^3*b+6/d*arctan(tan(d*x+c))*a^2*b^2-4/d*arctan(tan(d*x+c))*a*b^3+1/d*arctan(tan(d*x+c))*b^4","B"
251,1,154,73,0.031000," ","int((a+b*tan(d*x+c)^2)^3,x)","\frac{b^{3} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \,b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{d}-\frac{b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{3 a^{2} b \tan \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{b^{3} \tan \left(d x +c \right)}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d}"," ",0,"1/5*b^3*tan(d*x+c)^5/d+a*b^2*tan(d*x+c)^3/d-1/3/d*b^3*tan(d*x+c)^3+3/d*a^2*b*tan(d*x+c)-3*a*b^2*tan(d*x+c)/d+1/d*b^3*tan(d*x+c)+1/d*arctan(tan(d*x+c))*a^3-3/d*arctan(tan(d*x+c))*a^2*b+3/d*arctan(tan(d*x+c))*a*b^2-1/d*arctan(tan(d*x+c))*b^3","B"
252,1,87,44,0.035000," ","int((a+b*tan(d*x+c)^2)^2,x)","\frac{b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a b \tan \left(d x +c \right)}{d}-\frac{b^{2} \tan \left(d x +c \right)}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}-\frac{2 \arctan \left(\tan \left(d x +c \right)\right) a b}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}"," ",0,"1/3*b^2*tan(d*x+c)^3/d+2*a*b*tan(d*x+c)/d-b^2*tan(d*x+c)/d+1/d*arctan(tan(d*x+c))*a^2-2/d*arctan(tan(d*x+c))*a*b+1/d*arctan(tan(d*x+c))*b^2","A"
253,1,29,19,0.030000," ","int(a+b*tan(d*x+c)^2,x)","a x +\frac{b \tan \left(d x +c \right)}{d}-\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"a*x+b*tan(d*x+c)/d-1/d*b*arctan(tan(d*x+c))","A"
254,1,52,42,0.205000," ","int(1/(a+b*tan(d*x+c)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \left(a -b \right) \sqrt{a b}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \left(a -b \right)}"," ",0,"-1/d*b/(a-b)/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/d/(a-b)*arctan(tan(d*x+c))","A"
255,1,160,85,0.306000," ","int(1/(a+b*tan(d*x+c)^2)^2,x)","-\frac{b \tan \left(d x +c \right)}{2 d \left(a -b \right)^{2} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{b^{2} \tan \left(d x +c \right)}{2 d \left(a -b \right)^{2} a \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}-\frac{3 b \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a -b \right)^{2} \sqrt{a b}}+\frac{b^{2} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a -b \right)^{2} a \sqrt{a b}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \left(a -b \right)^{2}}"," ",0,"-1/2/d*b/(a-b)^2*tan(d*x+c)/(a+b*tan(d*x+c)^2)+1/2/d*b^2/(a-b)^2/a*tan(d*x+c)/(a+b*tan(d*x+c)^2)-3/2/d*b/(a-b)^2/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/2/d*b^2/(a-b)^2/a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/d/(a-b)^2*arctan(tan(d*x+c))","A"
256,1,350,136,0.333000," ","int(1/(a+b*tan(d*x+c)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{8 d \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{5 b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{4 d \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{2} a}-\frac{3 b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{8 d \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{2} a^{2}}-\frac{9 b a \tan \left(d x +c \right)}{8 d \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{7 b^{2} \tan \left(d x +c \right)}{4 d \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{5 b^{3} \tan \left(d x +c \right)}{8 d \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{2} a}-\frac{15 b \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a -b \right)^{3} \sqrt{a b}}+\frac{5 b^{2} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{4 d \left(a -b \right)^{3} a \sqrt{a b}}-\frac{3 b^{3} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a -b \right)^{3} a^{2} \sqrt{a b}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \left(a -b \right)^{3}}"," ",0,"-7/8/d*b^2/(a-b)^3/(a+b*tan(d*x+c)^2)^2*tan(d*x+c)^3+5/4/d*b^3/(a-b)^3/(a+b*tan(d*x+c)^2)^2/a*tan(d*x+c)^3-3/8/d*b^4/(a-b)^3/(a+b*tan(d*x+c)^2)^2/a^2*tan(d*x+c)^3-9/8/d*b/(a-b)^3/(a+b*tan(d*x+c)^2)^2*a*tan(d*x+c)+7/4/d*b^2/(a-b)^3/(a+b*tan(d*x+c)^2)^2*tan(d*x+c)-5/8/d*b^3/(a-b)^3/(a+b*tan(d*x+c)^2)^2/a*tan(d*x+c)-15/8/d*b/(a-b)^3/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+5/4/d*b^2/(a-b)^3/a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))-3/8/d*b^3/(a-b)^3/a^2/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/d/(a-b)^3*arctan(tan(d*x+c))","B"
257,1,56,42,0.302000," ","int((a+a*tan(x)^2)^(1/2)*tan(x)^4,x)","\frac{\tan \left(x \right) \left(a +a \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{4 a}-\frac{5 \sqrt{a +a \left(\tan^{2}\left(x \right)\right)}\, \tan \left(x \right)}{8}+\frac{3 \sqrt{a}\, \ln \left(\sqrt{a}\, \tan \left(x \right)+\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}\right)}{8}"," ",0,"1/4*tan(x)*(a+a*tan(x)^2)^(3/2)/a-5/8*(a+a*tan(x)^2)^(1/2)*tan(x)+3/8*a^(1/2)*ln(a^(1/2)*tan(x)+(a+a*tan(x)^2)^(1/2))","A"
258,1,29,24,0.196000," ","int((a+a*tan(x)^2)^(1/2)*tan(x)^3,x)","\frac{\left(a +a \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{3 a}-\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}"," ",0,"1/3/a*(a+a*tan(x)^2)^(3/2)-(a+a*tan(x)^2)^(1/2)","A"
259,1,39,28,0.164000," ","int((a+a*tan(x)^2)^(1/2)*tan(x)^2,x)","\frac{\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}\, \tan \left(x \right)}{2}-\frac{\sqrt{a}\, \ln \left(\sqrt{a}\, \tan \left(x \right)+\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}\right)}{2}"," ",0,"1/2*(a+a*tan(x)^2)^(1/2)*tan(x)-1/2*a^(1/2)*ln(a^(1/2)*tan(x)+(a+a*tan(x)^2)^(1/2))","A"
260,1,11,8,0.123000," ","int((a+a*tan(x)^2)^(1/2)*tan(x),x)","\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}"," ",0,"(a+a*tan(x)^2)^(1/2)","A"
261,1,23,18,0.589000," ","int(cot(x)*(a+a*tan(x)^2)^(1/2),x)","\cos \left(x \right) \sqrt{\frac{a}{\cos \left(x \right)^{2}}}\, \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)"," ",0,"cos(x)*(a/cos(x)^2)^(1/2)*ln(-(-1+cos(x))/sin(x))","A"
262,1,17,12,0.526000," ","int(cot(x)^2*(a+a*tan(x)^2)^(1/2),x)","-\frac{\cos \left(x \right) \sqrt{\frac{a}{\cos \left(x \right)^{2}}}}{\sin \left(x \right)}"," ",0,"-cos(x)*(a/cos(x)^2)^(1/2)/sin(x)","A"
263,1,51,33,0.557000," ","int(cot(x)^3*(a+a*tan(x)^2)^(1/2),x)","\frac{\left(\left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-\cos \left(x \right)-\ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)\right) \cos \left(x \right) \sqrt{\frac{a}{\cos \left(x \right)^{2}}}}{2 \sin \left(x \right)^{2}}"," ",0,"1/2*(cos(x)^2*ln(-(-1+cos(x))/sin(x))-cos(x)-ln(-(-1+cos(x))/sin(x)))*cos(x)*(a/cos(x)^2)^(1/2)/sin(x)^2","A"
264,1,25,28,0.635000," ","int(cot(x)^4*(a+a*tan(x)^2)^(1/2),x)","-\frac{\left(3 \left(\cos^{2}\left(x \right)\right)-2\right) \cos \left(x \right) \sqrt{\frac{a}{\cos \left(x \right)^{2}}}}{3 \sin \left(x \right)^{3}}"," ",0,"-1/3*(3*cos(x)^2-2)*cos(x)*(a/cos(x)^2)^(1/2)/sin(x)^3","A"
265,1,34,30,0.542000," ","int((a+a*tan(d*x+c)^2)^(1/2),x)","\frac{\sqrt{a}\, \ln \left(\sqrt{a}\, \tan \left(d x +c \right)+\sqrt{a +a \left(\tan^{2}\left(d x +c \right)\right)}\right)}{d}"," ",0,"1/d*a^(1/2)*ln(a^(1/2)*tan(d*x+c)+(a+a*tan(d*x+c)^2)^(1/2))","A"
266,1,29,24,0.131000," ","int(tan(x)^3*(a+a*tan(x)^2)^(3/2),x)","\frac{\left(a +a \left(\tan^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}{5 a}-\frac{\left(a +a \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{3}"," ",0,"1/5/a*(a+a*tan(x)^2)^(5/2)-1/3*(a+a*tan(x)^2)^(3/2)","A"
267,1,54,47,0.142000," ","int(tan(x)^2*(a+a*tan(x)^2)^(3/2),x)","\frac{\tan \left(x \right) \left(a +a \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{4}-\frac{a \tan \left(x \right) \sqrt{a +a \left(\tan^{2}\left(x \right)\right)}}{8}-\frac{a^{\frac{3}{2}} \ln \left(\sqrt{a}\, \tan \left(x \right)+\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}\right)}{8}"," ",0,"1/4*tan(x)*(a+a*tan(x)^2)^(3/2)-1/8*a*tan(x)*(a+a*tan(x)^2)^(1/2)-1/8*a^(3/2)*ln(a^(1/2)*tan(x)+(a+a*tan(x)^2)^(1/2))","A"
268,1,13,10,0.076000," ","int(tan(x)*(a+a*tan(x)^2)^(3/2),x)","\frac{\left(a +a \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{3}"," ",0,"1/3*(a+a*tan(x)^2)^(3/2)","A"
269,1,32,29,0.421000," ","int(cot(x)*(a+a*tan(x)^2)^(3/2),x)","\left(\cos \left(x \right) \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)+\cos \left(x \right)+1\right) \left(\cos^{2}\left(x \right)\right) \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}"," ",0,"(cos(x)*ln(-(-1+cos(x))/sin(x))+cos(x)+1)*cos(x)^2*(a/cos(x)^2)^(3/2)","A"
270,1,55,29,0.548000," ","int(cot(x)^2*(a+a*tan(x)^2)^(3/2),x)","-\frac{\left(\ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right) \sin \left(x \right)-\ln \left(\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right) \sin \left(x \right)+1\right) \left(\cos^{3}\left(x \right)\right) \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}{\sin \left(x \right)}"," ",0,"-(ln(-(-1+cos(x)+sin(x))/sin(x))*sin(x)-ln((1-cos(x)+sin(x))/sin(x))*sin(x)+1)*cos(x)^3*(a/cos(x)^2)^(3/2)/sin(x)","A"
271,1,62,56,0.282000," ","int((a+a*tan(d*x+c)^2)^(3/2),x)","\frac{a \tan \left(d x +c \right) \sqrt{a +a \left(\tan^{2}\left(d x +c \right)\right)}}{2 d}+\frac{a^{\frac{3}{2}} \ln \left(\sqrt{a}\, \tan \left(d x +c \right)+\sqrt{a +a \left(\tan^{2}\left(d x +c \right)\right)}\right)}{2 d}"," ",0,"1/2/d*a*tan(d*x+c)*(a+a*tan(d*x+c)^2)^(1/2)+1/2/d*a^(3/2)*ln(a^(1/2)*tan(d*x+c)+(a+a*tan(d*x+c)^2)^(1/2))","A"
272,1,90,82,0.260000," ","int((a+a*tan(d*x+c)^2)^(5/2),x)","\frac{a \tan \left(d x +c \right) \left(a +a \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{3}{2}}}{4 d}+\frac{3 a^{2} \tan \left(d x +c \right) \sqrt{a +a \left(\tan^{2}\left(d x +c \right)\right)}}{8 d}+\frac{3 a^{\frac{5}{2}} \ln \left(\sqrt{a}\, \tan \left(d x +c \right)+\sqrt{a +a \left(\tan^{2}\left(d x +c \right)\right)}\right)}{8 d}"," ",0,"1/4/d*a*tan(d*x+c)*(a+a*tan(d*x+c)^2)^(3/2)+3/8/d*a^2*tan(d*x+c)*(a+a*tan(d*x+c)^2)^(1/2)+3/8/d*a^(5/2)*ln(a^(1/2)*tan(d*x+c)+(a+a*tan(d*x+c)^2)^(1/2))","A"
273,1,26,21,0.225000," ","int(tan(x)^3/(a+a*tan(x)^2)^(1/2),x)","\frac{\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}}{a}+\frac{1}{\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}}"," ",0,"1/a*(a+a*tan(x)^2)^(1/2)+1/(a+a*tan(x)^2)^(1/2)","A"
274,1,38,27,0.226000," ","int(tan(x)^2/(a+a*tan(x)^2)^(1/2),x)","\frac{\ln \left(\sqrt{a}\, \tan \left(x \right)+\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}\right)}{\sqrt{a}}-\frac{\tan \left(x \right)}{\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}}"," ",0,"ln(a^(1/2)*tan(x)+(a+a*tan(x)^2)^(1/2))/a^(1/2)-tan(x)/(a+a*tan(x)^2)^(1/2)","A"
275,1,13,10,0.148000," ","int(tan(x)/(a+a*tan(x)^2)^(1/2),x)","-\frac{1}{\sqrt{a +a \left(\tan^{2}\left(x \right)\right)}}"," ",0,"-1/(a+a*tan(x)^2)^(1/2)","A"
276,1,29,27,0.625000," ","int(cot(x)/(a+a*tan(x)^2)^(1/2),x)","\frac{\cos \left(x \right)+\ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)+1}{\sqrt{\frac{a}{\cos \left(x \right)^{2}}}\, \cos \left(x \right)}"," ",0,"(cos(x)+ln(-(-1+cos(x))/sin(x))+1)/(a/cos(x)^2)^(1/2)/cos(x)","A"
277,1,24,27,0.575000," ","int(cot(x)^2/(a+a*tan(x)^2)^(1/2),x)","\frac{\cos^{2}\left(x \right)-2}{\sin \left(x \right) \cos \left(x \right) \sqrt{\frac{a}{\cos \left(x \right)^{2}}}}"," ",0,"(cos(x)^2-2)/sin(x)/cos(x)/(a/cos(x)^2)^(1/2)","A"
278,1,29,24,0.171000," ","int(tan(x)^3/(a+a*tan(x)^2)^(3/2),x)","-\frac{1}{a \sqrt{a +a \left(\tan^{2}\left(x \right)\right)}}+\frac{1}{3 \left(a +a \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/a/(a+a*tan(x)^2)^(1/2)+1/3/(a+a*tan(x)^2)^(3/2)","A"
279,1,56,19,0.175000," ","int(tan(x)^2/(a+a*tan(x)^2)^(3/2),x)","\frac{\tan \left(x \right)}{a \sqrt{a +a \left(\tan^{2}\left(x \right)\right)}}-a \left(\frac{\tan \left(x \right)}{3 a \left(a +a \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{2 \tan \left(x \right)}{3 a^{2} \sqrt{a +a \left(\tan^{2}\left(x \right)\right)}}\right)"," ",0,"1/a*tan(x)/(a+a*tan(x)^2)^(1/2)-a*(1/3/a*tan(x)/(a+a*tan(x)^2)^(3/2)+2/3/a^2*tan(x)/(a+a*tan(x)^2)^(1/2))","B"
280,1,13,10,0.118000," ","int(tan(x)/(a+a*tan(x)^2)^(3/2),x)","-\frac{1}{3 \left(a +a \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/3/(a+a*tan(x)^2)^(3/2)","A"
281,1,38,41,0.458000," ","int(cot(x)/(a+a*tan(x)^2)^(3/2),x)","\frac{\cos^{3}\left(x \right)+3 \cos \left(x \right)+3 \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)+4}{3 \cos \left(x \right)^{3} \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/3*(cos(x)^3+3*cos(x)+3*ln(-(-1+cos(x))/sin(x))+4)/cos(x)^3/(a/cos(x)^2)^(3/2)","A"
282,1,31,52,0.534000," ","int(cot(x)^2/(a+a*tan(x)^2)^(3/2),x)","\frac{\cos^{4}\left(x \right)+4 \left(\cos^{2}\left(x \right)\right)-8}{3 \sin \left(x \right) \cos \left(x \right)^{3} \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/3*(cos(x)^4+4*cos(x)^2-8)/sin(x)/cos(x)^3/(a/cos(x)^2)^(3/2)","A"
283,1,25,22,0.372000," ","int(1/(a+a*tan(d*x+c)^2)^(1/2),x)","\frac{\tan \left(d x +c \right)}{d \sqrt{a +a \left(\tan^{2}\left(d x +c \right)\right)}}"," ",0,"1/d*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(1/2)","A"
284,1,57,50,0.340000," ","int(1/(a+a*tan(d*x+c)^2)^(3/2),x)","\frac{a \left(\frac{\tan \left(d x +c \right)}{3 a \left(a +a \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{3}{2}}}+\frac{2 \tan \left(d x +c \right)}{3 a^{2} \sqrt{a +a \left(\tan^{2}\left(d x +c \right)\right)}}\right)}{d}"," ",0,"1/d*a*(1/3/a*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(3/2)+2/3/a^2*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(1/2))","A"
285,1,88,76,0.382000," ","int(1/(a+a*tan(d*x+c)^2)^(5/2),x)","\frac{a \left(\frac{\tan \left(d x +c \right)}{5 a \left(a +a \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{5}{2}}}+\frac{\frac{4 \tan \left(d x +c \right)}{15 a \left(a +a \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{3}{2}}}+\frac{8 \tan \left(d x +c \right)}{15 a^{2} \sqrt{a +a \left(\tan^{2}\left(d x +c \right)\right)}}}{a}\right)}{d}"," ",0,"1/d*a*(1/5/a*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(5/2)+4/5/a*(1/3/a*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(3/2)+2/3/a^2*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(1/2)))","A"
286,1,119,102,0.365000," ","int(1/(a+a*tan(d*x+c)^2)^(7/2),x)","\frac{a \left(\frac{\tan \left(d x +c \right)}{7 a \left(a +a \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{7}{2}}}+\frac{\frac{6 \tan \left(d x +c \right)}{35 a \left(a +a \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{5}{2}}}+\frac{6 \left(\frac{4 \tan \left(d x +c \right)}{15 a \left(a +a \left(\tan^{2}\left(d x +c \right)\right)\right)^{\frac{3}{2}}}+\frac{8 \tan \left(d x +c \right)}{15 a^{2} \sqrt{a +a \left(\tan^{2}\left(d x +c \right)\right)}}\right)}{7 a}}{a}\right)}{d}"," ",0,"1/d*a*(1/7/a*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(7/2)+6/7/a*(1/5/a*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(5/2)+4/5/a*(1/3/a*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(3/2)+2/3/a^2*tan(d*x+c)/(a+a*tan(d*x+c)^2)^(1/2))))","A"
287,1,19,16,0.144000," ","int((1+tan(x)^2)^(3/2),x)","\frac{\tan \left(x \right) \sqrt{1+\tan^{2}\left(x \right)}}{2}+\frac{\arcsinh \left(\tan \left(x \right)\right)}{2}"," ",0,"1/2*tan(x)*(1+tan(x)^2)^(1/2)+1/2*arcsinh(tan(x))","A"
288,1,4,3,0.135000," ","int((1+tan(x)^2)^(1/2),x)","\arcsinh \left(\tan \left(x \right)\right)"," ",0,"arcsinh(tan(x))","A"
289,1,12,9,0.087000," ","int(1/(1+tan(x)^2)^(1/2),x)","\frac{\tan \left(x \right)}{\sqrt{1+\tan^{2}\left(x \right)}}"," ",0,"1/(1+tan(x)^2)^(1/2)*tan(x)","A"
290,1,32,27,0.249000," ","int((-1-tan(x)^2)^(3/2),x)","-\frac{\tan \left(x \right) \sqrt{-1-\left(\tan^{2}\left(x \right)\right)}}{2}+\frac{\arctan \left(\frac{\tan \left(x \right)}{\sqrt{-1-\left(\tan^{2}\left(x \right)\right)}}\right)}{2}"," ",0,"-1/2*tan(x)*(-1-tan(x)^2)^(1/2)+1/2*arctan(tan(x)/(-1-tan(x)^2)^(1/2))","A"
291,1,17,14,0.257000," ","int((-1-tan(x)^2)^(1/2),x)","-\arctan \left(\frac{\tan \left(x \right)}{\sqrt{-1-\left(\tan^{2}\left(x \right)\right)}}\right)"," ",0,"-arctan(tan(x)/(-1-tan(x)^2)^(1/2))","A"
292,1,14,11,0.240000," ","int(1/(-1-tan(x)^2)^(1/2),x)","\frac{\tan \left(x \right)}{\sqrt{-1-\left(\tan^{2}\left(x \right)\right)}}"," ",0,"tan(x)/(-1-tan(x)^2)^(1/2)","A"
293,1,166,101,0.395000," ","int((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^5,x)","\frac{\left(\tan^{2}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{5 f b}-\frac{2 a \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{15 f \,b^{2}}-\frac{\left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{3 b f}+\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{f}-\frac{b \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}+\frac{a \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}"," ",0,"1/5/f*tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2)/b-2/15/f*a/b^2*(a+b*tan(f*x+e)^2)^(3/2)-1/3*(a+b*tan(f*x+e)^2)^(3/2)/b/f+(a+b*tan(f*x+e)^2)^(1/2)/f-1/f*b/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))+1/f*a/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
294,1,114,76,0.409000," ","int((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^3,x)","\frac{\left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{3 b f}-\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{f}+\frac{b \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}-\frac{a \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}"," ",0,"1/3*(a+b*tan(f*x+e)^2)^(3/2)/b/f-(a+b*tan(f*x+e)^2)^(1/2)/f+1/f*b/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))-1/f*a/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
295,1,91,54,0.235000," ","int((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e),x)","\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{f}-\frac{b \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}+\frac{a \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}"," ",0,"(a+b*tan(f*x+e)^2)^(1/2)/f-1/f*b/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))+1/f*a/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
296,1,615,62,1.695000," ","int(cot(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{4}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \left(\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \sqrt{a}\, \sqrt{a -b}-\sqrt{a}\, \ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right) \sqrt{a -b}+2 \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) a -2 \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) b \right)}{4 f \sin \left(f x +e \right)^{2} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a -b}}"," ",0,"-1/4/f*4^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)*(-1+cos(f*x+e))*(ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*a^(1/2)*(a-b)^(1/2)-a^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*(a-b)^(1/2)+2*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*a-2*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*b)/sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)/(a-b)^(1/2)","B"
297,1,2135,97,1.660000," ","int(cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/8/f*(-1+cos(f*x+e))*(4*cos(f*x+e)^2*a^(5/2)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*4^(1/2)+2*cos(f*x+e)^2*a^(3/2)*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*4^(1/2)-4*cos(f*x+e)^2*a^(3/2)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*4^(1/2)*b-8*cos(f*x+e)^2*a^(1/2)*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)-4*cos(f*x+e)^2*a^(1/2)*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*4^(1/2)*b+2*cos(f*x+e)^2*(a-b)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*4^(1/2)*a^2-cos(f*x+e)^2*(a-b)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*4^(1/2)*a*b-2*cos(f*x+e)^2*(a-b)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*4^(1/2)*a^2+cos(f*x+e)^2*(a-b)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*4^(1/2)*a*b-2*cos(f*x+e)*a^(3/2)*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*4^(1/2)-4*a^(5/2)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*4^(1/2)-16*cos(f*x+e)*a^(1/2)*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)+4*a^(3/2)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*4^(1/2)*b-8*a^(1/2)*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)+4*a^(1/2)*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*4^(1/2)*b-2*(a-b)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*4^(1/2)*a^2+(a-b)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*4^(1/2)*a*b+2*(a-b)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*4^(1/2)*a^2-(a-b)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*4^(1/2)*a*b)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)/sin(f*x+e)^4/a^(3/2)/(a-b)^(1/2)","B"
298,1,5676,141,1.284000," ","int(cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
299,1,451,196,0.369000," ","int((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^6,x)","\frac{\left(\tan^{3}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{6 f b}-\frac{a \tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{8 f \,b^{2}}+\frac{a^{2} \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{16 f \,b^{2}}+\frac{a^{3} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{16 f \,b^{\frac{5}{2}}}-\frac{\tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{4 f b}+\frac{a \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{8 f b}+\frac{a^{2} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{8 f \,b^{\frac{3}{2}}}+\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 f}+\frac{a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f \sqrt{b}}-\frac{\sqrt{b}\, \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}-\frac{a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/6/f*tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2)/b-1/8/f/b^2*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)+1/16/f/b^2*a^2*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)+1/16/f/b^(5/2)*a^3*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/4/f*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)/b+1/8/f/b*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)+1/8/f/b^(3/2)*a^2*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/2*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/f+1/2/f*a/b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*(b^4*(a-b))^(1/2)/b/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))-1/f*a*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
300,1,323,147,0.383000," ","int((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^4,x)","\frac{\tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{4 f b}-\frac{a \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{8 f b}-\frac{a^{2} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{8 f \,b^{\frac{3}{2}}}-\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 f}-\frac{a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f \sqrt{b}}+\frac{\sqrt{b}\, \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}+\frac{a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/4/f*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)/b-1/8/f/b*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)-1/8/f/b^(3/2)*a^2*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/2*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/f-1/2/f*a/b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*(b^4*(a-b))^(1/2)/b/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))+1/f*a*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
301,1,230,105,0.295000," ","int((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^2,x)","\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 f}+\frac{a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f \sqrt{b}}-\frac{\sqrt{b}\, \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}-\frac{a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/2*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/f+1/2/f*a/b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*(b^4*(a-b))^(1/2)/b/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))-1/f*a*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
302,1,169,73,0.419000," ","int((a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{b}\, \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}+\frac{a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/f*b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*(b^4*(a-b))^(1/2)/b/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))+1/f*a*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
303,1,2233,67,1.625000," ","int(cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a -\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) b \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a +2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) b +\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a \sin \left(f x +e \right)-\sin \left(f x +e \right) \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, b -2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a \sin \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sin \left(f x +e \right) b +\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b +\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b \right)}{f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right) \sin \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}"," ",0,"-1/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)*(2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a-2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*b-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a+2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*b+2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*a-2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*b-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)*a+2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)*b+cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a-cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b+((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/sin(f*x+e)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
304,1,4518,103,1.420000," ","int(cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/3/f*(-6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^2+6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a*b+3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^2-3*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a*b-6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2+6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a*b+3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2-3*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*cos(f*x+e)^2*a*b+6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2-6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a*b-3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2+3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a*b+4*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2-5*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2+6*a^2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)-6*b*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*sin(f*x+e)-3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*a^2+3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*b*a*sin(f*x+e)-3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a^2+8*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-2*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2-3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b+((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/sin(f*x+e)^3/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/a","C"
305,1,6894,149,1.362000," ","int(cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
306,1,256,125,0.343000," ","int(tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\left(\tan^{2}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}{7 f b}-\frac{2 a \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}{35 f \,b^{2}}-\frac{\left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}{5 b f}+\frac{b \left(\tan^{2}\left(f x +e \right)\right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{3 f}+\frac{4 a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{3 f}-\frac{b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{f}+\frac{b^{2} \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}-\frac{2 a b \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}+\frac{a^{2} \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}"," ",0,"1/7/f*tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^(5/2)/b-2/35/f*a/b^2*(a+b*tan(f*x+e)^2)^(5/2)-1/5*(a+b*tan(f*x+e)^2)^(5/2)/b/f+1/3/f*b*tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^(1/2)+4/3/f*a*(a+b*tan(f*x+e)^2)^(1/2)-b*(a+b*tan(f*x+e)^2)^(1/2)/f+1/f*b^2/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))-2/f*a*b/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))+1/f*a^2/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","B"
307,1,204,100,0.231000," ","int(tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}{5 b f}-\frac{b \left(\tan^{2}\left(f x +e \right)\right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{3 f}-\frac{4 a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{3 f}+\frac{b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{f}-\frac{b^{2} \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}+\frac{2 a b \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}-\frac{a^{2} \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}"," ",0,"1/5*(a+b*tan(f*x+e)^2)^(5/2)/b/f-1/3/f*b*tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^(1/2)-4/3/f*a*(a+b*tan(f*x+e)^2)^(1/2)+b*(a+b*tan(f*x+e)^2)^(1/2)/f-1/f*b^2/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))+2/f*a*b/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))-1/f*a^2/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","B"
308,1,181,78,0.196000," ","int(tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{b \left(\tan^{2}\left(f x +e \right)\right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{3 f}+\frac{4 a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{3 f}-\frac{b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{f}+\frac{b^{2} \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}-\frac{2 a b \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}+\frac{a^{2} \arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}"," ",0,"1/3/f*b*tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^(1/2)+4/3/f*a*(a+b*tan(f*x+e)^2)^(1/2)-b*(a+b*tan(f*x+e)^2)^(1/2)/f+1/f*b^2/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))-2/f*a*b/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))+1/f*a^2/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","B"
309,1,1765,81,1.553000," ","int(cot(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{3} \left(2 \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) \cos \left(f x +e \right) a^{\frac{9}{2}}-4 \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) \cos \left(f x +e \right) a^{\frac{7}{2}} b +2 \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) \cos \left(f x +e \right) a^{\frac{5}{2}} b^{2}+2 \cos \left(f x +e \right) a^{\frac{5}{2}} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a -b}\, b +2 b \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a^{\frac{5}{2}} \sqrt{a -b}+\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \cos \left(f x +e \right) \sqrt{a -b}\, a^{4}-3 \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \cos \left(f x +e \right) \sqrt{a -b}\, a^{3} b +6 \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \cos \left(f x +e \right) \sqrt{a -b}\, a^{2} b^{2}-3 \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \cos \left(f x +e \right) \sqrt{a -b}\, a \,b^{3}-\ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right) \cos \left(f x +e \right) \sqrt{a -b}\, a^{4}+3 \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \cos \left(f x +e \right) \sqrt{a -b}\, a^{3} b -6 \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \cos \left(f x +e \right) \sqrt{a -b}\, a^{2} b^{2}+3 \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \cos \left(f x +e \right) \sqrt{a -b}\, a \,b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sqrt{4}}{4 f \sin \left(f x +e \right)^{6} \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}} a^{\frac{5}{2}} \sqrt{a -b}}"," ",0,"-1/4/f*(-1+cos(f*x+e))^3*(2*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*cos(f*x+e)*a^(9/2)-4*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*cos(f*x+e)*a^(7/2)*b+2*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*cos(f*x+e)*a^(5/2)*b^2+2*cos(f*x+e)*a^(5/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*(a-b)^(1/2)*b+2*b*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(5/2)*(a-b)^(1/2)+ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*(a-b)^(1/2)*a^4-3*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*(a-b)^(1/2)*a^3*b+6*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*(a-b)^(1/2)*a^2*b^2-3*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*(a-b)^(1/2)*a*b^3-ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*(a-b)^(1/2)*a^4+3*ln(-4*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*(a-b)^(1/2)*a^3*b-6*ln(-4*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*(a-b)^(1/2)*a^2*b^2+3*ln(-4*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*(a-b)^(1/2)*a*b^3)*cos(f*x+e)^2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)*4^(1/2)/sin(f*x+e)^6/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)/a^(5/2)/(a-b)^(1/2)","B"
310,1,2011,98,1.506000," ","int(cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\sqrt{4}\, \left(-1+\cos \left(f x +e \right)\right)^{2} \left(2 \sqrt{a -b}\, a^{\frac{3}{2}} \cos \left(f x +e \right) \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right)-2 \sqrt{a -b}\, a^{\frac{3}{2}} \cos \left(f x +e \right) \ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right)-2 a^{\frac{3}{2}} \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \sqrt{a -b}+2 a^{\frac{3}{2}} \ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right) \sqrt{a -b}-3 \sqrt{a -b}\, \sqrt{a}\, \cos \left(f x +e \right) \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) b +3 \sqrt{a -b}\, \sqrt{a}\, \cos \left(f x +e \right) \ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right) b +3 \sqrt{a}\, b \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \sqrt{a -b}-3 \sqrt{a}\, \ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right) b \sqrt{a -b}-2 \sqrt{a -b}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a +4 \cos \left(f x +e \right) \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) a^{2}-8 \cos \left(f x +e \right) \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) a b +4 \cos \left(f x +e \right) \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) b^{2}-4 \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) a^{2}+8 \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) a b -4 \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) b^{2}\right) \left(\cos^{3}\left(f x +e \right)\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{8 f \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{6} \sqrt{a -b}}"," ",0,"1/8/f*4^(1/2)*(-1+cos(f*x+e))^2*(2*(a-b)^(1/2)*a^(3/2)*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))-2*(a-b)^(1/2)*a^(3/2)*cos(f*x+e)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))-2*a^(3/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*(a-b)^(1/2)+2*a^(3/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*(a-b)^(1/2)-3*(a-b)^(1/2)*a^(1/2)*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*b+3*(a-b)^(1/2)*a^(1/2)*cos(f*x+e)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b+3*a^(1/2)*b*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*(a-b)^(1/2)-3*a^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*b*(a-b)^(1/2)-2*(a-b)^(1/2)*cos(f*x+e)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a+4*cos(f*x+e)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*a^2-8*cos(f*x+e)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*a*b+4*cos(f*x+e)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*b^2-4*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*a^2+8*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*a*b-4*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*b^2)*cos(f*x+e)^3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(3/2)/sin(f*x+e)^6/(a-b)^(1/2)","B"
311,1,5224,139,1.399000," ","int(cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
312,1,669,264,0.284000," ","int(tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\left(\tan^{3}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}{8 f b}-\frac{a \tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}{16 f \,b^{2}}+\frac{a^{2} \tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{64 f \,b^{2}}+\frac{3 a^{3} \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{128 f \,b^{2}}+\frac{3 a^{4} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{128 f \,b^{\frac{5}{2}}}-\frac{\tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}{6 f b}+\frac{a \tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{24 f b}+\frac{a^{2} \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{16 f b}+\frac{a^{3} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{16 f \,b^{\frac{3}{2}}}+\frac{\tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{4 f}+\frac{3 a \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{8 f}+\frac{3 a^{2} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{8 f \sqrt{b}}-\frac{b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 f}-\frac{3 \sqrt{b}\, a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f}+\frac{b^{\frac{3}{2}} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)}+\frac{2 a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}-\frac{a^{2} \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/8/f*tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^(5/2)/b-1/16/f/b^2*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(5/2)+1/64/f/b^2*a^2*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)+3/128/f/b^2*a^3*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)+3/128/f/b^(5/2)*a^4*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/6/f*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(5/2)/b+1/24/f/b*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)+1/16/f/b*a^2*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)+1/16/f/b^(3/2)*a^3*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/4/f*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)+3/8/f*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)+3/8/f*a^2/b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/2*b*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/f-3/2/f*b^(1/2)*a*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*b^(3/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))+2/f*a/b*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))-1/f*a^2*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
313,1,510,198,0.377000," ","int(tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}{6 f b}-\frac{a \tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{24 f b}-\frac{a^{2} \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{16 f b}-\frac{a^{3} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{16 f \,b^{\frac{3}{2}}}-\frac{\tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{4 f}-\frac{3 a \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{8 f}-\frac{3 a^{2} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{8 f \sqrt{b}}+\frac{b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 f}+\frac{3 \sqrt{b}\, a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f}-\frac{b^{\frac{3}{2}} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)}-\frac{2 a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}+\frac{a^{2} \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/6/f*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(5/2)/b-1/24/f/b*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)-1/16/f/b*a^2*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)-1/16/f/b^(3/2)*a^3*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/4/f*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)-3/8/f*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)-3/8/f*a^2/b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/2*b*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/f+3/2/f*b^(1/2)*a*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*b^(3/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))-2/f*a/b*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))+1/f*a^2*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
314,1,386,150,0.312000," ","int(tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{4 f}+\frac{3 a \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{8 f}+\frac{3 a^{2} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{8 f \sqrt{b}}-\frac{b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 f}-\frac{3 \sqrt{b}\, a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f}+\frac{b^{\frac{3}{2}} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)}+\frac{2 a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}-\frac{a^{2} \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/4/f*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)+3/8/f*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)+3/8/f*a^2/b^(1/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/2*b*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/f-3/2/f*b^(1/2)*a*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*b^(3/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))+2/f*a/b*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))-1/f*a^2*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
315,1,297,107,0.311000," ","int((a+b*tan(f*x+e)^2)^(3/2),x)","\frac{b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 f}+\frac{3 \sqrt{b}\, a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f}-\frac{b^{\frac{3}{2}} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)}-\frac{2 a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f b \left(a -b \right)}+\frac{a^{2} \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/2*b*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/f+3/2/f*b^(1/2)*a*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*b^(3/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))-2/f*a/b*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))+1/f*a^2*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
316,1,3333,100,1.547000," ","int(cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"-1/f*(2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a*b-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2+4*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a*b-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2*sin(f*x+e)*cos(f*x+e)+2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2*sin(f*x+e)*cos(f*x+e)+2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*a^2-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*b*a*sin(f*x+e)-2*a^2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)+4*b*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a*sin(f*x+e)-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2*sin(f*x+e)+2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*b^2*sin(f*x+e)+((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a^2-((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a*b+((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b)*cos(f*x+e)^3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/sin(f*x+e)/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)","C"
317,1,6591,101,1.352000," ","int(cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
318,1,10026,147,1.413000," ","int(cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
319,1,461,148,0.567000," ","int((a+b*tan(d*x+c)^2)^(5/2),x)","\frac{b^{2} \left(\tan^{3}\left(d x +c \right)\right) \sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}}{4 d}+\frac{9 b a \tan \left(d x +c \right) \sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}}{8 d}+\frac{15 \sqrt{b}\, a^{2} \ln \left(\sqrt{b}\, \tan \left(d x +c \right)+\sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}\right)}{8 d}-\frac{b^{2} \tan \left(d x +c \right) \sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}}{2 d}-\frac{5 b^{\frac{3}{2}} a \ln \left(\sqrt{b}\, \tan \left(d x +c \right)+\sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}\right)}{2 d}+\frac{b^{\frac{5}{2}} \ln \left(\sqrt{b}\, \tan \left(d x +c \right)+\sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}\right)}{d}-\frac{b \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(d x +c \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}}\right)}{d \left(a -b \right)}+\frac{3 a \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(d x +c \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}}\right)}{d \left(a -b \right)}-\frac{3 a^{2} \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(d x +c \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}}\right)}{d b \left(a -b \right)}+\frac{a^{3} \sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(d x +c \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(d x +c \right)\right)}}\right)}{d \,b^{2} \left(a -b \right)}"," ",0,"1/4/d*b^2*tan(d*x+c)^3*(a+b*tan(d*x+c)^2)^(1/2)+9/8/d*b*a*tan(d*x+c)*(a+b*tan(d*x+c)^2)^(1/2)+15/8/d*b^(1/2)*a^2*ln(b^(1/2)*tan(d*x+c)+(a+b*tan(d*x+c)^2)^(1/2))-1/2/d*b^2*tan(d*x+c)*(a+b*tan(d*x+c)^2)^(1/2)-5/2/d*b^(3/2)*a*ln(b^(1/2)*tan(d*x+c)+(a+b*tan(d*x+c)^2)^(1/2))+1/d*b^(5/2)*ln(b^(1/2)*tan(d*x+c)+(a+b*tan(d*x+c)^2)^(1/2))-1/d*b*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(d*x+c)^2)^(1/2)*tan(d*x+c))+3/d*a*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(d*x+c)^2)^(1/2)*tan(d*x+c))-3/d*a^2/b*(b^4*(a-b))^(1/2)/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(d*x+c)^2)^(1/2)*tan(d*x+c))+1/d*a^3*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(d*x+c)^2)^(1/2)*tan(d*x+c))","B"
320,1,111,83,0.347000," ","int(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\left(\tan^{2}\left(f x +e \right)\right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{3 f b}-\frac{2 a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{3 f \,b^{2}}-\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{b f}+\frac{\arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}"," ",0,"1/3/f*tan(f*x+e)^2/b*(a+b*tan(f*x+e)^2)^(1/2)-2/3/f*a/b^2*(a+b*tan(f*x+e)^2)^(1/2)-(a+b*tan(f*x+e)^2)^(1/2)/b/f+1/f/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
321,1,58,56,0.300000," ","int(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{b f}-\frac{\arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}"," ",0,"(a+b*tan(f*x+e)^2)^(1/2)/b/f-1/f/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
322,1,35,35,0.203000," ","int(tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \sqrt{-a +b}}"," ",0,"1/f/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
323,1,496,62,1.488000," ","int(cot(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a}}\right) \sqrt{a -b}+2 \ln \left(4 \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a -b}+4 \sqrt{a -b}\, \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+4 a \cos \left(f x +e \right)-4 b \cos \left(f x +e \right)\right) \sqrt{a}-\ln \left(-\frac{4 \left(\sqrt{a}\, \cos \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+\sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{-1+\cos \left(f x +e \right)}\right) \sqrt{a -b}\right) \left(\sin^{2}\left(f x +e \right)\right)}{2 f \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{a}\, \sqrt{a -b}}"," ",0,"-1/2/f*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*(ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*(a-b)^(1/2)+2*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*a^(1/2)-ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*(a-b)^(1/2))*sin(f*x+e)^2/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/a^(1/2)/(a-b)^(1/2)","B"
324,1,3601,98,1.349000," ","int(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"1/4/f*(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*cos(f*x+e)^3*a^(5/2)+4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*cos(f*x+e)^2*a^(5/2)-2*cos(f*x+e)^3*a^(5/2)*(a-b)^(1/2)-4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*cos(f*x+e)*a^(5/2)+2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^3*(a-b)^(1/2)*a^2+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^3*(a-b)^(1/2)*a*b-2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^3*(a-b)^(1/2)*a^2-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^3*(a-b)^(1/2)*a*b+2*cos(f*x+e)^3*a^(3/2)*(a-b)^(1/2)*b-4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(4*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a-b)^(1/2)+4*(a-b)^(1/2)*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)+4*a*cos(f*x+e)-4*b*cos(f*x+e))*a^(5/2)+2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^2*(a-b)^(1/2)*a^2+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)^2*(a-b)^(1/2)*a*b-2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*(a-b)^(1/2)*a^2-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*(a-b)^(1/2)*a*b-2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*(a-b)^(1/2)*a^2-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*cos(f*x+e)*(a-b)^(1/2)*a*b+2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*(a-b)^(1/2)*a^2+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*(a-b)^(1/2)*a*b-2*cos(f*x+e)*a^(3/2)*(a-b)^(1/2)*b-2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*(a-b)^(1/2)*a^2-((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)+b)/sin(f*x+e)^2/a^(1/2))*(a-b)^(1/2)*a*b+2*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*(a-b)^(1/2)*a^2+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^(1/2)+((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(-1+cos(f*x+e)))*(a-b)^(1/2)*a*b)*sin(f*x+e)^2/(-1+cos(f*x+e))^2/cos(f*x+e)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/(1+cos(f*x+e))^2/a^(5/2)/(a-b)^(1/2)","B"
325,1,7641,144,1.958000," ","int(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
326,1,261,155,0.326000," ","int(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \left(\tan^{3}\left(f x +e \right)\right)}{4 b f}-\frac{3 a \tan \left(f x +e \right) \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{8 f \,b^{2}}+\frac{3 a^{2} \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{8 f \,b^{\frac{5}{2}}}-\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 b f}+\frac{a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f \,b^{\frac{3}{2}}}+\frac{\ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f \sqrt{b}}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/4*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^3/b/f-3/8/f/b^2*a*tan(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2)+3/8/f/b^(5/2)*a^2*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/2*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/b/f+1/2/f*a/b^(3/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))/b^(1/2)-1/f*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
327,1,165,107,0.268000," ","int(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\, \tan \left(f x +e \right)}{2 b f}-\frac{a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f \,b^{\frac{3}{2}}}-\frac{\ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f \sqrt{b}}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/2*(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)/b/f-1/2/f*a/b^(3/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))/b^(1/2)+1/f*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
328,1,102,74,0.328000," ","int(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f \sqrt{b}}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/f*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))/b^(1/2)-1/f*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
329,1,67,40,0.359000," ","int(1/(a+b*tan(f*x+e)^2)^(1/2),x)","\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \,b^{2} \left(a -b \right)}"," ",0,"1/f*(b^4*(a-b))^(1/2)/b^2/(a-b)*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
330,1,1195,70,1.349000," ","int(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a -2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a +\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sin \left(f x +e \right) a -2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a \sin \left(f x +e \right)+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b +\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b}{f \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a}"," ",0,"-1/f*(2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a+2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*a-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)*a+cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a-cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b+((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b)/cos(f*x+e)/sin(f*x+e)/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/a","C"
331,1,2433,106,1.769000," ","int(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^(1/2),x)","-\frac{-6 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+3 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-6 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+3 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+6 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}-3 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}+4 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}-2 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{4}\left(f x +e \right)\right) a b -2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}+6 a^{2} \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sin \left(f x +e \right) a^{2}-3 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}+5 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +4 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{2}\left(f x +e \right)\right) b^{2}-3 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -2 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}}{3 f \cos \left(f x +e \right) \sin \left(f x +e \right)^{3} \sqrt{\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2}}"," ",0,"-1/3/f*(-6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^2+3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^2-6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2+3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2+6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2-3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2+4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*a^2-2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*a*b-2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*b^2+6*a^2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)-3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*a^2-3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a^2+5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a*b+4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*b^2-3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2)/cos(f*x+e)/sin(f*x+e)^3/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/a^2","C"
332,1,3741,152,1.699000," ","int(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/15/f*(15*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^3+34*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*a^2*b+22*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*a*b^2-9*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6*a^2*b-6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6*a*b^2-40*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a^2*b-26*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a*b^2+23*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6*a^3-35*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*a^3-8*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^6*b^3+24*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*b^3-24*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*b^3+15*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a^3-30*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^3+15*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b+10*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^2+8*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^3+15*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a^3+60*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^3-30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^3-30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^5*sin(f*x+e)*a^3+60*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^3-30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^3-30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^3+15*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^3+15*cos(f*x+e)^5*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^3-30*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a^3)/cos(f*x+e)/sin(f*x+e)^5/((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/a^3","C"
333,1,141,88,0.266000," ","int(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\tan^{2}\left(f x +e \right)}{f b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{2 a}{f \,b^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{1}{f b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{1}{\left(a -b \right) f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \left(a -b \right) \sqrt{-a +b}}"," ",0,"1/f*tan(f*x+e)^2/b/(a+b*tan(f*x+e)^2)^(1/2)+2/f*a/b^2/(a+b*tan(f*x+e)^2)^(1/2)+1/f/b/(a+b*tan(f*x+e)^2)^(1/2)+1/(a-b)/f/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
334,1,92,65,0.296000," ","int(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{1}{f b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{1}{\left(a -b \right) f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{\arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \left(a -b \right) \sqrt{-a +b}}"," ",0,"-1/f/b/(a+b*tan(f*x+e)^2)^(1/2)-1/(a-b)/f/(a+b*tan(f*x+e)^2)^(1/2)-1/f/(a-b)/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
335,1,68,61,0.154000," ","int(tan(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{1}{\left(a -b \right) f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \left(a -b \right) \sqrt{-a +b}}"," ",0,"1/(a-b)/f/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
336,1,32888,92,2.190000," ","int(cot(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
337,1,54353,135,3.119000," ","int(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
338,1,79934,189,5.348000," ","int(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
339,1,286,162,0.394000," ","int(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\tan^{3}\left(f x +e \right)}{2 f b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{3 a \tan \left(f x +e \right)}{2 f \,b^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{3 a \ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{2 f \,b^{\frac{5}{2}}}+\frac{\tan \left(f x +e \right)}{f b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{\ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f \,b^{\frac{3}{2}}}+\frac{\tan \left(f x +e \right)}{f a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{b \tan \left(f x +e \right)}{a \left(a -b \right) f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{2} b^{2}}"," ",0,"1/2/f*tan(f*x+e)^3/b/(a+b*tan(f*x+e)^2)^(1/2)+3/2/f/b^2*a*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)-3/2/f/b^(5/2)*a*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*tan(f*x+e)/b/(a+b*tan(f*x+e)^2)^(1/2)-1/f/b^(3/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/f*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(1/2)+b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(1/2)-1/f/(a-b)^2*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
340,1,193,109,0.273000," ","int(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\tan \left(f x +e \right)}{f b \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f \,b^{\frac{3}{2}}}-\frac{\tan \left(f x +e \right)}{f a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{b \tan \left(f x +e \right)}{a \left(a -b \right) f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{2} b^{2}}"," ",0,"-1/f*tan(f*x+e)/b/(a+b*tan(f*x+e)^2)^(1/2)+1/f/b^(3/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))-1/f*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(1/2)-b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)^2*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
341,1,131,73,0.243000," ","int(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x)","\frac{\tan \left(f x +e \right)}{f a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{b \tan \left(f x +e \right)}{a \left(a -b \right) f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{2} b^{2}}"," ",0,"1/f*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(1/2)+b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(1/2)-1/f/(a-b)^2*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
342,1,104,77,0.441000," ","int(1/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{b \tan \left(f x +e \right)}{a \left(a -b \right) f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{2} b^{2}}"," ",0,"-b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)^2*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
343,1,1305,118,1.431000," ","int(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}-2 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}+\sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \sin \left(f x +e \right) a^{2}-2 a^{2} \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \sin \left(f x +e \right)+\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}-2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b +2 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{2}\left(f x +e \right)\right) b^{2}+\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a b -2 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{2}\right) \left(\cos^{3}\left(f x +e \right)\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \sin \left(f x +e \right) a^{2} \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(a -b \right)}"," ",0,"-1/f/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*(2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2-2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2+2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*sin(f*x+e)*a^2-2*a^2*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*sin(f*x+e)+((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a^2-2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a*b+2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*b^2+((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b-2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^2)*cos(f*x+e)^3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/sin(f*x+e)/a^2/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/(a-b)","C"
344,1,2577,168,1.211000," ","int(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x)","-\frac{\left(-6 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{3}+3 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{3}-6 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{3}+3 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{3}+6 \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{3}-3 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a^{3}+4 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{3}-3 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -6 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{4}\left(f x +e \right)\right) a \,b^{2}+8 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{4}\left(f x +e \right)\right) b^{3}+6 \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, -\frac{a}{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}, \frac{\sqrt{-\frac{2 i \sqrt{a -b}\, \sqrt{b}-a +2 b}{a}}}{\sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}\right) a^{3}-3 \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) a}}\, \sqrt{-\frac{2 \left(i \cos \left(f x +e \right) \sqrt{a -b}\, \sqrt{b}-i \sqrt{a -b}\, \sqrt{b}-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) a}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}}{\sin \left(f x +e \right)}, \sqrt{\frac{8 i \sqrt{a -b}\, b^{\frac{3}{2}}-4 i \sqrt{a -b}\, \sqrt{b}\, a +a^{2}-8 a b +8 b^{2}}{a^{2}}}\right) a^{3}-3 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{3}+5 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b +8 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-16 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(\cos^{2}\left(f x +e \right)\right) b^{3}-3 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a^{2} b -2 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, a \,b^{2}+8 \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, b^{3}\right) \left(\cos^{3}\left(f x +e \right)\right) \left(\frac{a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{3 f \left(a \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) b +b \right)^{2} \sin \left(f x +e \right)^{3} a^{3} \sqrt{\frac{2 i \sqrt{a -b}\, \sqrt{b}+a -2 b}{a}}\, \left(a -b \right)}"," ",0,"-1/3/f/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*(-6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^3+3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^3-6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^3+3*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^3+6*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^3-3*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^3+4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*a^3-3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*a^2*b-6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*a*b^2+8*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^4*b^3+6*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^3-3*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^3-3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a^3+5*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a^2*b+8*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*a*b^2-16*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*cos(f*x+e)^2*b^3-3*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b-2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^2+8*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^3)*cos(f*x+e)^3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/sin(f*x+e)^3/a^3/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/(a-b)","C"
345,1,3925,232,1.778000," ","int(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"-1/15/f/(a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)^2*(15*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^4+8*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^3+10*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b^2-30*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^4+48*cos(f*x+e)^6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^4+23*cos(f*x+e)^6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^4-35*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^4+15*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^4-144*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^4+144*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^4-12*cos(f*x+e)^6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^3*b+34*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^3*b-40*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^3*b-12*cos(f*x+e)^6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b^2-32*cos(f*x+e)^6*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^3+28*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b^2+72*cos(f*x+e)^4*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^3-26*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^2*b^2-48*cos(f*x+e)^2*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a*b^3+15*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*a^3*b+15*cos(f*x+e)^5*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^4-30*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^4-30*cos(f*x+e)^4*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^4-30*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^4+60*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^4-30*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^4+60*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^4+15*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^4-30*cos(f*x+e)^5*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),-1/(2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)*a,(-(2*I*(a-b)^(1/2)*b^(1/2)-a+2*b)/a)^(1/2)/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2))*a^4+15*cos(f*x+e)^4*sin(f*x+e)*2^(1/2)*((I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)+a*cos(f*x+e)-b*cos(f*x+e)+b)/(1+cos(f*x+e))/a)^(1/2)*(-2*(I*cos(f*x+e)*(a-b)^(1/2)*b^(1/2)-I*(a-b)^(1/2)*b^(1/2)-a*cos(f*x+e)+b*cos(f*x+e)-b)/(1+cos(f*x+e))/a)^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/sin(f*x+e),((8*I*(a-b)^(1/2)*b^(3/2)-4*I*(a-b)^(1/2)*b^(1/2)*a+a^2-8*a*b+8*b^2)/a^2)^(1/2))*a^4-48*((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)*b^4)*cos(f*x+e)^3*((a*cos(f*x+e)^2-cos(f*x+e)^2*b+b)/cos(f*x+e)^2)^(3/2)/sin(f*x+e)^5/a^4/((2*I*(a-b)^(1/2)*b^(1/2)+a-2*b)/a)^(1/2)/(a-b)","C"
346,1,169,103,0.344000," ","int(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{\tan^{2}\left(f x +e \right)}{f b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{2 a}{3 f \,b^{2} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{1}{3 f b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{1}{3 \left(a -b \right) f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{1}{\left(a -b \right)^{2} f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \left(a -b \right)^{2} \sqrt{-a +b}}"," ",0,"-1/f*tan(f*x+e)^2/b/(a+b*tan(f*x+e)^2)^(3/2)-2/3/f*a/b^2/(a+b*tan(f*x+e)^2)^(3/2)+1/3/f/b/(a+b*tan(f*x+e)^2)^(3/2)+1/3/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)+1/(a-b)^2/f/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)^2/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
347,1,118,91,0.277000," ","int(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{1}{3 f b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{1}{3 \left(a -b \right) f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{1}{\left(a -b \right)^{2} f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{\arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \left(a -b \right)^{2} \sqrt{-a +b}}"," ",0,"-1/3/f/b/(a+b*tan(f*x+e)^2)^(3/2)-1/3/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-1/(a-b)^2/f/(a+b*tan(f*x+e)^2)^(1/2)-1/f/(a-b)^2/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
348,1,94,87,0.186000," ","int(tan(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x)","\frac{1}{3 \left(a -b \right) f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{1}{\left(a -b \right)^{2} f \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\arctan \left(\frac{\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}{\sqrt{-a +b}}\right)}{f \left(a -b \right)^{2} \sqrt{-a +b}}"," ",0,"1/3/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)+1/(a-b)^2/f/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)^2/(-a+b)^(1/2)*arctan((a+b*tan(f*x+e)^2)^(1/2)/(-a+b)^(1/2))","A"
349,1,331597,129,21.095000," ","int(cot(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
350,1,531560,180,38.085000," ","int(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
351,1,790286,242,64.737000," ","int(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
352,1,382,153,0.352000," ","int(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{\tan^{3}\left(f x +e \right)}{3 f b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{\tan \left(f x +e \right)}{f \,b^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\ln \left(\tan \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}\right)}{f \,b^{\frac{5}{2}}}+\frac{\tan \left(f x +e \right)}{3 f b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{\tan \left(f x +e \right)}{3 f b a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\tan \left(f x +e \right)}{3 f a \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{2 \tan \left(f x +e \right)}{3 f \,a^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{b \tan \left(f x +e \right)}{3 a \left(a -b \right) f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{2 b \tan \left(f x +e \right)}{3 f \left(a -b \right) a^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{b \tan \left(f x +e \right)}{f \left(a -b \right)^{2} a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{3} b^{2}}"," ",0,"-1/3/f*tan(f*x+e)^3/b/(a+b*tan(f*x+e)^2)^(3/2)-1/f/b^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)+1/f/b^(5/2)*ln(tan(f*x+e)*b^(1/2)+(a+b*tan(f*x+e)^2)^(1/2))+1/3/f/b*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2)-1/3/f/b/a*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)+1/3/f*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(3/2)+2/3/f/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)+1/3*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)+2/3/f*b/(a-b)/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)+1/f*b/(a-b)^2*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(1/2)-1/f/(a-b)^3*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
353,1,291,117,0.319000," ","int(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{\tan \left(f x +e \right)}{3 f b \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{\tan \left(f x +e \right)}{3 f b a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{\tan \left(f x +e \right)}{3 f a \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{2 \tan \left(f x +e \right)}{3 f \,a^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{b \tan \left(f x +e \right)}{3 a \left(a -b \right) f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{2 b \tan \left(f x +e \right)}{3 f \left(a -b \right) a^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{b \tan \left(f x +e \right)}{f \left(a -b \right)^{2} a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{3} b^{2}}"," ",0,"-1/3/f/b*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2)+1/3/f/b/a*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)-1/3/f*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(3/2)-2/3/f/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)-1/3*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-2/3/f*b/(a-b)/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)-1/f*b/(a-b)^2*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)^3*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
354,1,232,114,0.259000," ","int(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x)","\frac{\tan \left(f x +e \right)}{3 f a \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{2 \tan \left(f x +e \right)}{3 f \,a^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{b \tan \left(f x +e \right)}{3 a \left(a -b \right) f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{2 b \tan \left(f x +e \right)}{3 f \left(a -b \right) a^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{b \tan \left(f x +e \right)}{f \left(a -b \right)^{2} a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{3} b^{2}}"," ",0,"1/3/f*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(3/2)+2/3/f/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)+1/3*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)+2/3/f*b/(a-b)/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)+1/f*b/(a-b)^2*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(1/2)-1/f/(a-b)^3*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","B"
355,1,176,120,0.434000," ","int(1/(a+b*tan(f*x+e)^2)^(5/2),x)","-\frac{b \tan \left(f x +e \right)}{3 a \left(a -b \right) f \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{2 b \tan \left(f x +e \right)}{3 f \left(a -b \right) a^{2} \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}-\frac{b \tan \left(f x +e \right)}{f \left(a -b \right)^{2} a \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}+\frac{\sqrt{b^{4} \left(a -b \right)}\, \arctan \left(\frac{\left(a -b \right) b^{2} \tan \left(f x +e \right)}{\sqrt{b^{4} \left(a -b \right)}\, \sqrt{a +b \left(\tan^{2}\left(f x +e \right)\right)}}\right)}{f \left(a -b \right)^{3} b^{2}}"," ",0,"-1/3*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-2/3/f*b/(a-b)/a^2*tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2)-1/f*b/(a-b)^2*tan(f*x+e)/a/(a+b*tan(f*x+e)^2)^(1/2)+1/f/(a-b)^3*(b^4*(a-b))^(1/2)/b^2*arctan((a-b)*b^2/(b^4*(a-b))^(1/2)/(a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e))","A"
356,0,0,168,1.134000," ","int(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x)","\int \frac{\cot^{2}\left(f x +e \right)}{\left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x)","F"
357,0,0,229,1.041000," ","int(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x)","\int \frac{\cot^{4}\left(f x +e \right)}{\left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x)","F"
358,0,0,301,1.385000," ","int(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x)","\int \frac{\cot^{6}\left(f x +e \right)}{\left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x)","F"
359,0,0,66,3.059000," ","int((d*tan(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","\int \left(d \tan \left(f x +e \right)\right)^{m} \left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*tan(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","F"
360,0,0,96,2.197000," ","int((d*tan(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","\int \left(d \tan \left(f x +e \right)\right)^{m} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*tan(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","F"
361,0,0,125,1.155000," ","int(tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\tan^{5}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x)","F"
362,0,0,93,0.970000," ","int(tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\tan^{3}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x)","F"
363,0,0,63,0.921000," ","int(tan(f*x+e)*(a+b*tan(f*x+e)^2)^p,x)","\int \tan \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(tan(f*x+e)*(a+b*tan(f*x+e)^2)^p,x)","F"
364,0,0,118,1.323000," ","int(cot(f*x+e)*(a+b*tan(f*x+e)^2)^p,x)","\int \cot \left(f x +e \right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)*(a+b*tan(f*x+e)^2)^p,x)","F"
365,0,0,156,1.078000," ","int(cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\cot^{3}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x)","F"
366,0,0,213,1.376000," ","int(cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\cot^{5}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x)","F"
367,0,0,77,1.436000," ","int(tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\tan^{6}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x)","F"
368,0,0,77,1.008000," ","int(tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\tan^{4}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x)","F"
369,0,0,77,0.896000," ","int(tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\tan^{2}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x)","F"
370,0,0,74,0.022000," ","int((a+b*tan(f*x+e)^2)^p,x)","\int \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*tan(f*x+e)^2)^p,x)","F"
371,0,0,75,1.065000," ","int(cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x)","F"
372,0,0,77,1.062000," ","int(cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\cot^{4}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x)","F"
373,0,0,77,1.120000," ","int(cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x)","\int \left(\cot^{6}\left(f x +e \right)\right) \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x)","F"
374,1,321,241,0.027000," ","int((a+b*tan(d*x+c)^3)^4,x)","\frac{b^{4} \left(\tan^{11}\left(d x +c \right)\right)}{11 d}-\frac{b^{4} \left(\tan^{9}\left(d x +c \right)\right)}{9 d}+\frac{a \,b^{3} \left(\tan^{8}\left(d x +c \right)\right)}{2 d}+\frac{b^{4} \left(\tan^{7}\left(d x +c \right)\right)}{7 d}-\frac{2 a \,b^{3} \left(\tan^{6}\left(d x +c \right)\right)}{3 d}+\frac{6 \left(\tan^{5}\left(d x +c \right)\right) a^{2} b^{2}}{5 d}-\frac{\left(\tan^{5}\left(d x +c \right)\right) b^{4}}{5 d}+\frac{a \,b^{3} \left(\tan^{4}\left(d x +c \right)\right)}{d}-\frac{2 \left(\tan^{3}\left(d x +c \right)\right) a^{2} b^{2}}{d}+\frac{b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{3} b \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 a \,b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2} \tan \left(d x +c \right)}{d}-\frac{b^{4} \tan \left(d x +c \right)}{d}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3} b}{d}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a \,b^{3}}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d}-\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d}"," ",0,"1/11*b^4*tan(d*x+c)^11/d-1/9*b^4*tan(d*x+c)^9/d+1/2*a*b^3*tan(d*x+c)^8/d+1/7*b^4*tan(d*x+c)^7/d-2/3*a*b^3*tan(d*x+c)^6/d+6/5/d*tan(d*x+c)^5*a^2*b^2-1/5/d*tan(d*x+c)^5*b^4+a*b^3*tan(d*x+c)^4/d-2/d*tan(d*x+c)^3*a^2*b^2+1/3*b^4*tan(d*x+c)^3/d+2/d*a^3*b*tan(d*x+c)^2-2*a*b^3*tan(d*x+c)^2/d+6*a^2*b^2*tan(d*x+c)/d-1/d*b^4*tan(d*x+c)-2/d*ln(1+tan(d*x+c)^2)*a^3*b+2/d*ln(1+tan(d*x+c)^2)*a*b^3+1/d*arctan(tan(d*x+c))*a^4-6/d*arctan(tan(d*x+c))*a^2*b^2+1/d*arctan(tan(d*x+c))*b^4","A"
375,1,201,158,0.026000," ","int((a+b*tan(d*x+c)^3)^3,x)","\frac{b^{3} \left(\tan^{8}\left(d x +c \right)\right)}{8 d}-\frac{b^{3} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}+\frac{3 a \,b^{2} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{b^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \,b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{3}}{2 d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d}"," ",0,"1/8*b^3*tan(d*x+c)^8/d-1/6*b^3*tan(d*x+c)^6/d+3/5*a*b^2*tan(d*x+c)^5/d+1/4*b^3*tan(d*x+c)^4/d-a*b^2*tan(d*x+c)^3/d+3/2/d*a^2*b*tan(d*x+c)^2-1/2*b^3*tan(d*x+c)^2/d+3*a*b^2*tan(d*x+c)/d-3/2/d*ln(1+tan(d*x+c)^2)*a^2*b+1/2/d*ln(1+tan(d*x+c)^2)*b^3+1/d*arctan(tan(d*x+c))*a^3-3/d*arctan(tan(d*x+c))*a*b^2","A"
376,1,108,85,0.025000," ","int((a+b*tan(d*x+c)^3)^2,x)","\frac{b^{2} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a b \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{b^{2} \tan \left(d x +c \right)}{d}-\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}"," ",0,"1/5*b^2*tan(d*x+c)^5/d-1/3*b^2*tan(d*x+c)^3/d+a*b*tan(d*x+c)^2/d+b^2*tan(d*x+c)/d-1/d*a*b*ln(1+tan(d*x+c)^2)+1/d*arctan(tan(d*x+c))*a^2-1/d*arctan(tan(d*x+c))*b^2","A"
377,1,36,30,0.025000," ","int(a+b*tan(d*x+c)^3,x)","a x +\frac{b \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"a*x+1/2*b*tan(d*x+c)^2/d-1/2/d*b*ln(1+tan(d*x+c)^2)","A"
378,1,355,206,0.280000," ","int(1/(a+b*tan(d*x+c)^3),x)","\frac{b \ln \left(\tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{b \ln \left(\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{a \ln \left(\tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{a \ln \left(\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d \left(a^{2}+b^{2}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{b \ln \left(a +b \left(\tan^{3}\left(d x +c \right)\right)\right)}{3 d \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/3/d*b/(a^2+b^2)/(1/b*a)^(2/3)*ln(tan(d*x+c)+(1/b*a)^(1/3))-1/6/d*b/(a^2+b^2)/(1/b*a)^(2/3)*ln(tan(d*x+c)^2-(1/b*a)^(1/3)*tan(d*x+c)+(1/b*a)^(2/3))+1/3/d*b/(a^2+b^2)/(1/b*a)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)-1))+1/3/d/(a^2+b^2)*a/(1/b*a)^(1/3)*ln(tan(d*x+c)+(1/b*a)^(1/3))-1/6/d/(a^2+b^2)*a/(1/b*a)^(1/3)*ln(tan(d*x+c)^2-(1/b*a)^(1/3)*tan(d*x+c)+(1/b*a)^(2/3))-1/3/d/(a^2+b^2)*a*3^(1/2)/(1/b*a)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)-1))-1/3/d*b/(a^2+b^2)*ln(a+b*tan(d*x+c)^3)+1/2/d/(a^2+b^2)*b*ln(1+tan(d*x+c)^2)+1/d/(a^2+b^2)*a*arctan(tan(d*x+c))","A"
379,1,1086,455,0.352000," ","int(1/(a+b*tan(d*x+c)^3)^2,x)","-\frac{b \left(\tan^{2}\left(d x +c \right)\right) a^{2}}{3 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a +b \left(\tan^{3}\left(d x +c \right)\right)\right)}-\frac{b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{3 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a +b \left(\tan^{3}\left(d x +c \right)\right)\right)}+\frac{b^{2} a \tan \left(d x +c \right)}{3 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a +b \left(\tan^{3}\left(d x +c \right)\right)\right)}+\frac{b^{4} \tan \left(d x +c \right)}{3 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a +b \left(\tan^{3}\left(d x +c \right)\right)\right) a}+\frac{b \,a^{2}}{3 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a +b \left(\tan^{3}\left(d x +c \right)\right)\right)}+\frac{b^{3}}{3 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a +b \left(\tan^{3}\left(d x +c \right)\right)\right)}+\frac{8 b a \ln \left(\tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 b^{3} \ln \left(\tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{4 b a \ln \left(\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{b^{3} \ln \left(\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{8 b a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 b^{3} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{4 a^{2} \ln \left(\tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{2 b^{2} \ln \left(\tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{2 a^{2} \ln \left(\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{b^{2} \ln \left(\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \tan \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{4 a^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{2 b^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{2 b a \ln \left(a +b \left(\tan^{3}\left(d x +c \right)\right)\right)}{3 d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}+\frac{a b \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}"," ",0,"-1/3/d*b/(a^4+2*a^2*b^2+b^4)/(a+b*tan(d*x+c)^3)*tan(d*x+c)^2*a^2-1/3/d*b^3/(a^4+2*a^2*b^2+b^4)/(a+b*tan(d*x+c)^3)*tan(d*x+c)^2+1/3/d*b^2/(a^4+2*a^2*b^2+b^4)/(a+b*tan(d*x+c)^3)*a*tan(d*x+c)+1/3/d*b^4/(a^4+2*a^2*b^2+b^4)/(a+b*tan(d*x+c)^3)/a*tan(d*x+c)+1/3/d*b/(a^4+2*a^2*b^2+b^4)/(a+b*tan(d*x+c)^3)*a^2+1/3/d*b^3/(a^4+2*a^2*b^2+b^4)/(a+b*tan(d*x+c)^3)+8/9/d*b/(a^4+2*a^2*b^2+b^4)*a/(1/b*a)^(2/3)*ln(tan(d*x+c)+(1/b*a)^(1/3))+2/9/d*b^3/(a^4+2*a^2*b^2+b^4)/a/(1/b*a)^(2/3)*ln(tan(d*x+c)+(1/b*a)^(1/3))-4/9/d*b/(a^4+2*a^2*b^2+b^4)*a/(1/b*a)^(2/3)*ln(tan(d*x+c)^2-(1/b*a)^(1/3)*tan(d*x+c)+(1/b*a)^(2/3))-1/9/d*b^3/(a^4+2*a^2*b^2+b^4)/a/(1/b*a)^(2/3)*ln(tan(d*x+c)^2-(1/b*a)^(1/3)*tan(d*x+c)+(1/b*a)^(2/3))+8/9/d*b/(a^4+2*a^2*b^2+b^4)*a/(1/b*a)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)-1))+2/9/d*b^3/(a^4+2*a^2*b^2+b^4)/a/(1/b*a)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)-1))+4/9/d/(a^4+2*a^2*b^2+b^4)*a^2/(1/b*a)^(1/3)*ln(tan(d*x+c)+(1/b*a)^(1/3))-2/9/d*b^2/(a^4+2*a^2*b^2+b^4)/(1/b*a)^(1/3)*ln(tan(d*x+c)+(1/b*a)^(1/3))-2/9/d/(a^4+2*a^2*b^2+b^4)*a^2/(1/b*a)^(1/3)*ln(tan(d*x+c)^2-(1/b*a)^(1/3)*tan(d*x+c)+(1/b*a)^(2/3))+1/9/d*b^2/(a^4+2*a^2*b^2+b^4)/(1/b*a)^(1/3)*ln(tan(d*x+c)^2-(1/b*a)^(1/3)*tan(d*x+c)+(1/b*a)^(2/3))-4/9/d/(a^4+2*a^2*b^2+b^4)*a^2*3^(1/2)/(1/b*a)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)-1))+2/9/d*b^2/(a^4+2*a^2*b^2+b^4)*3^(1/2)/(1/b*a)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*tan(d*x+c)-1))-2/3/d*b/(a^4+2*a^2*b^2+b^4)*a*ln(a+b*tan(d*x+c)^3)+1/d/(a^4+2*a^2*b^2+b^4)*a*b*ln(1+tan(d*x+c)^2)+1/d/(a^4+2*a^2*b^2+b^4)*arctan(tan(d*x+c))*a^2-1/d/(a^4+2*a^2*b^2+b^4)*arctan(tan(d*x+c))*b^2","B"
380,1,34,29,0.102000," ","int(1/(1+tan(x)^3),x)","-\frac{\ln \left(1-\tan \left(x \right)+\tan^{2}\left(x \right)\right)}{3}+\frac{\ln \left(1+\tan \left(x \right)\right)}{6}+\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{4}+\frac{x}{2}"," ",0,"-1/3*ln(1-tan(x)+tan(x)^2)+1/6*ln(1+tan(x))+1/4*ln(1+tan(x)^2)+1/2*x","A"
381,1,412,202,0.033000," ","int((a+b*tan(d*x+c)^4)^4,x)","-\frac{b^{4} \left(\tan^{9}\left(d x +c \right)\right)}{9 d}+\frac{4 \left(\tan^{11}\left(d x +c \right)\right) a \,b^{3}}{11 d}-\frac{6 \left(\tan^{5}\left(d x +c \right)\right) a^{2} b^{2}}{5 d}+\frac{2 \left(\tan^{3}\left(d x +c \right)\right) a^{2} b^{2}}{d}+\frac{4 \left(\tan^{7}\left(d x +c \right)\right) a \,b^{3}}{7 d}+\frac{6 \left(\tan^{7}\left(d x +c \right)\right) a^{2} b^{2}}{7 d}-\frac{4 \left(\tan^{9}\left(d x +c \right)\right) a \,b^{3}}{9 d}+\frac{b^{4} \left(\tan^{15}\left(d x +c \right)\right)}{15 d}-\frac{\left(\tan^{5}\left(d x +c \right)\right) b^{4}}{5 d}+\frac{4 \left(\tan^{3}\left(d x +c \right)\right) a \,b^{3}}{3 d}+\frac{4 \left(\tan^{3}\left(d x +c \right)\right) a^{3} b}{3 d}-\frac{4 \left(\tan^{5}\left(d x +c \right)\right) a \,b^{3}}{5 d}+\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b}{d}+\frac{4 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{3}}{d}+\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d}-\frac{4 a^{3} b \tan \left(d x +c \right)}{d}+\frac{b^{4} \left(\tan^{11}\left(d x +c \right)\right)}{11 d}+\frac{b^{4} \left(\tan^{7}\left(d x +c \right)\right)}{7 d}-\frac{b^{4} \tan \left(d x +c \right)}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d}-\frac{b^{4} \left(\tan^{13}\left(d x +c \right)\right)}{13 d}+\frac{b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{6 a^{2} b^{2} \tan \left(d x +c \right)}{d}-\frac{4 a \,b^{3} \tan \left(d x +c \right)}{d}"," ",0,"4/3/d*tan(d*x+c)^3*a*b^3+4/3/d*tan(d*x+c)^3*a^3*b-4/5/d*tan(d*x+c)^5*a*b^3+4/7/d*tan(d*x+c)^7*a*b^3+6/7/d*tan(d*x+c)^7*a^2*b^2-4/9/d*tan(d*x+c)^9*a*b^3+4/11/d*tan(d*x+c)^11*a*b^3+4/d*arctan(tan(d*x+c))*a^3*b+4/d*arctan(tan(d*x+c))*a*b^3-6/5/d*tan(d*x+c)^5*a^2*b^2+2/d*tan(d*x+c)^3*a^2*b^2+6/d*arctan(tan(d*x+c))*a^2*b^2-4/d*a^3*b*tan(d*x+c)-1/5/d*tan(d*x+c)^5*b^4-1/d*b^4*tan(d*x+c)+1/d*arctan(tan(d*x+c))*a^4+1/d*arctan(tan(d*x+c))*b^4+1/3*b^4*tan(d*x+c)^3/d-6*a^2*b^2*tan(d*x+c)/d-4*a*b^3*tan(d*x+c)/d-1/9*b^4*tan(d*x+c)^9/d+1/11*b^4*tan(d*x+c)^11/d-1/13*b^4*tan(d*x+c)^13/d+1/15*b^4*tan(d*x+c)^15/d+1/7*b^4*tan(d*x+c)^7/d","B"
382,1,252,134,0.027000," ","int((a+b*tan(d*x+c)^4)^3,x)","\frac{b^{3} \left(\tan^{11}\left(d x +c \right)\right)}{11 d}-\frac{b^{3} \left(\tan^{9}\left(d x +c \right)\right)}{9 d}+\frac{3 \left(\tan^{7}\left(d x +c \right)\right) a \,b^{2}}{7 d}+\frac{\left(\tan^{7}\left(d x +c \right)\right) b^{3}}{7 d}-\frac{3 a \,b^{2} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{b^{3} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{\left(\tan^{3}\left(d x +c \right)\right) a^{2} b}{d}+\frac{a \,b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{3 a^{2} b \tan \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}-\frac{b^{3} \tan \left(d x +c \right)}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b}{d}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{3}}{d}"," ",0,"1/11*b^3*tan(d*x+c)^11/d-1/9*b^3*tan(d*x+c)^9/d+3/7/d*tan(d*x+c)^7*a*b^2+1/7/d*tan(d*x+c)^7*b^3-3/5*a*b^2*tan(d*x+c)^5/d-1/5*b^3*tan(d*x+c)^5/d+1/d*tan(d*x+c)^3*a^2*b+a*b^2*tan(d*x+c)^3/d+1/3/d*b^3*tan(d*x+c)^3-3/d*a^2*b*tan(d*x+c)-3*a*b^2*tan(d*x+c)/d-1/d*b^3*tan(d*x+c)+1/d*arctan(tan(d*x+c))*a^3+3/d*arctan(tan(d*x+c))*a^2*b+3/d*arctan(tan(d*x+c))*a*b^2+1/d*arctan(tan(d*x+c))*b^3","A"
383,1,134,76,0.027000," ","int((a+b*tan(d*x+c)^4)^2,x)","\frac{b^{2} \left(\tan^{7}\left(d x +c \right)\right)}{7 d}-\frac{b^{2} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{2 a b \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a b \tan \left(d x +c \right)}{d}-\frac{b^{2} \tan \left(d x +c \right)}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d}+\frac{2 \arctan \left(\tan \left(d x +c \right)\right) a b}{d}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d}"," ",0,"1/7*b^2*tan(d*x+c)^7/d-1/5*b^2*tan(d*x+c)^5/d+2/3*a*b*tan(d*x+c)^3/d+1/3*b^2*tan(d*x+c)^3/d-2*a*b*tan(d*x+c)/d-b^2*tan(d*x+c)/d+1/d*arctan(tan(d*x+c))*a^2+2/d*arctan(tan(d*x+c))*a*b+1/d*arctan(tan(d*x+c))*b^2","A"
384,1,43,33,0.024000," ","int(a+b*tan(d*x+c)^4,x)","a x +\frac{b \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{b \tan \left(d x +c \right)}{d}+\frac{b \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"a*x+1/3*b*tan(d*x+c)^3/d-b*tan(d*x+c)/d+1/d*b*arctan(tan(d*x+c))","A"
385,1,374,222,0.207000," ","int(1/(a+b*tan(d*x+c)^4),x)","\frac{b \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{\tan^{2}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}{\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}\right)}{8 d \left(a +b \right) a}+\frac{b \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 d \left(a +b \right) a}-\frac{b \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 d \left(a +b \right) a}-\frac{\sqrt{2}\, \ln \left(\frac{\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}{\tan^{2}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}\right)}{8 d \left(a +b \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 d \left(a +b \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 d \left(a +b \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \left(a +b \right)}"," ",0,"1/8/d*b/(a+b)*(1/b*a)^(1/4)/a*2^(1/2)*ln((tan(d*x+c)^2+(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2))/(tan(d*x+c)^2-(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2)))+1/4/d*b/(a+b)*(1/b*a)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)-1/4/d*b/(a+b)*(1/b*a)^(1/4)/a*2^(1/2)*arctan(-2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)-1/8/d/(a+b)/(1/b*a)^(1/4)*2^(1/2)*ln((tan(d*x+c)^2-(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2))/(tan(d*x+c)^2+(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2)))-1/4/d/(a+b)/(1/b*a)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)+1/4/d/(a+b)/(1/b*a)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)+1/d/(a+b)*arctan(tan(d*x+c))","A"
386,1,886,486,0.207000," ","int(1/(a+b*tan(d*x+c)^4)^2,x)","-\frac{b \left(\tan^{3}\left(d x +c \right)\right)}{4 d \left(a +b \right)^{2} \left(a +b \left(\tan^{4}\left(d x +c \right)\right)\right)}-\frac{b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{4 d \left(a +b \right)^{2} \left(a +b \left(\tan^{4}\left(d x +c \right)\right)\right) a}+\frac{b \tan \left(d x +c \right)}{4 d \left(a +b \right)^{2} \left(a +b \left(\tan^{4}\left(d x +c \right)\right)\right)}+\frac{b^{2} \tan \left(d x +c \right)}{4 d \left(a +b \right)^{2} \left(a +b \left(\tan^{4}\left(d x +c \right)\right)\right) a}+\frac{7 b \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{\tan^{2}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}{\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}\right)}{32 d \left(a +b \right)^{2} a}+\frac{3 b^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{\tan^{2}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}{\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}\right)}{32 d \left(a +b \right)^{2} a^{2}}-\frac{7 b \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 d \left(a +b \right)^{2} a}-\frac{3 b^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 d \left(a +b \right)^{2} a^{2}}+\frac{7 b \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 d \left(a +b \right)^{2} a}+\frac{3 b^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 d \left(a +b \right)^{2} a^{2}}-\frac{5 \sqrt{2}\, \ln \left(\frac{\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}{\tan^{2}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}\right)}{32 d \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \ln \left(\frac{\tan^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}{\tan^{2}\left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}} \tan \left(d x +c \right) \sqrt{2}+\sqrt{\frac{a}{b}}}\right)}{32 d \left(a +b \right)^{2} a \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{5 \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 d \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 d \left(a +b \right)^{2} a \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 d \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 d \left(a +b \right)^{2} a \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \left(a +b \right)^{2}}"," ",0,"-1/4/d*b/(a+b)^2/(a+b*tan(d*x+c)^4)*tan(d*x+c)^3-1/4/d*b^2/(a+b)^2/(a+b*tan(d*x+c)^4)/a*tan(d*x+c)^3+1/4/d*b/(a+b)^2/(a+b*tan(d*x+c)^4)*tan(d*x+c)+1/4/d*b^2/(a+b)^2/(a+b*tan(d*x+c)^4)/a*tan(d*x+c)+7/32/d*b/(a+b)^2/a*(1/b*a)^(1/4)*2^(1/2)*ln((tan(d*x+c)^2+(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2))/(tan(d*x+c)^2-(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2)))+3/32/d*b^2/(a+b)^2/a^2*(1/b*a)^(1/4)*2^(1/2)*ln((tan(d*x+c)^2+(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2))/(tan(d*x+c)^2-(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2)))-7/16/d*b/(a+b)^2/a*(1/b*a)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)-3/16/d*b^2/(a+b)^2/a^2*(1/b*a)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)+7/16/d*b/(a+b)^2/a*(1/b*a)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)+3/16/d*b^2/(a+b)^2/a^2*(1/b*a)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)-5/32/d/(a+b)^2/(1/b*a)^(1/4)*2^(1/2)*ln((tan(d*x+c)^2-(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2))/(tan(d*x+c)^2+(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2)))-1/32/d*b/(a+b)^2/a/(1/b*a)^(1/4)*2^(1/2)*ln((tan(d*x+c)^2-(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2))/(tan(d*x+c)^2+(1/b*a)^(1/4)*tan(d*x+c)*2^(1/2)+(1/b*a)^(1/2)))+5/16/d/(a+b)^2/(1/b*a)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)+1/16/d*b/(a+b)^2/a/(1/b*a)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)-5/16/d/(a+b)^2/(1/b*a)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)-1/16/d*b/(a+b)^2/a/(1/b*a)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/b*a)^(1/4)*tan(d*x+c)+1)+1/d/(a+b)^2*arctan(tan(d*x+c))","A"
387,1,531,694,0.574000," ","int((a+b*tan(d*x+c)^4)^(1/2),x)","\frac{-\frac{b \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \EllipticF \left(\tan \left(d x +c \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(d x +c \right)\right)}}+\frac{i \sqrt{b}\, \sqrt{a}\, \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \EllipticF \left(\tan \left(d x +c \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(d x +c \right)\right)}}-\frac{i \sqrt{b}\, \sqrt{a}\, \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \EllipticE \left(\tan \left(d x +c \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(d x +c \right)\right)}}+\frac{a \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tan \left(d x +c \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, \frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(d x +c \right)\right)}}+\frac{b \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tan \left(d x +c \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, \frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(d x +c \right)\right)}}}{d}"," ",0,"1/d*(-b/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)/(a+b*tan(d*x+c)^4)^(1/2)*EllipticF(tan(d*x+c)*(I/a^(1/2)*b^(1/2))^(1/2),I)+I*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)/(a+b*tan(d*x+c)^4)^(1/2)*EllipticF(tan(d*x+c)*(I/a^(1/2)*b^(1/2))^(1/2),I)-I*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)/(a+b*tan(d*x+c)^4)^(1/2)*EllipticE(tan(d*x+c)*(I/a^(1/2)*b^(1/2))^(1/2),I)+a/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)/(a+b*tan(d*x+c)^4)^(1/2)*EllipticPi(tan(d*x+c)*(I/a^(1/2)*b^(1/2))^(1/2),I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))+b/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)/(a+b*tan(d*x+c)^4)^(1/2)*EllipticPi(tan(d*x+c)*(I/a^(1/2)*b^(1/2))^(1/2),I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)))","C"
388,1,123,360,0.311000," ","int(1/(a+b*tan(d*x+c)^4)^(1/2),x)","\frac{\sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(d x +c \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tan \left(d x +c \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, \frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{d \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(d x +c \right)\right)}}"," ",0,"1/d/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(d*x+c)^2)^(1/2)/(a+b*tan(d*x+c)^4)^(1/2)*EllipticPi(tan(d*x+c)*(I/a^(1/2)*b^(1/2))^(1/2),I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))","C"
389,1,181,83,0.307000," ","int((a+b*tan(x)^4)^(1/2)*tan(x)^3,x)","\frac{\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\, \left(\tan^{2}\left(x \right)\right)}{4}+\frac{a \ln \left(\sqrt{b}\, \left(\tan^{2}\left(x \right)\right)+\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\right)}{4 \sqrt{b}}-\frac{\sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{2}+\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\tan^{2}\left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right)}{2}"," ",0,"1/4*(a+b*tan(x)^4)^(1/2)*tan(x)^2+1/4*a/b^(1/2)*ln(b^(1/2)*tan(x)^2+(a+b*tan(x)^4)^(1/2))-1/2*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2)+1/2*b^(1/2)*ln(((1+tan(x)^2)*b-b)/b^(1/2)+((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))","B"
390,1,139,70,0.245000," ","int((a+b*tan(x)^4)^(1/2)*tan(x),x)","\frac{\sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\tan^{2}\left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}\right)}{2}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right)}{2}"," ",0,"1/2*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((1+tan(x)^2)*b-b)/b^(1/2)+((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))","A"
391,0,0,78,0.520000," ","int(cot(x)*(a+b*tan(x)^4)^(1/2),x)","\int \cot \left(x \right) \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\, dx"," ",0,"int(cot(x)*(a+b*tan(x)^4)^(1/2),x)","F"
392,1,537,664,0.231000," ","int((a+b*tan(x)^4)^(1/2)*tan(x)^2,x)","\frac{\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\, \tan \left(x \right)}{3}+\frac{2 a \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticF \left(\tan \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}+\frac{b \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticF \left(\tan \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}-\frac{i \sqrt{b}\, \sqrt{a}\, \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticF \left(\tan \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}+\frac{i \sqrt{b}\, \sqrt{a}\, \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticE \left(\tan \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}-\frac{a \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tan \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, \frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}-\frac{b \sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tan \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, \frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}"," ",0,"1/3*(a+b*tan(x)^4)^(1/2)*tan(x)+2/3*a/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)/(a+b*tan(x)^4)^(1/2)*EllipticF(tan(x)*(I/a^(1/2)*b^(1/2))^(1/2),I)+b/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)/(a+b*tan(x)^4)^(1/2)*EllipticF(tan(x)*(I/a^(1/2)*b^(1/2))^(1/2),I)-I*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)/(a+b*tan(x)^4)^(1/2)*EllipticF(tan(x)*(I/a^(1/2)*b^(1/2))^(1/2),I)+I*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)/(a+b*tan(x)^4)^(1/2)*EllipticE(tan(x)*(I/a^(1/2)*b^(1/2))^(1/2),I)-a/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)/(a+b*tan(x)^4)^(1/2)*EllipticPi(tan(x)*(I/a^(1/2)*b^(1/2))^(1/2),I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))-b/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)/(a+b*tan(x)^4)^(1/2)*EllipticPi(tan(x)*(I/a^(1/2)*b^(1/2))^(1/2),I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))","C"
393,1,374,125,0.209000," ","int(tan(x)^3*(a+b*tan(x)^4)^(3/2),x)","\frac{b \left(\tan^{6}\left(x \right)\right) \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{8}+\frac{5 a \left(\tan^{2}\left(x \right)\right) \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{16}+\frac{3 a^{2} \ln \left(\sqrt{b}\, \left(\tan^{2}\left(x \right)\right)+\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\right)}{16 \sqrt{b}}-\frac{b \left(\tan^{4}\left(x \right)\right) \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{6}-\frac{2 a \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{3}+\frac{b \left(\tan^{2}\left(x \right)\right) \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{4}+\frac{3 a \sqrt{b}\, \ln \left(\sqrt{b}\, \left(\tan^{2}\left(x \right)\right)+\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\right)}{4}-\frac{b \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{2}+\frac{b^{\frac{3}{2}} \ln \left(\sqrt{b}\, \left(\tan^{2}\left(x \right)\right)+\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\right)}{2}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right) a^{2}}{2 \sqrt{a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right) a b}{\sqrt{a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right) b^{2}}{2 \sqrt{a +b}}"," ",0,"1/8*b*tan(x)^6*(a+b*tan(x)^4)^(1/2)+5/16*a*tan(x)^2*(a+b*tan(x)^4)^(1/2)+3/16*a^2*ln(b^(1/2)*tan(x)^2+(a+b*tan(x)^4)^(1/2))/b^(1/2)-1/6*b*tan(x)^4*(a+b*tan(x)^4)^(1/2)-2/3*a*(a+b*tan(x)^4)^(1/2)+1/4*b*tan(x)^2*(a+b*tan(x)^4)^(1/2)+3/4*a*b^(1/2)*ln(b^(1/2)*tan(x)^2+(a+b*tan(x)^4)^(1/2))-1/2*b*(a+b*tan(x)^4)^(1/2)+1/2*b^(3/2)*ln(b^(1/2)*tan(x)^2+(a+b*tan(x)^4)^(1/2))+1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))*a^2+1/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))*a*b+1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))*b^2","B"
394,1,313,103,0.220000," ","int(tan(x)*(a+b*tan(x)^4)^(3/2),x)","\frac{b \left(\tan^{4}\left(x \right)\right) \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{6}+\frac{2 a \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{3}-\frac{b \left(\tan^{2}\left(x \right)\right) \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{4}-\frac{3 a \sqrt{b}\, \ln \left(\sqrt{b}\, \left(\tan^{2}\left(x \right)\right)+\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\right)}{4}+\frac{b \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}{2}-\frac{b^{\frac{3}{2}} \ln \left(\sqrt{b}\, \left(\tan^{2}\left(x \right)\right)+\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\right)}{2}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right) a^{2}}{2 \sqrt{a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right) a b}{\sqrt{a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right) b^{2}}{2 \sqrt{a +b}}"," ",0,"1/6*b*tan(x)^4*(a+b*tan(x)^4)^(1/2)+2/3*a*(a+b*tan(x)^4)^(1/2)-1/4*b*tan(x)^2*(a+b*tan(x)^4)^(1/2)-3/4*a*b^(1/2)*ln(b^(1/2)*tan(x)^2+(a+b*tan(x)^4)^(1/2))+1/2*b*(a+b*tan(x)^4)^(1/2)-1/2*b^(3/2)*ln(b^(1/2)*tan(x)^2+(a+b*tan(x)^4)^(1/2))-1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))*a^2-1/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))*a*b-1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))*b^2","B"
395,0,0,124,0.437000," ","int(cot(x)*(a+b*tan(x)^4)^(3/2),x)","\int \cot \left(x \right) \left(a +b \left(\tan^{4}\left(x \right)\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(cot(x)*(a+b*tan(x)^4)^(3/2),x)","F"
396,1,91,58,0.275000," ","int(tan(x)^3/(a+b*tan(x)^4)^(1/2),x)","\frac{\ln \left(\sqrt{b}\, \left(\tan^{2}\left(x \right)\right)+\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\right)}{2 \sqrt{b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"1/2*ln(b^(1/2)*tan(x)^2+(a+b*tan(x)^4)^(1/2))/b^(1/2)+1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))","A"
397,1,65,33,0.231000," ","int(tan(x)/(a+b*tan(x)^4)^(1/2),x)","-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"-1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))","A"
398,0,0,54,0.515000," ","int(cot(x)/(a+b*tan(x)^4)^(1/2),x)","\int \frac{\cot \left(x \right)}{\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}\, dx"," ",0,"int(cot(x)/(a+b*tan(x)^4)^(1/2),x)","F"
399,1,179,287,0.352000," ","int(tan(x)^2/(a+b*tan(x)^4)^(1/2),x)","\frac{\sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticF \left(\tan \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}-\frac{\sqrt{1-\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tan^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tan \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, \frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}"," ",0,"1/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)/(a+b*tan(x)^4)^(1/2)*EllipticF(tan(x)*(I/a^(1/2)*b^(1/2))^(1/2),I)-1/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tan(x)^2)^(1/2)/(a+b*tan(x)^4)^(1/2)*EllipticPi(tan(x)*(I/a^(1/2)*b^(1/2))^(1/2),I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))","C"
400,1,267,57,0.385000," ","int(tan(x)^3/(a+b*tan(x)^4)^(3/2),x)","\frac{\tan^{2}\left(x \right)}{2 a \sqrt{a +b \left(\tan^{4}\left(x \right)\right)}}+\frac{\sqrt{\left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}}{4 \left(\sqrt{-a b}-b \right) a \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}-\frac{\sqrt{\left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}}{4 \left(\sqrt{-a b}+b \right) a \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}-\frac{b \ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right)}{2 \left(\sqrt{-a b}+b \right) \left(\sqrt{-a b}-b \right) \sqrt{a +b}}"," ",0,"1/2*tan(x)^2/a/(a+b*tan(x)^4)^(1/2)+1/4/((-a*b)^(1/2)-b)/a/(tan(x)^2+(-a*b)^(1/2)/b)*((tan(x)^2+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(tan(x)^2+(-a*b)^(1/2)/b))^(1/2)-1/4/((-a*b)^(1/2)+b)/a/(tan(x)^2-(-a*b)^(1/2)/b)*((tan(x)^2-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(tan(x)^2-(-a*b)^(1/2)/b))^(1/2)-1/2*b/((-a*b)^(1/2)+b)/((-a*b)^(1/2)-b)/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))","B"
401,1,248,62,0.230000," ","int(tan(x)/(a+b*tan(x)^4)^(3/2),x)","-\frac{\sqrt{\left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}}{4 \left(\sqrt{-a b}-b \right) a \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}+\frac{\sqrt{\left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}}{4 \left(\sqrt{-a b}+b \right) a \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}+\frac{b \ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right)}{2 \left(\sqrt{-a b}+b \right) \left(\sqrt{-a b}-b \right) \sqrt{a +b}}"," ",0,"-1/4/((-a*b)^(1/2)-b)/a/(tan(x)^2+(-a*b)^(1/2)/b)*((tan(x)^2+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(tan(x)^2+(-a*b)^(1/2)/b))^(1/2)+1/4/((-a*b)^(1/2)+b)/a/(tan(x)^2-(-a*b)^(1/2)/b)*((tan(x)^2-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(tan(x)^2-(-a*b)^(1/2)/b))^(1/2)+1/2*b/((-a*b)^(1/2)+b)/((-a*b)^(1/2)-b)/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))","B"
402,0,0,100,0.443000," ","int(cot(x)/(a+b*tan(x)^4)^(3/2),x)","\int \frac{\cot \left(x \right)}{\left(a +b \left(\tan^{4}\left(x \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(cot(x)/(a+b*tan(x)^4)^(3/2),x)","F"
403,1,654,92,0.286000," ","int(tan(x)^3/(a+b*tan(x)^4)^(5/2),x)","\frac{\sqrt{a +b \left(\tan^{4}\left(x \right)\right)}\, \left(\tan^{2}\left(x \right)\right) \left(2 b \left(\tan^{4}\left(x \right)\right)+3 a \right)}{6 a^{2} \left(\left(\tan^{8}\left(x \right)\right) b^{2}+2 \left(\tan^{4}\left(x \right)\right) a b +a^{2}\right)}-\frac{\left(2 \sqrt{-a b}+b \right) \sqrt{\left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}}{8 \left(\sqrt{-a b}+b \right)^{2} a^{2} \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}+\frac{\left(2 \sqrt{-a b}-b \right) \sqrt{\left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}}{8 \left(\sqrt{-a b}-b \right)^{2} a^{2} \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}-\frac{\sqrt{\left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}}{24 \left(\sqrt{-a b}-b \right) a \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2}}+\frac{\sqrt{\left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}}{24 \left(\sqrt{-a b}-b \right) a^{2} \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}+\frac{b^{2} \ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right)}{2 \left(\sqrt{-a b}+b \right)^{2} \left(\sqrt{-a b}-b \right)^{2} \sqrt{a +b}}-\frac{\sqrt{\left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}}{24 \left(\sqrt{-a b}+b \right) a \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{\sqrt{\left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}}{24 \left(\sqrt{-a b}+b \right) a^{2} \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}"," ",0,"1/6*(a+b*tan(x)^4)^(1/2)*tan(x)^2*(2*b*tan(x)^4+3*a)/a^2/(tan(x)^8*b^2+2*tan(x)^4*a*b+a^2)-1/8*(2*(-a*b)^(1/2)+b)/((-a*b)^(1/2)+b)^2/a^2/(tan(x)^2-(-a*b)^(1/2)/b)*((tan(x)^2-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(tan(x)^2-(-a*b)^(1/2)/b))^(1/2)+1/8*(2*(-a*b)^(1/2)-b)/((-a*b)^(1/2)-b)^2/a^2/(tan(x)^2+(-a*b)^(1/2)/b)*((tan(x)^2+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(tan(x)^2+(-a*b)^(1/2)/b))^(1/2)-1/24/((-a*b)^(1/2)-b)/a/(-a*b)^(1/2)/(tan(x)^2+(-a*b)^(1/2)/b)^2*((tan(x)^2+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(tan(x)^2+(-a*b)^(1/2)/b))^(1/2)+1/24/((-a*b)^(1/2)-b)/a^2/(tan(x)^2+(-a*b)^(1/2)/b)*((tan(x)^2+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(tan(x)^2+(-a*b)^(1/2)/b))^(1/2)+1/2*b^2/((-a*b)^(1/2)+b)^2/((-a*b)^(1/2)-b)^2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))-1/24/((-a*b)^(1/2)+b)/a/(-a*b)^(1/2)/(tan(x)^2-(-a*b)^(1/2)/b)^2*((tan(x)^2-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(tan(x)^2-(-a*b)^(1/2)/b))^(1/2)-1/24/((-a*b)^(1/2)+b)/a^2/(tan(x)^2-(-a*b)^(1/2)/b)*((tan(x)^2-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(tan(x)^2-(-a*b)^(1/2)/b))^(1/2)","B"
404,1,602,101,0.247000," ","int(tan(x)/(a+b*tan(x)^4)^(5/2),x)","\frac{\left(2 \sqrt{-a b}+b \right) \sqrt{\left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}}{8 \left(\sqrt{-a b}+b \right)^{2} a^{2} \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}-\frac{\left(2 \sqrt{-a b}-b \right) \sqrt{\left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}}{8 \left(\sqrt{-a b}-b \right)^{2} a^{2} \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}+\frac{\sqrt{\left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}}{24 \left(\sqrt{-a b}-b \right) a \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{\sqrt{\left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}}{24 \left(\sqrt{-a b}-b \right) a^{2} \left(\tan^{2}\left(x \right)+\frac{\sqrt{-a b}}{b}\right)}-\frac{b^{2} \ln \left(\frac{2 a +2 b -2 \left(1+\tan^{2}\left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tan^{2}\left(x \right)\right)^{2} b -2 \left(1+\tan^{2}\left(x \right)\right) b +a +b}}{1+\tan^{2}\left(x \right)}\right)}{2 \left(\sqrt{-a b}+b \right)^{2} \left(\sqrt{-a b}-b \right)^{2} \sqrt{a +b}}+\frac{\sqrt{\left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}}{24 \left(\sqrt{-a b}+b \right) a \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2}}+\frac{\sqrt{\left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}}{24 \left(\sqrt{-a b}+b \right) a^{2} \left(\tan^{2}\left(x \right)-\frac{\sqrt{-a b}}{b}\right)}"," ",0,"1/8*(2*(-a*b)^(1/2)+b)/((-a*b)^(1/2)+b)^2/a^2/(tan(x)^2-(-a*b)^(1/2)/b)*((tan(x)^2-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(tan(x)^2-(-a*b)^(1/2)/b))^(1/2)-1/8*(2*(-a*b)^(1/2)-b)/((-a*b)^(1/2)-b)^2/a^2/(tan(x)^2+(-a*b)^(1/2)/b)*((tan(x)^2+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(tan(x)^2+(-a*b)^(1/2)/b))^(1/2)+1/24/((-a*b)^(1/2)-b)/a/(-a*b)^(1/2)/(tan(x)^2+(-a*b)^(1/2)/b)^2*((tan(x)^2+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(tan(x)^2+(-a*b)^(1/2)/b))^(1/2)-1/24/((-a*b)^(1/2)-b)/a^2/(tan(x)^2+(-a*b)^(1/2)/b)*((tan(x)^2+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(tan(x)^2+(-a*b)^(1/2)/b))^(1/2)-1/2*b^2/((-a*b)^(1/2)+b)^2/((-a*b)^(1/2)-b)^2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tan(x)^2)*b+2*(a+b)^(1/2)*((1+tan(x)^2)^2*b-2*(1+tan(x)^2)*b+a+b)^(1/2))/(1+tan(x)^2))+1/24/((-a*b)^(1/2)+b)/a/(-a*b)^(1/2)/(tan(x)^2-(-a*b)^(1/2)/b)^2*((tan(x)^2-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(tan(x)^2-(-a*b)^(1/2)/b))^(1/2)+1/24/((-a*b)^(1/2)+b)/a^2/(tan(x)^2-(-a*b)^(1/2)/b)*((tan(x)^2-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(tan(x)^2-(-a*b)^(1/2)/b))^(1/2)","B"
405,0,0,155,0.461000," ","int(cot(x)/(a+b*tan(x)^4)^(5/2),x)","\int \frac{\cot \left(x \right)}{\left(a +b \left(\tan^{4}\left(x \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(cot(x)/(a+b*tan(x)^4)^(5/2),x)","F"
406,0,0,196,1.928000," ","int((a+b*(c*tan(f*x+e))^(1/2))^2*(d*tan(f*x+e))^m,x)","\int \left(a +b \sqrt{c \tan \left(f x +e \right)}\right)^{2} \left(d \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*(c*tan(f*x+e))^(1/2))^2*(d*tan(f*x+e))^m,x)","F"
407,0,0,111,1.332000," ","int((a+b*(c*tan(f*x+e))^(1/2))*(d*tan(f*x+e))^m,x)","\int \left(a +b \sqrt{c \tan \left(f x +e \right)}\right) \left(d \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*(c*tan(f*x+e))^(1/2))*(d*tan(f*x+e))^m,x)","F"
408,0,0,420,1.324000," ","int((d*tan(f*x+e))^m/(a+b*(c*tan(f*x+e))^(1/2)),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{m}}{a +b \sqrt{c \tan \left(f x +e \right)}}\, dx"," ",0,"int((d*tan(f*x+e))^m/(a+b*(c*tan(f*x+e))^(1/2)),x)","F"
409,0,0,573,2.118000," ","int((d*tan(f*x+e))^m/(a+b*(c*tan(f*x+e))^(1/2))^2,x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{m}}{\left(a +b \sqrt{c \tan \left(f x +e \right)}\right)^{2}}\, dx"," ",0,"int((d*tan(f*x+e))^m/(a+b*(c*tan(f*x+e))^(1/2))^2,x)","F"
410,0,0,74,12.612000," ","int((d*tan(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \tan \left(f x +e \right)\right)^{m} \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*tan(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","F"
411,0,0,59,12.824000," ","int(tan(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\tan^{2}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(tan(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","F"
412,0,0,57,12.279000," ","int((b*(c*tan(f*x+e))^n)^p,x)","\int \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((b*(c*tan(f*x+e))^n)^p,x)","F"
413,0,0,59,12.760000," ","int(cot(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","F"
414,0,0,61,12.633000," ","int(cot(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\cot^{4}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x)","F"
415,0,0,61,11.127000," ","int(cot(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\cot^{6}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x)","F"
416,0,0,59,2.006000," ","int(tan(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\tan^{3}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(tan(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","F"
417,0,0,59,12.880000," ","int(tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","\int \tan \left(f x +e \right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","F"
418,0,0,48,13.428000," ","int(cot(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","\int \cot \left(f x +e \right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cot(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","F"
419,0,0,59,10.357000," ","int(cot(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\cot^{3}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","F"
420,0,0,29,1.763000," ","int((d*tan(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \tan \left(f x +e \right)\right)^{m} \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*tan(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
421,0,0,68,2.002000," ","int((d*cot(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","\int \left(d \cot \left(f x +e \right)\right)^{m} \left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*cot(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","F"
422,0,0,99,1.916000," ","int((d*cot(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","\int \left(d \cot \left(f x +e \right)\right)^{m} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*cot(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","F"
423,-1,0,76,180.000000," ","int((d*cot(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \cot \left(f x +e \right)\right)^{m} \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*cot(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","F"
424,0,0,56,1.998000," ","int((d*cot(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \cot \left(f x +e \right)\right)^{m} \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*cot(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
425,1,116,64,0.567000," ","int(sec(d*x+c)^3*(a+b*tan(d*x+c)^2),x)","\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{b \sin \left(d x +c \right)}{8 d}-\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/4/d*b*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*b*sin(d*x+c)^3/cos(d*x+c)^2+1/8*b*sin(d*x+c)/d-1/8/d*b*ln(sec(d*x+c)+tan(d*x+c))+1/2*a*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
426,1,75,38,0.294000," ","int(sec(d*x+c)*(a+b*tan(d*x+c)^2),x)","\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b \sin \left(d x +c \right)}{2 d}-\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*b*sin(d*x+c)^3/cos(d*x+c)^2+1/2*b*sin(d*x+c)/d-1/2/d*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
427,1,44,28,0.374000," ","int(cos(d*x+c)*(a+b*tan(d*x+c)^2),x)","\frac{a \sin \left(d x +c \right)}{d}-\frac{b \sin \left(d x +c \right)}{d}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"a*sin(d*x+c)/d-b*sin(d*x+c)/d+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
428,1,36,30,0.631000," ","int(cos(d*x+c)^3*(a+b*tan(d*x+c)^2),x)","\frac{\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/3*b*sin(d*x+c)^3+1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
429,1,72,50,0.801000," ","int(cos(d*x+c)^5*(a+b*tan(d*x+c)^2),x)","\frac{\frac{a \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)}{d}"," ",0,"1/d*(1/5*a*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+b*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c)))","A"
430,1,92,70,0.719000," ","int(cos(d*x+c)^7*(a+b*tan(d*x+c)^2),x)","\frac{\frac{a \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}+b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)}{d}"," ",0,"1/d*(1/7*a*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)+b*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
431,1,94,62,0.615000," ","int(sec(d*x+c)^6*(a+b*tan(d*x+c)^2),x)","\frac{b \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)-a \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(b*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)-a*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","A"
432,1,66,42,0.586000," ","int(sec(d*x+c)^4*(a+b*tan(d*x+c)^2),x)","\frac{b \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)-a \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(b*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)-a*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","A"
433,1,33,26,0.496000," ","int(sec(d*x+c)^2*(a+b*tan(d*x+c)^2),x)","\frac{\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+a \tan \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*b*sin(d*x+c)^3/cos(d*x+c)^3+a*tan(d*x+c))","A"
434,1,54,29,0.339000," ","int(cos(d*x+c)^2*(a+b*tan(d*x+c)^2),x)","\frac{b \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(b*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
435,1,81,55,0.586000," ","int(cos(d*x+c)^4*(a+b*tan(d*x+c)^2),x)","\frac{a \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+b \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)}{d}"," ",0,"1/d*(a*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+b*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c))","A"
436,1,102,79,0.737000," ","int(cos(d*x+c)^6*(a+b*tan(d*x+c)^2),x)","\frac{a \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+b \left(-\frac{\left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)}{d}"," ",0,"1/d*(a*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)+b*(-1/6*cos(d*x+c)^5*sin(d*x+c)+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c))","A"
437,1,248,120,0.612000," ","int(sec(d*x+c)^3*(a+b*tan(d*x+c)^2)^2,x)","\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}-\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{2}}-\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{48 d}-\frac{b^{2} \sin \left(d x +c \right)}{16 d}+\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}+\frac{a b \sin \left(d x +c \right)}{4 d}-\frac{a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/6/d*b^2*sin(d*x+c)^5/cos(d*x+c)^6+1/24/d*b^2*sin(d*x+c)^5/cos(d*x+c)^4-1/48/d*b^2*sin(d*x+c)^5/cos(d*x+c)^2-1/48/d*b^2*sin(d*x+c)^3-1/16/d*b^2*sin(d*x+c)+1/16/d*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*b*sin(d*x+c)^3/cos(d*x+c)^4+1/4/d*a*b*sin(d*x+c)^3/cos(d*x+c)^2+1/4*a*b*sin(d*x+c)/d-1/4/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/2*a^2*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))","B"
438,1,178,90,0.378000," ","int(sec(d*x+c)*(a+b*tan(d*x+c)^2)^2,x)","\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 b^{2} \sin \left(d x +c \right)}{8 d}+\frac{3 b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{a b \sin \left(d x +c \right)}{d}-\frac{a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*b^2*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*b^2*sin(d*x+c)^5/cos(d*x+c)^2-1/8/d*b^2*sin(d*x+c)^3-3/8/d*b^2*sin(d*x+c)+3/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*b*sin(d*x+c)^3/cos(d*x+c)^2+a*b*sin(d*x+c)/d-1/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))","A"
439,1,125,58,0.400000," ","int(cos(d*x+c)*(a+b*tan(d*x+c)^2)^2,x)","\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 b^{2} \sin \left(d x +c \right)}{2 d}-\frac{3 b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{2 a b \sin \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} \sin \left(d x +c \right)}{d}"," ",0,"1/2/d*b^2*sin(d*x+c)^5/cos(d*x+c)^2+1/2/d*b^2*sin(d*x+c)^3+3/2/d*b^2*sin(d*x+c)-3/2/d*b^2*ln(sec(d*x+c)+tan(d*x+c))-2*a*b*sin(d*x+c)/d+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+a^2*sin(d*x+c)/d","B"
440,1,104,54,0.615000," ","int(cos(d*x+c)^3*(a+b*tan(d*x+c)^2)^2,x)","-\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{2} \sin \left(d x +c \right)}{d}+\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 a b \left(\sin^{3}\left(d x +c \right)\right)}{3 d}+\frac{\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2}}{3 d}+\frac{2 a^{2} \sin \left(d x +c \right)}{3 d}"," ",0,"-1/3/d*b^2*sin(d*x+c)^3-1/d*b^2*sin(d*x+c)+1/d*b^2*ln(sec(d*x+c)+tan(d*x+c))+2/3*a*b*sin(d*x+c)^3/d+1/3/d*sin(d*x+c)*cos(d*x+c)^2*a^2+2/3*a^2*sin(d*x+c)/d","A"
441,1,89,53,0.849000," ","int(cos(d*x+c)^5*(a+b*tan(d*x+c)^2)^2,x)","\frac{\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{5}+2 a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)+\frac{a^{2} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(1/5*b^2*sin(d*x+c)^5+2*a*b*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))+1/5*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
442,1,153,80,0.984000," ","int(cos(d*x+c)^7*(a+b*tan(d*x+c)^2)^2,x)","\frac{b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)+2 a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+\frac{a^{2} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(b^2*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*sin(d*x+c)*cos(d*x+c)^4+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))+2*a*b*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+1/7*a^2*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
443,1,183,106,1.062000," ","int(cos(d*x+c)^9*(a+b*tan(d*x+c)^2)^2,x)","\frac{b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+2 a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)+\frac{a^{2} \left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{9}}{d}"," ",0,"1/d*(b^2*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+2*a*b*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+1/9*a^2*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))","A"
444,1,157,88,0.765000," ","int(sec(d*x+c)^6*(a+b*tan(d*x+c)^2)^2,x)","\frac{-a^{2} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+2 a b \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+b^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{4 \left(\sin^{5}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{5}}\right)}{d}"," ",0,"1/d*(-a^2*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+2*a*b*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+b^2*(1/9*sin(d*x+c)^5/cos(d*x+c)^9+4/63*sin(d*x+c)^5/cos(d*x+c)^7+8/315*sin(d*x+c)^5/cos(d*x+c)^5))","A"
445,1,111,68,0.647000," ","int(sec(d*x+c)^4*(a+b*tan(d*x+c)^2)^2,x)","\frac{-a^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+2 a b \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+b^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}\right)}{d}"," ",0,"1/d*(-a^2*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+2*a*b*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+b^2*(1/7*sin(d*x+c)^5/cos(d*x+c)^7+2/35*sin(d*x+c)^5/cos(d*x+c)^5))","A"
446,1,57,45,0.638000," ","int(sec(d*x+c)^2*(a+b*tan(d*x+c)^2)^2,x)","\frac{a^{2} \tan \left(d x +c \right)+\frac{2 a b \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{5 \cos \left(d x +c \right)^{5}}}{d}"," ",0,"1/d*(a^2*tan(d*x+c)+2/3*a*b*sin(d*x+c)^3/cos(d*x+c)^3+1/5*b^2*sin(d*x+c)^5/cos(d*x+c)^5)","A"
447,1,111,51,0.561000," ","int(cos(d*x+c)^2*(a+b*tan(d*x+c)^2)^2,x)","\frac{a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+2 a b \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+b^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)}{d}"," ",0,"1/d*(a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2*a*b*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+b^2*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c))","B"
448,1,122,81,0.789000," ","int(cos(d*x+c)^4*(a+b*tan(d*x+c)^2)^2,x)","\frac{b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+2 a b \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+a^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b^2*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)+2*a*b*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
449,1,166,114,0.832000," ","int(cos(d*x+c)^6*(a+b*tan(d*x+c)^2)^2,x)","\frac{b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+2 a b \left(-\frac{\left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+a^{2} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(b^2*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+2*a*b*(-1/6*cos(d*x+c)^5*sin(d*x+c)+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+a^2*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
450,1,224,78,0.708000," ","int(sec(d*x+c)^5/(a+b*tan(d*x+c)^2),x)","\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right) a^{2}}{d \,b^{2} \sqrt{a \left(a -b \right)}}-\frac{2 \arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right) a}{d b \sqrt{a \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{d \sqrt{a \left(a -b \right)}}-\frac{1}{4 d b \left(-1+\sin \left(d x +c \right)\right)}-\frac{3 \ln \left(-1+\sin \left(d x +c \right)\right)}{4 d b}+\frac{\ln \left(-1+\sin \left(d x +c \right)\right) a}{2 d \,b^{2}}-\frac{1}{4 d b \left(\sin \left(d x +c \right)+1\right)}+\frac{3 \ln \left(\sin \left(d x +c \right)+1\right)}{4 d b}-\frac{\ln \left(\sin \left(d x +c \right)+1\right) a}{2 d \,b^{2}}"," ",0,"1/d/b^2/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))*a^2-2/d/b/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))*a+1/d/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))-1/4/d/b/(-1+sin(d*x+c))-3/4/d/b*ln(-1+sin(d*x+c))+1/2/d/b^2*ln(-1+sin(d*x+c))*a-1/4/d/b/(sin(d*x+c)+1)+3/4/d/b*ln(sin(d*x+c)+1)-1/2/d/b^2*ln(sin(d*x+c)+1)*a","B"
451,1,111,51,0.607000," ","int(sec(d*x+c)^3/(a+b*tan(d*x+c)^2),x)","-\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right) a}{d b \sqrt{a \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{d \sqrt{a \left(a -b \right)}}-\frac{\ln \left(-1+\sin \left(d x +c \right)\right)}{2 d b}+\frac{\ln \left(\sin \left(d x +c \right)+1\right)}{2 d b}"," ",0,"-1/d/b/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))*a+1/d/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))-1/2/d/b*ln(-1+sin(d*x+c))+1/2/d/b*ln(sin(d*x+c)+1)","B"
452,1,36,32,0.550000," ","int(sec(d*x+c)/(a+b*tan(d*x+c)^2),x)","\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{d \sqrt{a \left(a -b \right)}}"," ",0,"1/d/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))","A"
453,1,61,52,0.552000," ","int(cos(d*x+c)/(a+b*tan(d*x+c)^2),x)","\frac{\frac{\sin \left(d x +c \right)}{a -b}-\frac{b \arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{\left(a -b \right) \sqrt{a \left(a -b \right)}}}{d}"," ",0,"1/d*(1/(a-b)*sin(d*x+c)-b/(a-b)/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2)))","A"
454,1,98,78,0.795000," ","int(cos(d*x+c)^3/(a+b*tan(d*x+c)^2),x)","\frac{-\frac{\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{3}-\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{3}-a \sin \left(d x +c \right)+2 b \sin \left(d x +c \right)}{\left(a -b \right)^{2}}+\frac{b^{2} \arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{\left(a -b \right)^{2} \sqrt{a \left(a -b \right)}}}{d}"," ",0,"1/d*(-1/(a-b)^2*(1/3*a*sin(d*x+c)^3-1/3*b*sin(d*x+c)^3-a*sin(d*x+c)+2*b*sin(d*x+c))+b^2/(a-b)^2/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2)))","A"
455,1,165,114,0.832000," ","int(cos(d*x+c)^5/(a+b*tan(d*x+c)^2),x)","\frac{\frac{\frac{\left(\sin^{5}\left(d x +c \right)\right) a^{2}}{5}-\frac{2 \left(\sin^{5}\left(d x +c \right)\right) a b}{5}+\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{5}-\frac{2 \left(\sin^{3}\left(d x +c \right)\right) a^{2}}{3}+\frac{5 \left(\sin^{3}\left(d x +c \right)\right) a b}{3}-\left(\sin^{3}\left(d x +c \right)\right) b^{2}+a^{2} \sin \left(d x +c \right)-3 \sin \left(d x +c \right) a b +3 b^{2} \sin \left(d x +c \right)}{\left(a -b \right)^{3}}-\frac{b^{3} \arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{\left(a -b \right)^{3} \sqrt{a \left(a -b \right)}}}{d}"," ",0,"1/d*(1/(a-b)^3*(1/5*sin(d*x+c)^5*a^2-2/5*sin(d*x+c)^5*a*b+1/5*b^2*sin(d*x+c)^5-2/3*sin(d*x+c)^3*a^2+5/3*sin(d*x+c)^3*a*b-sin(d*x+c)^3*b^2+a^2*sin(d*x+c)-3*sin(d*x+c)*a*b+3*b^2*sin(d*x+c))-b^3/(a-b)^3/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2)))","A"
456,1,206,96,0.685000," ","int(sec(d*x+c)^8/(a+b*tan(d*x+c)^2),x)","\frac{\tan^{5}\left(d x +c \right)}{5 b d}-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 b^{2} d}+\frac{\tan^{3}\left(d x +c \right)}{b d}+\frac{a^{2} \tan \left(d x +c \right)}{d \,b^{3}}-\frac{3 a \tan \left(d x +c \right)}{b^{2} d}+\frac{3 \tan \left(d x +c \right)}{b d}-\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right) a^{3}}{d \,b^{3} \sqrt{a b}}+\frac{3 \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right) a^{2}}{d \,b^{2} \sqrt{a b}}-\frac{3 \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right) a}{d b \sqrt{a b}}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \sqrt{a b}}"," ",0,"1/5*tan(d*x+c)^5/b/d-1/3*a*tan(d*x+c)^3/b^2/d+tan(d*x+c)^3/b/d+1/d/b^3*a^2*tan(d*x+c)-3*a*tan(d*x+c)/b^2/d+3*tan(d*x+c)/b/d-1/d/b^3/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))*a^3+3/d/b^2/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))*a^2-3/d/b/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))*a+1/d/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))","B"
457,1,127,67,0.703000," ","int(sec(d*x+c)^6/(a+b*tan(d*x+c)^2),x)","\frac{\tan^{3}\left(d x +c \right)}{3 b d}-\frac{a \tan \left(d x +c \right)}{b^{2} d}+\frac{2 \tan \left(d x +c \right)}{b d}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right) a^{2}}{d \,b^{2} \sqrt{a b}}-\frac{2 \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right) a}{d b \sqrt{a b}}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \sqrt{a b}}"," ",0,"1/3*tan(d*x+c)^3/b/d-a*tan(d*x+c)/b^2/d+2*tan(d*x+c)/b/d+1/d/b^2/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))*a^2-2/d/b/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))*a+1/d/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))","A"
458,1,66,44,0.587000," ","int(sec(d*x+c)^4/(a+b*tan(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)}{b d}-\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right) a}{d b \sqrt{a b}}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \sqrt{a b}}"," ",0,"tan(d*x+c)/b/d-1/d/b/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))*a+1/d/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))","A"
459,1,24,24,0.591000," ","int(sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x)","\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \sqrt{a b}}"," ",0,"1/d/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))","A"
460,1,137,71,0.648000," ","int(cos(d*x+c)^2/(a+b*tan(d*x+c)^2),x)","\frac{b^{2} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \left(a -b \right)^{2} \sqrt{a b}}+\frac{\tan \left(d x +c \right) a}{2 d \left(a -b \right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{\tan \left(d x +c \right) b}{2 d \left(a -b \right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a}{2 d \left(a -b \right)^{2}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) b}{2 d \left(a -b \right)^{2}}"," ",0,"1/d*b^2/(a-b)^2/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/2/d/(a-b)^2*tan(d*x+c)/(1+tan(d*x+c)^2)*a-1/2/d/(a-b)^2*tan(d*x+c)/(1+tan(d*x+c)^2)*b+1/2/d/(a-b)^2*arctan(tan(d*x+c))*a-3/2/d/(a-b)^2*arctan(tan(d*x+c))*b","A"
461,1,303,115,0.671000," ","int(cos(d*x+c)^4/(a+b*tan(d*x+c)^2),x)","-\frac{b^{3} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \left(a -b \right)^{3} \sqrt{a b}}+\frac{3 \left(\tan^{3}\left(d x +c \right)\right) a^{2}}{8 d \left(a -b \right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a b}{4 d \left(a -b \right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{7 \left(\tan^{3}\left(d x +c \right)\right) b^{2}}{8 d \left(a -b \right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{7 \tan \left(d x +c \right) a b}{4 d \left(a -b \right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{9 \tan \left(d x +c \right) b^{2}}{8 d \left(a -b \right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \tan \left(d x +c \right) a^{2}}{8 d \left(a -b \right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{15 \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{8 d \left(a -b \right)^{3}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{8 d \left(a -b \right)^{3}}-\frac{5 \arctan \left(\tan \left(d x +c \right)\right) a b}{4 d \left(a -b \right)^{3}}"," ",0,"-1/d*b^3/(a-b)^3/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+3/8/d/(a-b)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^2-5/4/d/(a-b)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a*b+7/8/d/(a-b)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^2-7/4/d/(a-b)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a*b+9/8/d/(a-b)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^2+5/8/d/(a-b)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^2+15/8/d/(a-b)^3*arctan(tan(d*x+c))*b^2+3/8/d/(a-b)^3*arctan(tan(d*x+c))*a^2-5/4/d/(a-b)^3*arctan(tan(d*x+c))*a*b","B"
462,1,389,151,0.737000," ","int(sec(d*x+c)^7/(a+b*tan(d*x+c)^2)^2,x)","-\frac{a \sin \left(d x +c \right)}{2 d \,b^{2} \left(a \left(\sin^{2}\left(d x +c \right)\right)-b \left(\sin^{2}\left(d x +c \right)\right)-a \right)}+\frac{\sin \left(d x +c \right)}{d b \left(a \left(\sin^{2}\left(d x +c \right)\right)-b \left(\sin^{2}\left(d x +c \right)\right)-a \right)}-\frac{\sin \left(d x +c \right)}{2 d a \left(a \left(\sin^{2}\left(d x +c \right)\right)-b \left(\sin^{2}\left(d x +c \right)\right)-a \right)}+\frac{2 \arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right) a^{2}}{d \,b^{3} \sqrt{a \left(a -b \right)}}-\frac{7 \arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right) a}{2 d \,b^{2} \sqrt{a \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{d b \sqrt{a \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{2 d a \sqrt{a \left(a -b \right)}}-\frac{1}{4 d \,b^{2} \left(-1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(-1+\sin \left(d x +c \right)\right) a}{d \,b^{3}}-\frac{5 \ln \left(-1+\sin \left(d x +c \right)\right)}{4 d \,b^{2}}-\frac{1}{4 d \,b^{2} \left(\sin \left(d x +c \right)+1\right)}-\frac{\ln \left(\sin \left(d x +c \right)+1\right) a}{d \,b^{3}}+\frac{5 \ln \left(\sin \left(d x +c \right)+1\right)}{4 d \,b^{2}}"," ",0,"-1/2/d/b^2*a*sin(d*x+c)/(a*sin(d*x+c)^2-b*sin(d*x+c)^2-a)+1/d/b*sin(d*x+c)/(a*sin(d*x+c)^2-b*sin(d*x+c)^2-a)-1/2/d/a*sin(d*x+c)/(a*sin(d*x+c)^2-b*sin(d*x+c)^2-a)+2/d/b^3/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))*a^2-7/2/d/b^2/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))*a+1/d/b/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))+1/2/d/a/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))-1/4/d/b^2/(-1+sin(d*x+c))+1/d/b^3*ln(-1+sin(d*x+c))*a-5/4/d/b^2*ln(-1+sin(d*x+c))-1/4/d/b^2/(sin(d*x+c)+1)-1/d/b^3*ln(sin(d*x+c)+1)*a+5/4/d/b^2*ln(sin(d*x+c)+1)","B"
463,1,236,97,0.767000," ","int(sec(d*x+c)^5/(a+b*tan(d*x+c)^2)^2,x)","\frac{\sin \left(d x +c \right)}{2 d b \left(a \left(\sin^{2}\left(d x +c \right)\right)-b \left(\sin^{2}\left(d x +c \right)\right)-a \right)}-\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right) a}{d \,b^{2} \sqrt{a \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{2 d b \sqrt{a \left(a -b \right)}}-\frac{\sin \left(d x +c \right)}{2 d a \left(a \left(\sin^{2}\left(d x +c \right)\right)-b \left(\sin^{2}\left(d x +c \right)\right)-a \right)}+\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{2 d a \sqrt{a \left(a -b \right)}}-\frac{\ln \left(-1+\sin \left(d x +c \right)\right)}{2 d \,b^{2}}+\frac{\ln \left(\sin \left(d x +c \right)+1\right)}{2 d \,b^{2}}"," ",0,"1/2/d/b*sin(d*x+c)/(a*sin(d*x+c)^2-b*sin(d*x+c)^2-a)-1/d/b^2/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))*a+1/2/d/b/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))-1/2/d/a*sin(d*x+c)/(a*sin(d*x+c)^2-b*sin(d*x+c)^2-a)+1/2/d/a/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))-1/2/d/b^2*ln(-1+sin(d*x+c))+1/2/d/b^2*ln(sin(d*x+c)+1)","B"
464,1,80,67,0.683000," ","int(sec(d*x+c)^3/(a+b*tan(d*x+c)^2)^2,x)","\frac{-\frac{\sin \left(d x +c \right)}{2 a \left(a \left(\sin^{2}\left(d x +c \right)\right)-b \left(\sin^{2}\left(d x +c \right)\right)-a \right)}+\frac{\arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{2 a \sqrt{a \left(a -b \right)}}}{d}"," ",0,"1/d*(-1/2*sin(d*x+c)/a/(a*sin(d*x+c)^2-b*sin(d*x+c)^2-a)+1/2/a/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2)))","A"
465,1,102,82,0.593000," ","int(sec(d*x+c)/(a+b*tan(d*x+c)^2)^2,x)","\frac{\frac{b \sin \left(d x +c \right)}{2 a \left(a -b \right) \left(a \left(\sin^{2}\left(d x +c \right)\right)-b \left(\sin^{2}\left(d x +c \right)\right)-a \right)}+\frac{\left(2 a -b \right) \arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{2 a \left(a -b \right) \sqrt{a \left(a -b \right)}}}{d}"," ",0,"1/d*(1/2*b/a/(a-b)*sin(d*x+c)/(a*sin(d*x+c)^2-b*sin(d*x+c)^2-a)+1/2*(2*a-b)/a/(a-b)/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2)))","A"
466,1,118,102,0.616000," ","int(cos(d*x+c)/(a+b*tan(d*x+c)^2)^2,x)","\frac{\frac{\sin \left(d x +c \right)}{a^{2}-2 a b +b^{2}}+\frac{b \left(-\frac{b \sin \left(d x +c \right)}{2 a \left(a \left(\sin^{2}\left(d x +c \right)\right)-b \left(\sin^{2}\left(d x +c \right)\right)-a \right)}-\frac{\left(4 a -b \right) \arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{2 a \sqrt{a \left(a -b \right)}}\right)}{\left(a -b \right)^{2}}}{d}"," ",0,"1/d*(1/(a^2-2*a*b+b^2)*sin(d*x+c)+b/(a-b)^2*(-1/2/a*b*sin(d*x+c)/(a*sin(d*x+c)^2-b*sin(d*x+c)^2-a)-1/2*(4*a-b)/a/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))))","A"
467,1,164,129,0.812000," ","int(cos(d*x+c)^3/(a+b*tan(d*x+c)^2)^2,x)","\frac{-\frac{\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{3}-\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{3}-a \sin \left(d x +c \right)+3 b \sin \left(d x +c \right)}{\left(a^{2}-2 a b +b^{2}\right) \left(a -b \right)}-\frac{b^{2} \left(-\frac{b \sin \left(d x +c \right)}{2 a \left(a \left(\sin^{2}\left(d x +c \right)\right)-b \left(\sin^{2}\left(d x +c \right)\right)-a \right)}-\frac{\left(6 a -b \right) \arctanh \left(\frac{\left(a -b \right) \sin \left(d x +c \right)}{\sqrt{a \left(a -b \right)}}\right)}{2 a \sqrt{a \left(a -b \right)}}\right)}{\left(a -b \right)^{3}}}{d}"," ",0,"1/d*(-1/(a^2-2*a*b+b^2)/(a-b)*(1/3*a*sin(d*x+c)^3-1/3*b*sin(d*x+c)^3-a*sin(d*x+c)+3*b*sin(d*x+c))-b^2/(a-b)^3*(-1/2/a*b*sin(d*x+c)/(a*sin(d*x+c)^2-b*sin(d*x+c)^2-a)-1/2*(6*a-b)/a/(a*(a-b))^(1/2)*arctanh((a-b)*sin(d*x+c)/(a*(a-b))^(1/2))))","A"
468,1,275,113,0.919000," ","int(sec(d*x+c)^8/(a+b*tan(d*x+c)^2)^2,x)","\frac{\tan^{3}\left(d x +c \right)}{3 b^{2} d}-\frac{2 a \tan \left(d x +c \right)}{d \,b^{3}}+\frac{3 \tan \left(d x +c \right)}{b^{2} d}-\frac{a^{2} \tan \left(d x +c \right)}{2 d \,b^{3} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{3 a \tan \left(d x +c \right)}{2 d \,b^{2} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}-\frac{3 \tan \left(d x +c \right)}{2 d b \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{\tan \left(d x +c \right)}{2 a d \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{5 a^{2} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \,b^{3} \sqrt{a b}}-\frac{9 a \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \,b^{2} \sqrt{a b}}+\frac{3 \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d b \sqrt{a b}}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d a \sqrt{a b}}"," ",0,"1/3*tan(d*x+c)^3/b^2/d-2/d/b^3*a*tan(d*x+c)+3*tan(d*x+c)/b^2/d-1/2/d/b^3*a^2*tan(d*x+c)/(a+b*tan(d*x+c)^2)+3/2/d/b^2*a*tan(d*x+c)/(a+b*tan(d*x+c)^2)-3/2/d/b*tan(d*x+c)/(a+b*tan(d*x+c)^2)+1/2*tan(d*x+c)/a/d/(a+b*tan(d*x+c)^2)+5/2/d/b^3*a^2/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))-9/2/d/b^2*a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+3/2/d/b/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/2/d/a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))","B"
469,1,181,92,0.652000," ","int(sec(d*x+c)^6/(a+b*tan(d*x+c)^2)^2,x)","\frac{\tan \left(d x +c \right)}{b^{2} d}+\frac{a \tan \left(d x +c \right)}{2 d \,b^{2} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}-\frac{\tan \left(d x +c \right)}{d b \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{\tan \left(d x +c \right)}{2 a d \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}-\frac{3 a \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \,b^{2} \sqrt{a b}}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{d b \sqrt{a b}}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d a \sqrt{a b}}"," ",0,"tan(d*x+c)/b^2/d+1/2/d/b^2*a*tan(d*x+c)/(a+b*tan(d*x+c)^2)-1/d/b*tan(d*x+c)/(a+b*tan(d*x+c)^2)+1/2*tan(d*x+c)/a/d/(a+b*tan(d*x+c)^2)-3/2/d/b^2*a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/d/b/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/2/d/a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))","A"
470,1,112,65,0.675000," ","int(sec(d*x+c)^4/(a+b*tan(d*x+c)^2)^2,x)","-\frac{\tan \left(d x +c \right)}{2 d b \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{\tan \left(d x +c \right)}{2 a d \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d b \sqrt{a b}}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d a \sqrt{a b}}"," ",0,"-1/2/d/b*tan(d*x+c)/(a+b*tan(d*x+c)^2)+1/2*tan(d*x+c)/a/d/(a+b*tan(d*x+c)^2)+1/2/d/b/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/2/d/a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))","A"
471,1,57,54,0.641000," ","int(sec(d*x+c)^2/(a+b*tan(d*x+c)^2)^2,x)","\frac{\tan \left(d x +c \right)}{2 a d \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d a \sqrt{a b}}"," ",0,"1/2*tan(d*x+c)/a/d/(a+b*tan(d*x+c)^2)+1/2/d/a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))","A"
472,1,248,132,0.767000," ","int(cos(d*x+c)^2/(a+b*tan(d*x+c)^2)^2,x)","\frac{b^{2} \tan \left(d x +c \right)}{2 d \left(a -b \right)^{3} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}-\frac{b^{3} \tan \left(d x +c \right)}{2 d \left(a -b \right)^{3} a \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{5 b^{2} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a -b \right)^{3} \sqrt{a b}}-\frac{b^{3} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a -b \right)^{3} a \sqrt{a b}}+\frac{\tan \left(d x +c \right) a}{2 d \left(a -b \right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{\tan \left(d x +c \right) b}{2 d \left(a -b \right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a}{2 d \left(a -b \right)^{3}}-\frac{5 \arctan \left(\tan \left(d x +c \right)\right) b}{2 d \left(a -b \right)^{3}}"," ",0,"1/2/d*b^2/(a-b)^3*tan(d*x+c)/(a+b*tan(d*x+c)^2)-1/2/d*b^3/(a-b)^3/a*tan(d*x+c)/(a+b*tan(d*x+c)^2)+5/2/d*b^2/(a-b)^3/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))-1/2/d*b^3/(a-b)^3/a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/2/d/(a-b)^3*tan(d*x+c)/(1+tan(d*x+c)^2)*a-1/2/d/(a-b)^3*tan(d*x+c)/(1+tan(d*x+c)^2)*b+1/2/d/(a-b)^3*arctan(tan(d*x+c))*a-5/2/d/(a-b)^3*arctan(tan(d*x+c))*b","A"
473,1,413,194,0.946000," ","int(cos(d*x+c)^4/(a+b*tan(d*x+c)^2)^2,x)","-\frac{b^{3} \tan \left(d x +c \right)}{2 d \left(a -b \right)^{4} \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}+\frac{b^{4} \tan \left(d x +c \right)}{2 d \left(a -b \right)^{4} a \left(a +b \left(\tan^{2}\left(d x +c \right)\right)\right)}-\frac{7 b^{3} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a -b \right)^{4} \sqrt{a b}}+\frac{b^{4} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a -b \right)^{4} a \sqrt{a b}}+\frac{3 \left(\tan^{3}\left(d x +c \right)\right) a^{2}}{8 d \left(a -b \right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{7 \left(\tan^{3}\left(d x +c \right)\right) a b}{4 d \left(a -b \right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{11 \left(\tan^{3}\left(d x +c \right)\right) b^{2}}{8 d \left(a -b \right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{9 \tan \left(d x +c \right) a b}{4 d \left(a -b \right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{13 \tan \left(d x +c \right) b^{2}}{8 d \left(a -b \right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \tan \left(d x +c \right) a^{2}}{8 d \left(a -b \right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{35 \arctan \left(\tan \left(d x +c \right)\right) b^{2}}{8 d \left(a -b \right)^{4}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2}}{8 d \left(a -b \right)^{4}}-\frac{7 \arctan \left(\tan \left(d x +c \right)\right) a b}{4 d \left(a -b \right)^{4}}"," ",0,"-1/2/d*b^3/(a-b)^4*tan(d*x+c)/(a+b*tan(d*x+c)^2)+1/2/d*b^4/(a-b)^4/a*tan(d*x+c)/(a+b*tan(d*x+c)^2)-7/2/d*b^3/(a-b)^4/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+1/2/d*b^4/(a-b)^4/a/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))+3/8/d/(a-b)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^2-7/4/d/(a-b)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a*b+11/8/d/(a-b)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^2-9/4/d/(a-b)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a*b+13/8/d/(a-b)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^2+5/8/d/(a-b)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^2+35/8/d/(a-b)^4*arctan(tan(d*x+c))*b^2+3/8/d/(a-b)^4*arctan(tan(d*x+c))*a^2-7/4/d/(a-b)^4*arctan(tan(d*x+c))*a*b","B"
474,0,0,77,2.845000," ","int((d*sec(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","\int \left(d \sec \left(f x +e \right)\right)^{m} \left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*sec(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","F"
475,0,0,102,2.873000," ","int((d*sec(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","\int \left(d \sec \left(f x +e \right)\right)^{m} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*sec(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","F"
476,0,0,91,1.252000," ","int((d*sec(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \sec \left(f x +e \right)\right)^{m} \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*sec(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","F"
477,0,0,99,2.179000," ","int(sec(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sec^{6}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x)","F"
478,0,0,65,2.143000," ","int(sec(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x)","F"
479,-1,0,31,180.000000," ","int(sec(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","F"
480,0,0,57,0.022000," ","int((b*(c*tan(f*x+e))^n)^p,x)","\int \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((b*(c*tan(f*x+e))^n)^p,x)","F"
481,-1,0,57,180.000000," ","int(cos(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x)","F"
482,0,0,83,2.065000," ","int(sec(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sec^{3}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","F"
483,0,0,81,11.997000," ","int(sec(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","\int \sec \left(f x +e \right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","F"
484,0,0,71,15.824000," ","int(cos(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","\int \cos \left(f x +e \right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cos(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x)","F"
485,0,0,73,24.817000," ","int(cos(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(\cos^{3}\left(f x +e \right)\right) \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x)","F"
486,0,0,29,5.478000," ","int((d*sec(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \sec \left(f x +e \right)\right)^{m} \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*sec(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
487,0,0,27,1.730000," ","int(sec(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sec^{3}\left(f x +e \right)\right) \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
488,0,0,25,1.287000," ","int(sec(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \sec \left(f x +e \right) \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
489,0,0,25,1.440000," ","int(cos(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \cos \left(f x +e \right) \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cos(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
490,0,0,27,4.514000," ","int(cos(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(\cos^{3}\left(f x +e \right)\right) \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
491,0,0,246,1.803000," ","int(sec(f*x+e)^6*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sec^{6}\left(f x +e \right)\right) \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^6*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
492,0,0,162,1.819000," ","int(sec(f*x+e)^4*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^4*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
493,0,0,77,1.608000," ","int(sec(f*x+e)^2*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^2*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
494,0,0,18,1.462000," ","int((a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((a+b*(c*tan(f*x+e))^n)^p,x)","F"
495,0,0,27,2.767000," ","int(cos(f*x+e)^2*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*(c*tan(f*x+e))^n)^p,x)","F"
496,0,0,80,3.359000," ","int((d*csc(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","\int \left(d \csc \left(f x +e \right)\right)^{m} \left(b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*csc(f*x+e))^m*(b*tan(f*x+e)^2)^p,x)","F"
497,0,0,117,2.711000," ","int((d*csc(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","\int \left(d \csc \left(f x +e \right)\right)^{m} \left(a +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*csc(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x)","F"
498,0,0,94,1.373000," ","int((d*csc(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \csc \left(f x +e \right)\right)^{m} \left(b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*csc(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x)","F"
499,0,0,56,5.107000," ","int((d*csc(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","\int \left(d \csc \left(f x +e \right)\right)^{m} \left(a +b \left(c \tan \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((d*csc(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x)","F"