1,1,102,79,1.004000," ","int((a+b*sec(f*x+e)^2)*sin(f*x+e)^7,x)","\frac{-\frac{a \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)}{7}+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*(-1/7*a*(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*(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"
2,1,82,62,1.099000," ","int((a+b*sec(f*x+e)^2)*sin(f*x+e)^5,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^{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*(-1/5*a*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+b*(sin(f*x+e)^6/cos(f*x+e)+(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)))","A"
3,1,62,42,1.050000," ","int((a+b*sec(f*x+e)^2)*sin(f*x+e)^3,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^{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*(-1/3*a*(2+sin(f*x+e)^2)*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"
4,1,25,24,0.357000," ","int((a+b*sec(f*x+e)^2)*sin(f*x+e),x)","\frac{b \sec \left(f x +e \right)-\frac{a}{\sec \left(f x +e \right)}}{f}"," ",0,"1/f*(b*sec(f*x+e)-a/sec(f*x+e))","A"
5,1,57,27,0.492000," ","int(csc(f*x+e)*(a+b*sec(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)}+\frac{b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}"," ",0,"1/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))","B"
6,1,100,49,0.967000," ","int(csc(f*x+e)^3*(a+b*sec(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}{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,"-1/2*a*cot(f*x+e)*csc(f*x+e)/f+1/2/f*a*ln(csc(f*x+e)-cot(f*x+e))-1/2/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))","B"
7,1,142,75,0.899000," ","int(csc(f*x+e)^5*(a+b*sec(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}{4 f \sin \left(f x +e \right)^{4} \cos \left(f x +e \right)}-\frac{5 b}{8 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)}+\frac{15 b}{8 f \cos \left(f x +e \right)}+\frac{15 b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{8 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))-1/4/f*b/sin(f*x+e)^4/cos(f*x+e)-5/8/f*b/sin(f*x+e)^2/cos(f*x+e)+15/8/f*b/cos(f*x+e)+15/8/f*b*ln(csc(f*x+e)-cot(f*x+e))","A"
8,1,112,90,0.903000," ","int((a+b*sec(f*x+e)^2)*sin(f*x+e)^6,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^{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*(-1/6*(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)^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"
9,1,92,64,0.942000," ","int((a+b*sec(f*x+e)^2)*sin(f*x+e)^4,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^{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*(-1/4*(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)^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"
10,1,46,38,0.716000," ","int((a+b*sec(f*x+e)^2)*sin(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(\tan \left(f x +e \right)-f x -e \right)}{f}"," ",0,"1/f*(a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+b*(tan(f*x+e)-f*x-e))","A"
11,1,16,15,0.872000," ","int(a+b*sec(f*x+e)^2,x)","a x +\frac{b \tan \left(f x +e \right)}{f}"," ",0,"a*x+b*tan(f*x+e)/f","A"
12,1,43,26,0.919000," ","int(csc(f*x+e)^2*(a+b*sec(f*x+e)^2),x)","\frac{-a \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*cot(f*x+e)+b*(1/sin(f*x+e)/cos(f*x+e)-2*cot(f*x+e)))","A"
13,1,73,44,1.122000," ","int(csc(f*x+e)^4*(a+b*sec(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}{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*(-2/3-1/3*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"
14,1,101,64,1.175000," ","int(csc(f*x+e)^6*(a+b*sec(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}{5 \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}-\frac{2}{5 \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)}+\frac{8}{5 \sin \left(f x +e \right) \cos \left(f x +e \right)}-\frac{16 \cot \left(f x +e \right)}{5}\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*(-1/5/sin(f*x+e)^5/cos(f*x+e)-2/5/sin(f*x+e)^3/cos(f*x+e)+8/5/sin(f*x+e)/cos(f*x+e)-16/5*cot(f*x+e)))","A"
15,1,155,91,0.905000," ","int((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^5,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^{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^{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*(-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)^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)^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)))","A"
16,1,125,68,0.894000," ","int((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^3,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^{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^{4}\left(f x +e \right)}{3 \cos \left(f x +e \right)^{3}}-\frac{\sin^{4}\left(f x +e \right)}{3 \cos \left(f x +e \right)}-\frac{\left(2+\sin^{2}\left(f x +e \right)\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)^4/cos(f*x+e)+(2+sin(f*x+e)^2)*cos(f*x+e))+b^2*(1/3*sin(f*x+e)^4/cos(f*x+e)^3-1/3*sin(f*x+e)^4/cos(f*x+e)-1/3*(2+sin(f*x+e)^2)*cos(f*x+e)))","A"
17,1,42,44,0.275000," ","int((a+b*sec(f*x+e)^2)^2*sin(f*x+e),x)","\frac{\frac{\left(\sec^{3}\left(f x +e \right)\right) b^{2}}{3}+2 a b \sec \left(f x +e \right)-\frac{a^{2}}{\sec \left(f x +e \right)}}{f}"," ",0,"1/f*(1/3*sec(f*x+e)^3*b^2+2*a*b*sec(f*x+e)-a^2/sec(f*x+e))","A"
18,1,117,50,0.775000," ","int(csc(f*x+e)*(a+b*sec(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{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}}+\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/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+1/f*b^2/cos(f*x+e)+1/f*b^2*ln(csc(f*x+e)-cot(f*x+e))","B"
19,1,195,96,1.381000," ","int(csc(f*x+e)^3*(a+b*sec(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{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 \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)^{3}}-\frac{5 b^{2}}{6 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)}+\frac{5 b^{2}}{2 f \cos \left(f x +e \right)}+\frac{5 b^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}"," ",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))-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/sin(f*x+e)^2/cos(f*x+e)^3-5/6/f*b^2/sin(f*x+e)^2/cos(f*x+e)+5/2/f*b^2/cos(f*x+e)+5/2/f*b^2*ln(csc(f*x+e)-cot(f*x+e))","B"
20,1,264,131,1.207000," ","int(csc(f*x+e)^5*(a+b*sec(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}{2 f \sin \left(f x +e \right)^{4} \cos \left(f x +e \right)}-\frac{5 a b}{4 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)}+\frac{15 a b}{4 f \cos \left(f x +e \right)}+\frac{15 a b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{4 f}-\frac{b^{2}}{4 f \sin \left(f x +e \right)^{4} \cos \left(f x +e \right)^{3}}+\frac{7 b^{2}}{12 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)^{3}}-\frac{35 b^{2}}{24 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)}+\frac{35 b^{2}}{8 f \cos \left(f x +e \right)}+\frac{35 b^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{8 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))-1/2/f*a*b/sin(f*x+e)^4/cos(f*x+e)-5/4/f*a*b/sin(f*x+e)^2/cos(f*x+e)+15/4/f*a*b/cos(f*x+e)+15/4/f*a*b*ln(csc(f*x+e)-cot(f*x+e))-1/4/f*b^2/sin(f*x+e)^4/cos(f*x+e)^3+7/12/f*b^2/sin(f*x+e)^2/cos(f*x+e)^3-35/24/f*b^2/sin(f*x+e)^2/cos(f*x+e)+35/8/f*b^2/cos(f*x+e)+35/8/f*b^2*ln(csc(f*x+e)-cot(f*x+e))","B"
21,1,199,136,0.918000," ","int((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^6,x)","\frac{a^{2} \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)+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^{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*(-1/6*(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)+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)^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))","A"
22,1,123,104,0.904000," ","int((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^4,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^{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{\left(\tan^{3}\left(f x +e \right)\right)}{3}-\tan \left(f x +e \right)+f x +e \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)^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*tan(f*x+e)^3-tan(f*x+e)+f*x+e))","A"
23,1,71,65,0.516000," ","int((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^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(\tan \left(f x +e \right)-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*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2*a*b*(tan(f*x+e)-f*x-e)+1/3*b^2*sin(f*x+e)^3/cos(f*x+e)^3)","A"
24,1,48,38,0.980000," ","int((a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \left(f x +e \right)+2 a b \tan \left(f x +e \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*(f*x+e)+2*a*b*tan(f*x+e)-b^2*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e))","A"
25,1,96,48,0.898000," ","int(csc(f*x+e)^2*(a+b*sec(f*x+e)^2)^2,x)","\frac{-a^{2} \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{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*cot(f*x+e)+2*a*b*(1/sin(f*x+e)/cos(f*x+e)-2*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"
26,1,144,72,1.377000," ","int(csc(f*x+e)^4*(a+b*sec(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}{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)^{3} \cos \left(f x +e \right)^{3}}-\frac{2}{3 \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)}+\frac{8}{3 \sin \left(f x +e \right) \cos \left(f x +e \right)}-\frac{16 \cot \left(f x +e \right)}{3}\right)}{f}"," ",0,"1/f*(a^2*(-2/3-1/3*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)^3/cos(f*x+e)^3-2/3/sin(f*x+e)^3/cos(f*x+e)+8/3/sin(f*x+e)/cos(f*x+e)-16/3*cot(f*x+e)))","A"
27,1,190,97,1.692000," ","int(csc(f*x+e)^6*(a+b*sec(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}{5 \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}-\frac{2}{5 \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)}+\frac{8}{5 \sin \left(f x +e \right) \cos \left(f x +e \right)}-\frac{16 \cot \left(f x +e \right)}{5}\right)+b^{2} \left(-\frac{1}{5 \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)^{3}}+\frac{8}{15 \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)^{3}}-\frac{16}{15 \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)}+\frac{64}{15 \sin \left(f x +e \right) \cos \left(f x +e \right)}-\frac{128 \cot \left(f x +e \right)}{15}\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*(-1/5/sin(f*x+e)^5/cos(f*x+e)-2/5/sin(f*x+e)^3/cos(f*x+e)+8/5/sin(f*x+e)/cos(f*x+e)-16/5*cot(f*x+e))+b^2*(-1/5/sin(f*x+e)^5/cos(f*x+e)^3+8/15/sin(f*x+e)^3/cos(f*x+e)^3-16/15/sin(f*x+e)^3/cos(f*x+e)+64/15/sin(f*x+e)/cos(f*x+e)-128/15*cot(f*x+e)))","A"
28,1,183,86,0.898000," ","int(sin(f*x+e)^5/(a+b*sec(f*x+e)^2),x)","-\frac{\cos^{5}\left(f x +e \right)}{5 a f}+\frac{2 \left(\cos^{3}\left(f x +e \right)\right)}{3 a f}+\frac{\left(\cos^{3}\left(f x +e \right)\right) b}{3 f \,a^{2}}-\frac{\cos \left(f x +e \right)}{a f}-\frac{2 b \cos \left(f x +e \right)}{f \,a^{2}}-\frac{\cos \left(f x +e \right) b^{2}}{f \,a^{3}}+\frac{b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{f a \sqrt{a b}}+\frac{2 b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{f \,a^{2} \sqrt{a b}}+\frac{b^{3} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{f \,a^{3} \sqrt{a b}}"," ",0,"-1/5*cos(f*x+e)^5/a/f+2/3*cos(f*x+e)^3/a/f+1/3/f/a^2*cos(f*x+e)^3*b-cos(f*x+e)/a/f-2/f/a^2*b*cos(f*x+e)-1/f/a^3*cos(f*x+e)*b^2+1/f*b/a/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+2/f*b^2/a^2/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+1/f*b^3/a^3/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))","B"
29,1,103,61,0.930000," ","int(sin(f*x+e)^3/(a+b*sec(f*x+e)^2),x)","\frac{\cos^{3}\left(f x +e \right)}{3 a f}-\frac{\cos \left(f x +e \right)}{a f}-\frac{b \cos \left(f x +e \right)}{f \,a^{2}}+\frac{b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{f a \sqrt{a b}}+\frac{b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{f \,a^{2} \sqrt{a b}}"," ",0,"1/3*cos(f*x+e)^3/a/f-cos(f*x+e)/a/f-1/f/a^2*b*cos(f*x+e)+1/f*b/a/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+1/f*b^2/a^2/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))","A"
30,1,46,39,0.402000," ","int(sin(f*x+e)/(a+b*sec(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\sec \left(f x +e \right) b}{\sqrt{a b}}\right)}{f a \sqrt{a b}}-\frac{1}{f a \sec \left(f x +e \right)}"," ",0,"-1/f/a*b/(a*b)^(1/2)*arctan(sec(f*x+e)*b/(a*b)^(1/2))-1/f/a/sec(f*x+e)","A"
31,1,76,47,0.784000," ","int(csc(f*x+e)/(a+b*sec(f*x+e)^2),x)","\frac{b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{f \left(a +b \right) \sqrt{a b}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{f \left(2 a +2 b \right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{f \left(2 a +2 b \right)}"," ",0,"1/f*b/(a+b)/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+1/f/(2*a+2*b)*ln(-1+cos(f*x+e))-1/f/(2*a+2*b)*ln(1+cos(f*x+e))","A"
32,1,158,74,0.938000," ","int(csc(f*x+e)^3/(a+b*sec(f*x+e)^2),x)","\frac{a b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{f \left(a +b \right)^{2} \sqrt{a b}}+\frac{1}{f \left(4 a +4 b \right) \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a}{4 f \left(a +b \right)^{2}}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b}{4 f \left(a +b \right)^{2}}+\frac{1}{f \left(4 a +4 b \right) \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) a}{4 f \left(a +b \right)^{2}}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) b}{4 f \left(a +b \right)^{2}}"," ",0,"1/f*a*b/(a+b)^2/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+1/f/(4*a+4*b)/(-1+cos(f*x+e))+1/4/f/(a+b)^2*ln(-1+cos(f*x+e))*a-1/4/f/(a+b)^2*ln(-1+cos(f*x+e))*b+1/f/(4*a+4*b)/(1+cos(f*x+e))-1/4/f/(a+b)^2*ln(1+cos(f*x+e))*a+1/4/f/(a+b)^2*ln(1+cos(f*x+e))*b","B"
33,1,296,115,0.963000," ","int(csc(f*x+e)^5/(a+b*sec(f*x+e)^2),x)","\frac{a^{2} b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{f \left(a +b \right)^{3} \sqrt{a b}}-\frac{1}{2 f \left(8 a +8 b \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}+\frac{3 a}{16 f \left(a +b \right)^{2} \left(-1+\cos \left(f x +e \right)\right)}-\frac{b}{16 f \left(a +b \right)^{2} \left(-1+\cos \left(f x +e \right)\right)}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) a^{2}}{16 f \left(a +b \right)^{3}}-\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) a b}{8 f \left(a +b \right)^{3}}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{16 f \left(a +b \right)^{3}}+\frac{1}{2 f \left(8 a +8 b \right) \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{3 a}{16 f \left(a +b \right)^{2} \left(1+\cos \left(f x +e \right)\right)}-\frac{b}{16 f \left(a +b \right)^{2} \left(1+\cos \left(f x +e \right)\right)}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) a^{2}}{16 f \left(a +b \right)^{3}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) a b}{8 f \left(a +b \right)^{3}}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{16 f \left(a +b \right)^{3}}"," ",0,"1/f*a^2*b/(a+b)^3/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))-1/2/f/(8*a+8*b)/(-1+cos(f*x+e))^2+3/16/f/(a+b)^2/(-1+cos(f*x+e))*a-1/16/f/(a+b)^2/(-1+cos(f*x+e))*b+3/16/f/(a+b)^3*ln(-1+cos(f*x+e))*a^2-3/8/f/(a+b)^3*ln(-1+cos(f*x+e))*a*b-1/16/f/(a+b)^3*ln(-1+cos(f*x+e))*b^2+1/2/f/(8*a+8*b)/(1+cos(f*x+e))^2+3/16/f/(a+b)^2/(1+cos(f*x+e))*a-1/16/f/(a+b)^2/(1+cos(f*x+e))*b-3/16/f/(a+b)^3*ln(1+cos(f*x+e))*a^2+3/8/f/(a+b)^3*ln(1+cos(f*x+e))*a*b+1/16/f/(a+b)^3*ln(1+cos(f*x+e))*b^2","B"
34,1,460,150,0.854000," ","int(sin(f*x+e)^6/(a+b*sec(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f a \sqrt{\left(a +b \right) b}}-\frac{3 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \sqrt{\left(a +b \right) b}}-\frac{3 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \sqrt{\left(a +b \right) b}}-\frac{b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{4} \sqrt{\left(a +b \right) b}}-\frac{9 \left(\tan^{5}\left(f x +e \right)\right) b}{8 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{\left(\tan^{5}\left(f x +e \right)\right) b^{2}}{2 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{11 \left(\tan^{5}\left(f x +e \right)\right)}{16 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{2 \left(\tan^{3}\left(f x +e \right)\right) b}{f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b^{2}}{f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{6 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \tan \left(f x +e \right)}{16 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{7 \tan \left(f x +e \right) b}{8 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{\tan \left(f x +e \right) b^{2}}{2 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{15 \arctan \left(\tan \left(f x +e \right)\right) b}{8 f \,a^{2}}+\frac{5 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{2 f \,a^{3}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3}}{f \,a^{4}}+\frac{5 \arctan \left(\tan \left(f x +e \right)\right)}{16 f a}"," ",0,"-1/f*b/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-3/f*b^2/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-3/f*b^3/a^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f*b^4/a^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-9/8/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b-1/2/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b^2-11/16/f/a/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5-2/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b-1/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b^2-5/6/f/a/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3-5/16/f/a/(tan(f*x+e)^2+1)^3*tan(f*x+e)-7/8/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b-1/2/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b^2+15/8/f/a^2*arctan(tan(f*x+e))*b+5/2/f/a^3*arctan(tan(f*x+e))*b^2+1/f/a^4*arctan(tan(f*x+e))*b^3+5/16/f/a*arctan(tan(f*x+e))","B"
35,1,260,103,1.015000," ","int(sin(f*x+e)^4/(a+b*sec(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f a \sqrt{\left(a +b \right) b}}-\frac{2 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \sqrt{\left(a +b \right) b}}-\frac{b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \sqrt{\left(a +b \right) b}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b}{2 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{8 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \tan \left(f x +e \right)}{8 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{\tan \left(f x +e \right) b}{2 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b}{2 f \,a^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f \,a^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right)}{8 f a}"," ",0,"-1/f*b/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-2/f*b^2/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f*b^3/a^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/2/f/a^2/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3*b-5/8/f/a/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3-3/8/f/a/(tan(f*x+e)^2+1)^2*tan(f*x+e)-1/2/f/a^2/(tan(f*x+e)^2+1)^2*tan(f*x+e)*b+3/2/f/a^2*arctan(tan(f*x+e))*b+1/f/a^3*arctan(tan(f*x+e))*b^2+3/8/f/a*arctan(tan(f*x+e))","B"
36,1,124,64,0.947000," ","int(sin(f*x+e)^2/(a+b*sec(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f a \sqrt{\left(a +b \right) b}}-\frac{b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \sqrt{\left(a +b \right) b}}-\frac{\tan \left(f x +e \right)}{2 f a \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{2 f a}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b}{f \,a^{2}}"," ",0,"-1/f*b/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f*b^2/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/2/f/a*tan(f*x+e)/(tan(f*x+e)^2+1)+1/2/f/a*arctan(tan(f*x+e))+1/f/a^2*arctan(tan(f*x+e))*b","A"
37,1,48,37,1.000000," ","int(1/(a+b*sec(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f a \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f a}"," ",0,"-1/f*b/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a*arctan(tan(f*x+e))","A"
38,1,54,46,0.827000," ","int(csc(f*x+e)^2/(a+b*sec(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right) \sqrt{\left(a +b \right) b}}-\frac{1}{f \left(a +b \right) \tan \left(f x +e \right)}"," ",0,"-1/f*b/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/(a+b)/tan(f*x+e)","A"
39,1,74,66,0.960000," ","int(csc(f*x+e)^4/(a+b*sec(f*x+e)^2),x)","-\frac{a b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{2} \sqrt{\left(a +b \right) b}}-\frac{1}{3 f \left(a +b \right) \tan \left(f x +e \right)^{3}}-\frac{a}{f \left(a +b \right)^{2} \tan \left(f x +e \right)}"," ",0,"-1/f*a*b/(a+b)^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/3/f/(a+b)/tan(f*x+e)^3-1/f*a/(a+b)^2/tan(f*x+e)","A"
40,1,116,93,1.014000," ","int(csc(f*x+e)^6/(a+b*sec(f*x+e)^2),x)","-\frac{a^{2} b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{3} \sqrt{\left(a +b \right) b}}-\frac{1}{5 f \left(a +b \right) \tan \left(f x +e \right)^{5}}-\frac{a^{2}}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}-\frac{2 a}{3 f \left(a +b \right)^{2} \tan \left(f x +e \right)^{3}}-\frac{b}{3 f \left(a +b \right)^{2} \tan \left(f x +e \right)^{3}}"," ",0,"-1/f*a^2*b/(a+b)^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/5/f/(a+b)/tan(f*x+e)^5-1/f*a^2/(a+b)^3/tan(f*x+e)-2/3/f/(a+b)^2/tan(f*x+e)^3*a-1/3/f/(a+b)^2/tan(f*x+e)^3*b","A"
41,1,276,143,0.949000," ","int(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x)","-\frac{\cos^{5}\left(f x +e \right)}{5 a^{2} f}+\frac{2 \left(\cos^{3}\left(f x +e \right)\right)}{3 a^{2} f}+\frac{2 \left(\cos^{3}\left(f x +e \right)\right) b}{3 f \,a^{3}}-\frac{\cos \left(f x +e \right)}{a^{2} f}-\frac{4 \cos \left(f x +e \right) b}{f \,a^{3}}-\frac{3 \cos \left(f x +e \right) b^{2}}{f \,a^{4}}-\frac{b \cos \left(f x +e \right)}{2 f \,a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{b^{2} \cos \left(f x +e \right)}{f \,a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{b^{3} \cos \left(f x +e \right)}{2 f \,a^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{3 b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{2 f \,a^{2} \sqrt{a b}}+\frac{5 b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{f \,a^{3} \sqrt{a b}}+\frac{7 b^{3} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{2 f \,a^{4} \sqrt{a b}}"," ",0,"-1/5*cos(f*x+e)^5/a^2/f+2/3*cos(f*x+e)^3/a^2/f+2/3/f/a^3*cos(f*x+e)^3*b-cos(f*x+e)/a^2/f-4/f/a^3*cos(f*x+e)*b-3/f/a^4*cos(f*x+e)*b^2-1/2/f*b/a^2*cos(f*x+e)/(b+a*cos(f*x+e)^2)-1/f*b^2/a^3*cos(f*x+e)/(b+a*cos(f*x+e)^2)-1/2/f*b^3/a^4*cos(f*x+e)/(b+a*cos(f*x+e)^2)+3/2/f*b/a^2/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+5/f*b^2/a^3/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+7/2/f*b^3/a^4/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))","A"
42,1,165,100,0.906000," ","int(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x)","\frac{\cos^{3}\left(f x +e \right)}{3 a^{2} f}-\frac{\cos \left(f x +e \right)}{a^{2} f}-\frac{2 \cos \left(f x +e \right) b}{f \,a^{3}}-\frac{b \cos \left(f x +e \right)}{2 f \,a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{b^{2} \cos \left(f x +e \right)}{2 f \,a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{3 b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{2 f \,a^{2} \sqrt{a b}}+\frac{5 b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{2 f \,a^{3} \sqrt{a b}}"," ",0,"1/3*cos(f*x+e)^3/a^2/f-cos(f*x+e)/a^2/f-2/f/a^3*cos(f*x+e)*b-1/2/f*b/a^2*cos(f*x+e)/(b+a*cos(f*x+e)^2)-1/2/f*b^2/a^3*cos(f*x+e)/(b+a*cos(f*x+e)^2)+3/2/f*b/a^2/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+5/2/f*b^2/a^3/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))","A"
43,1,75,70,0.619000," ","int(sin(f*x+e)/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \sec \left(f x +e \right)}{2 f \,a^{2} \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)}-\frac{3 b \arctan \left(\frac{\sec \left(f x +e \right) b}{\sqrt{a b}}\right)}{2 f \,a^{2} \sqrt{a b}}-\frac{1}{f \,a^{2} \sec \left(f x +e \right)}"," ",0,"-1/2/f*b/a^2*sec(f*x+e)/(a+b*sec(f*x+e)^2)-3/2/f*b/a^2/(a*b)^(1/2)*arctan(sec(f*x+e)*b/(a*b)^(1/2))-1/f/a^2/sec(f*x+e)","A"
44,1,172,87,1.187000," ","int(csc(f*x+e)/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \cos \left(f x +e \right)}{2 f \left(a +b \right)^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{b^{2} \cos \left(f x +e \right)}{2 f \left(a +b \right)^{2} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{3 b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{2 f \left(a +b \right)^{2} \sqrt{a b}}+\frac{b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{2 f \left(a +b \right)^{2} a \sqrt{a b}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \left(a +b \right)^{2}}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \left(a +b \right)^{2}}"," ",0,"-1/2/f*b/(a+b)^2*cos(f*x+e)/(b+a*cos(f*x+e)^2)-1/2/f*b^2/(a+b)^2/a*cos(f*x+e)/(b+a*cos(f*x+e)^2)+3/2/f*b/(a+b)^2/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+1/2/f*b^2/(a+b)^2/a/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+1/2/f/(a+b)^2*ln(-1+cos(f*x+e))-1/2/f/(a+b)^2*ln(1+cos(f*x+e))","A"
45,1,250,131,1.309000," ","int(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \cos \left(f x +e \right) a}{2 f \left(a +b \right)^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{b^{2} \cos \left(f x +e \right)}{2 f \left(a +b \right)^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{3 b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right) a}{2 f \left(a +b \right)^{3} \sqrt{a b}}-\frac{b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{2 f \left(a +b \right)^{3} \sqrt{a b}}+\frac{1}{4 f \left(a +b \right)^{2} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a}{4 f \left(a +b \right)^{3}}-\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b}{4 f \left(a +b \right)^{3}}+\frac{1}{4 f \left(a +b \right)^{2} \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) a}{4 f \left(a +b \right)^{3}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b}{4 f \left(a +b \right)^{3}}"," ",0,"-1/2/f*b/(a+b)^3*cos(f*x+e)/(b+a*cos(f*x+e)^2)*a-1/2/f*b^2/(a+b)^3*cos(f*x+e)/(b+a*cos(f*x+e)^2)+3/2/f*b/(a+b)^3/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))*a-1/2/f*b^2/(a+b)^3/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+1/4/f/(a+b)^2/(-1+cos(f*x+e))+1/4/f/(a+b)^3*ln(-1+cos(f*x+e))*a-3/4/f/(a+b)^3*ln(-1+cos(f*x+e))*b+1/4/f/(a+b)^2/(1+cos(f*x+e))-1/4/f/(a+b)^3*ln(1+cos(f*x+e))*a+3/4/f/(a+b)^3*ln(1+cos(f*x+e))*b","A"
46,1,390,179,0.969000," ","int(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x)","-\frac{a^{2} b \cos \left(f x +e \right)}{2 f \left(a +b \right)^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{a \,b^{2} \cos \left(f x +e \right)}{2 f \left(a +b \right)^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{3 a^{2} b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{2 f \left(a +b \right)^{4} \sqrt{a b}}-\frac{3 a \,b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{2 f \left(a +b \right)^{4} \sqrt{a b}}-\frac{1}{16 f \left(a +b \right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2}}+\frac{3 a}{16 f \left(a +b \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}-\frac{5 b}{16 f \left(a +b \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) a^{2}}{16 f \left(a +b \right)^{4}}-\frac{9 \ln \left(-1+\cos \left(f x +e \right)\right) a b}{8 f \left(a +b \right)^{4}}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{16 f \left(a +b \right)^{4}}+\frac{1}{16 f \left(a +b \right)^{2} \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{3 a}{16 f \left(a +b \right)^{3} \left(1+\cos \left(f x +e \right)\right)}-\frac{5 b}{16 f \left(a +b \right)^{3} \left(1+\cos \left(f x +e \right)\right)}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) a^{2}}{16 f \left(a +b \right)^{4}}+\frac{9 \ln \left(1+\cos \left(f x +e \right)\right) a b}{8 f \left(a +b \right)^{4}}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{16 f \left(a +b \right)^{4}}"," ",0,"-1/2/f*a^2*b/(a+b)^4*cos(f*x+e)/(b+a*cos(f*x+e)^2)-1/2/f*a*b^2/(a+b)^4*cos(f*x+e)/(b+a*cos(f*x+e)^2)+3/2/f*a^2*b/(a+b)^4/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))-3/2/f*a*b^2/(a+b)^4/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))-1/16/f/(a+b)^2/(-1+cos(f*x+e))^2+3/16/f/(a+b)^3/(-1+cos(f*x+e))*a-5/16/f/(a+b)^3/(-1+cos(f*x+e))*b+3/16/f/(a+b)^4*ln(-1+cos(f*x+e))*a^2-9/8/f/(a+b)^4*ln(-1+cos(f*x+e))*a*b+3/16/f/(a+b)^4*ln(-1+cos(f*x+e))*b^2+1/16/f/(a+b)^2/(1+cos(f*x+e))^2+3/16/f/(a+b)^3/(1+cos(f*x+e))*a-5/16/f/(a+b)^3/(1+cos(f*x+e))*b-3/16/f/(a+b)^4*ln(1+cos(f*x+e))*a^2+9/8/f/(a+b)^4*ln(1+cos(f*x+e))*a*b-3/16/f/(a+b)^4*ln(1+cos(f*x+e))*b^2","B"
47,1,555,247,0.952000," ","int(sin(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 a^{2} f \left(a +b +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 +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 +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{\left(a +b \right) b}}\right)}{2 f \,a^{2} \sqrt{\left(a +b \right) b}}-\frac{7 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \sqrt{\left(a +b \right) b}}-\frac{19 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,a^{4} \sqrt{\left(a +b \right) b}}-\frac{4 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{5} \sqrt{\left(a +b \right) b}}-\frac{9 \left(\tan^{5}\left(f x +e \right)\right) b}{4 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{3 \left(\tan^{5}\left(f x +e \right)\right) b^{2}}{2 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{11 \left(\tan^{5}\left(f x +e \right)\right)}{16 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{4 \left(\tan^{3}\left(f x +e \right)\right) b}{f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{3 \left(\tan^{3}\left(f x +e \right)\right) b^{2}}{f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{6 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \tan \left(f x +e \right)}{16 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{7 \tan \left(f x +e \right) b}{4 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{3 \tan \left(f x +e \right) b^{2}}{2 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{15 \arctan \left(\tan \left(f x +e \right)\right) b}{4 f \,a^{3}}+\frac{15 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{2 f \,a^{4}}+\frac{4 \arctan \left(\tan \left(f x +e \right)\right) b^{3}}{f \,a^{5}}+\frac{5 \arctan \left(\tan \left(f x +e \right)\right)}{16 f \,a^{2}}"," ",0,"-1/2*b*tan(f*x+e)/a^2/f/(a+b+b*tan(f*x+e)^2)-1/f*b^2/a^3*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)-1/2/f*b^3/a^4*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)-3/2/f*b/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-7/f*b^2/a^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-19/2/f*b^3/a^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-4/f*b^4/a^5/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-9/4/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b-3/2/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b^2-11/16/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5-4/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b-3/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b^2-5/6/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3-5/16/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)-7/4/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b-3/2/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b^2+15/4/f/a^3*arctan(tan(f*x+e))*b+15/2/f/a^4*arctan(tan(f*x+e))*b^2+4/f/a^5*arctan(tan(f*x+e))*b^3+5/16/f/a^2*arctan(tan(f*x+e))","B"
48,1,323,173,0.893000," ","int(sin(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 a^{2} f \left(a +b +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{\left(a +b \right) b}}\right)}{2 f \,a^{2} \sqrt{\left(a +b \right) b}}-\frac{9 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,a^{3} \sqrt{\left(a +b \right) b}}-\frac{b^{2} \tan \left(f x +e \right)}{2 f \,a^{3} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{4} \sqrt{\left(a +b \right) b}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b}{f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \tan \left(f x +e \right)}{8 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{\tan \left(f x +e \right) b}{f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b}{f \,a^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f \,a^{4}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right)}{8 f \,a^{2}}"," ",0,"-1/2*b*tan(f*x+e)/a^2/f/(a+b+b*tan(f*x+e)^2)-3/2/f*b/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-9/2/f*b^2/a^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/2/f*b^2/a^3*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)-3/f*b^3/a^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a^3/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3*b-5/8/f/a^2/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3-3/8/f/a^2/(tan(f*x+e)^2+1)^2*tan(f*x+e)-1/f/a^3/(tan(f*x+e)^2+1)^2*tan(f*x+e)*b+3/f/a^3*arctan(tan(f*x+e))*b+3/f/a^4*arctan(tan(f*x+e))*b^2+3/8/f/a^2*arctan(tan(f*x+e))","A"
49,1,155,116,0.820000," ","int(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 a^{2} f \left(a +b +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{\left(a +b \right) b}}\right)}{2 f \,a^{2} \sqrt{\left(a +b \right) b}}-\frac{2 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \sqrt{\left(a +b \right) b}}-\frac{\tan \left(f x +e \right)}{2 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{2 f \,a^{2}}+\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b}{f \,a^{3}}"," ",0,"-1/2*b*tan(f*x+e)/a^2/f/(a+b+b*tan(f*x+e)^2)-3/2/f*b/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-2/f*b^2/a^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/2/f/a^2*tan(f*x+e)/(tan(f*x+e)^2+1)+1/2/f/a^2*arctan(tan(f*x+e))+2/f/a^3*arctan(tan(f*x+e))*b","A"
50,1,127,80,0.896000," ","int(1/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 a \left(a +b \right) f \left(a +b +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{\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{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"-1/2*b*tan(f*x+e)/a/(a+b)/f/(a+b+b*tan(f*x+e)^2)-3/2/f*b/a/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f*b^2/a^2/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a^2*arctan(tan(f*x+e))","A"
51,1,86,77,1.050000," ","int(csc(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 f \left(a +b \right)^{2} \left(a +b +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{\left(a +b \right) b}}\right)}{2 f \left(a +b \right)^{2} \sqrt{\left(a +b \right) b}}-\frac{1}{f \left(a +b \right)^{2} \tan \left(f x +e \right)}"," ",0,"-1/2/f*b/(a+b)^2*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)-3/2/f*b/(a+b)^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/(a+b)^2/tan(f*x+e)","A"
52,1,160,109,1.424000," ","int(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x)","-\frac{a b \tan \left(f x +e \right)}{2 \left(a +b \right)^{3} f \left(a +b +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{\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{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{3} \sqrt{\left(a +b \right) b}}-\frac{1}{3 f \left(a +b \right)^{2} \tan \left(f x +e \right)^{3}}-\frac{a}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}+\frac{b}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}"," ",0,"-1/2*a*b*tan(f*x+e)/(a+b)^3/f/(a+b+b*tan(f*x+e)^2)-3/2/f/(a+b)^3*b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))*a+1/f/(a+b)^3*b^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/3/f/(a+b)^2/tan(f*x+e)^3-1/f/(a+b)^3/tan(f*x+e)*a+1/f/(a+b)^3/tan(f*x+e)*b","A"
53,1,189,170,1.252000," ","int(csc(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \,a^{2} \tan \left(f x +e \right)}{2 f \left(a +b \right)^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 b \,a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \left(a +b \right)^{4} \sqrt{\left(a +b \right) b}}+\frac{2 b^{2} a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{4} \sqrt{\left(a +b \right) b}}-\frac{1}{5 f \left(a +b \right)^{2} \tan \left(f x +e \right)^{5}}-\frac{a^{2}}{f \left(a +b \right)^{4} \tan \left(f x +e \right)}+\frac{2 a b}{f \left(a +b \right)^{4} \tan \left(f x +e \right)}-\frac{2 a}{3 f \left(a +b \right)^{3} \tan \left(f x +e \right)^{3}}"," ",0,"-1/2/f*b*a^2/(a+b)^4*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)-3/2/f*b*a^2/(a+b)^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+2/f*b^2*a/(a+b)^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/5/f/(a+b)^2/tan(f*x+e)^5-1/f*a^2/(a+b)^4/tan(f*x+e)+2/f*a/(a+b)^4/tan(f*x+e)*b-2/3/f*a/(a+b)^3/tan(f*x+e)^3","A"
54,1,374,194,1.023000," ","int(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x)","-\frac{\cos^{5}\left(f x +e \right)}{5 a^{3} f}+\frac{2 \left(\cos^{3}\left(f x +e \right)\right)}{3 a^{3} f}+\frac{\left(\cos^{3}\left(f x +e \right)\right) b}{f \,a^{4}}-\frac{\cos \left(f x +e \right)}{a^{3} f}-\frac{6 b \cos \left(f x +e \right)}{f \,a^{4}}-\frac{6 \cos \left(f x +e \right) b^{2}}{f \,a^{5}}-\frac{9 b \left(\cos^{3}\left(f x +e \right)\right)}{8 f \,a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{13 b^{2} \left(\cos^{3}\left(f x +e \right)\right)}{4 f \,a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{17 b^{3} \left(\cos^{3}\left(f x +e \right)\right)}{8 f \,a^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{7 b^{2} \cos \left(f x +e \right)}{8 f \,a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{11 b^{3} \cos \left(f x +e \right)}{4 f \,a^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{15 b^{4} \cos \left(f x +e \right)}{8 f \,a^{5} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{15 b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{8 f \,a^{3} \sqrt{a b}}+\frac{35 b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{4 f \,a^{4} \sqrt{a b}}+\frac{63 b^{3} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{8 f \,a^{5} \sqrt{a b}}"," ",0,"-1/5*cos(f*x+e)^5/a^3/f+2/3*cos(f*x+e)^3/a^3/f+1/f/a^4*cos(f*x+e)^3*b-cos(f*x+e)/a^3/f-6/f/a^4*b*cos(f*x+e)-6/f/a^5*cos(f*x+e)*b^2-9/8/f*b/a^2/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3-13/4/f*b^2/a^3/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3-17/8/f*b^3/a^4/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3-7/8/f*b^2/a^3/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)-11/4/f*b^3/a^4/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)-15/8/f*b^4/a^5/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)+15/8/f*b/a^3/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+35/4/f*b^2/a^4/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+63/8/f*b^3/a^5/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))","A"
55,1,231,138,0.942000," ","int(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x)","\frac{\cos^{3}\left(f x +e \right)}{3 a^{3} f}-\frac{\cos \left(f x +e \right)}{a^{3} f}-\frac{3 b \cos \left(f x +e \right)}{f \,a^{4}}-\frac{9 b \left(\cos^{3}\left(f x +e \right)\right)}{8 f \,a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{13 b^{2} \left(\cos^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{7 b^{2} \cos \left(f x +e \right)}{8 f \,a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{11 b^{3} \cos \left(f x +e \right)}{8 f \,a^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{15 b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{8 f \,a^{3} \sqrt{a b}}+\frac{35 b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{8 f \,a^{4} \sqrt{a b}}"," ",0,"1/3*cos(f*x+e)^3/a^3/f-cos(f*x+e)/a^3/f-3/f/a^4*b*cos(f*x+e)-9/8/f*b/a^2/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3-13/8/f*b^2/a^3/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3-7/8/f*b^2/a^3/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)-11/8/f*b^3/a^4/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)+15/8/f*b/a^3/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+35/8/f*b^2/a^4/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))","A"
56,1,108,100,0.581000," ","int(sin(f*x+e)/(a+b*sec(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\sec^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 b \sec \left(f x +e \right)}{8 f \,a^{2} \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{15 b \arctan \left(\frac{\sec \left(f x +e \right) b}{\sqrt{a b}}\right)}{8 f \,a^{3} \sqrt{a b}}-\frac{1}{f \,a^{3} \sec \left(f x +e \right)}"," ",0,"-7/8/f/a^3*b^2/(a+b*sec(f*x+e)^2)^2*sec(f*x+e)^3-9/8/f/a^2*b/(a+b*sec(f*x+e)^2)^2*sec(f*x+e)-15/8/f/a^3*b/(a*b)^(1/2)*arctan(sec(f*x+e)*b/(a*b)^(1/2))-1/f/a^3/sec(f*x+e)","A"
57,1,352,140,0.933000," ","int(csc(f*x+e)/(a+b*sec(f*x+e)^2)^3,x)","-\frac{9 b a \left(\cos^{3}\left(f x +e \right)\right)}{8 f \left(a +b \right)^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{7 b^{2} \left(\cos^{3}\left(f x +e \right)\right)}{4 f \left(a +b \right)^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{5 b^{3} \left(\cos^{3}\left(f x +e \right)\right)}{8 f \left(a +b \right)^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} a}-\frac{7 b^{2} \cos \left(f x +e \right)}{8 f \left(a +b \right)^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{5 b^{3} \cos \left(f x +e \right)}{4 f \left(a +b \right)^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} a}-\frac{3 b^{4} \cos \left(f x +e \right)}{8 f \left(a +b \right)^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} a^{2}}+\frac{15 b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{8 f \left(a +b \right)^{3} \sqrt{a b}}+\frac{5 b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{4 f \left(a +b \right)^{3} a \sqrt{a b}}+\frac{3 b^{3} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{8 f \left(a +b \right)^{3} a^{2} \sqrt{a b}}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \left(a +b \right)^{3}}-\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \left(a +b \right)^{3}}"," ",0,"-9/8/f*b/(a+b)^3/(b+a*cos(f*x+e)^2)^2*a*cos(f*x+e)^3-7/4/f*b^2/(a+b)^3/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3-5/8/f*b^3/(a+b)^3/(b+a*cos(f*x+e)^2)^2/a*cos(f*x+e)^3-7/8/f*b^2/(a+b)^3/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)-5/4/f*b^3/(a+b)^3/(b+a*cos(f*x+e)^2)^2/a*cos(f*x+e)-3/8/f*b^4/(a+b)^3/(b+a*cos(f*x+e)^2)^2/a^2*cos(f*x+e)+15/8/f*b/(a+b)^3/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+5/4/f*b^2/(a+b)^3/a/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+3/8/f*b^3/(a+b)^3/a^2/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+1/2/f/(a+b)^3*ln(-1+cos(f*x+e))-1/2/f/(a+b)^3*ln(1+cos(f*x+e))","B"
58,1,430,195,1.164000," ","int(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x)","-\frac{9 b \left(\cos^{3}\left(f x +e \right)\right) a^{2}}{8 f \left(a +b \right)^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{5 b^{2} \left(\cos^{3}\left(f x +e \right)\right) a}{4 f \left(a +b \right)^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{3} \left(\cos^{3}\left(f x +e \right)\right)}{8 f \left(a +b \right)^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{7 b^{2} a \cos \left(f x +e \right)}{8 f \left(a +b \right)^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{3 b^{3} \cos \left(f x +e \right)}{4 f \left(a +b \right)^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{4} \cos \left(f x +e \right)}{8 f \left(a +b \right)^{4} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} a}+\frac{15 b a \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{8 f \left(a +b \right)^{4} \sqrt{a b}}-\frac{5 b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{4 f \left(a +b \right)^{4} \sqrt{a b}}-\frac{b^{3} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{8 f \left(a +b \right)^{4} a \sqrt{a b}}+\frac{1}{4 f \left(a +b \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a}{4 f \left(a +b \right)^{4}}-\frac{5 \ln \left(-1+\cos \left(f x +e \right)\right) b}{4 f \left(a +b \right)^{4}}+\frac{1}{4 f \left(a +b \right)^{3} \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) a}{4 f \left(a +b \right)^{4}}+\frac{5 \ln \left(1+\cos \left(f x +e \right)\right) b}{4 f \left(a +b \right)^{4}}"," ",0,"-9/8/f*b/(a+b)^4/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3*a^2-5/4/f*b^2/(a+b)^4/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3*a-1/8/f*b^3/(a+b)^4/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3-7/8/f*b^2/(a+b)^4/(b+a*cos(f*x+e)^2)^2*a*cos(f*x+e)-3/4/f*b^3/(a+b)^4/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)+1/8/f*b^4/(a+b)^4/(b+a*cos(f*x+e)^2)^2/a*cos(f*x+e)+15/8/f*b/(a+b)^4*a/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))-5/4/f*b^2/(a+b)^4/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))-1/8/f*b^3/(a+b)^4/a/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))+1/4/f/(a+b)^3/(-1+cos(f*x+e))+1/4/f/(a+b)^4*ln(-1+cos(f*x+e))*a-5/4/f/(a+b)^4*ln(-1+cos(f*x+e))*b+1/4/f/(a+b)^3/(1+cos(f*x+e))-1/4/f/(a+b)^4*ln(1+cos(f*x+e))*a+5/4/f/(a+b)^4*ln(1+cos(f*x+e))*b","B"
59,1,567,237,1.240000," ","int(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x)","-\frac{9 b \left(\cos^{3}\left(f x +e \right)\right) a^{3}}{8 f \left(a +b \right)^{5} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{3 b^{2} \left(\cos^{3}\left(f x +e \right)\right) a^{2}}{4 f \left(a +b \right)^{5} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 b^{3} \left(\cos^{3}\left(f x +e \right)\right) a}{8 f \left(a +b \right)^{5} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{7 b^{2} \cos \left(f x +e \right) a^{2}}{8 f \left(a +b \right)^{5} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{3} \cos \left(f x +e \right) a}{4 f \left(a +b \right)^{5} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{5 b^{4} \cos \left(f x +e \right)}{8 f \left(a +b \right)^{5} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{15 b \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right) a^{2}}{8 f \left(a +b \right)^{5} \sqrt{a b}}-\frac{15 b^{2} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right) a}{4 f \left(a +b \right)^{5} \sqrt{a b}}+\frac{3 b^{3} \arctan \left(\frac{a \cos \left(f x +e \right)}{\sqrt{a b}}\right)}{8 f \left(a +b \right)^{5} \sqrt{a b}}-\frac{1}{16 f \left(a +b \right)^{3} \left(-1+\cos \left(f x +e \right)\right)^{2}}+\frac{3 a}{16 f \left(a +b \right)^{4} \left(-1+\cos \left(f x +e \right)\right)}-\frac{9 b}{16 f \left(a +b \right)^{4} \left(-1+\cos \left(f x +e \right)\right)}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) a^{2}}{16 f \left(a +b \right)^{5}}-\frac{15 \ln \left(-1+\cos \left(f x +e \right)\right) a b}{8 f \left(a +b \right)^{5}}+\frac{15 \ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{16 f \left(a +b \right)^{5}}+\frac{1}{16 f \left(a +b \right)^{3} \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{3 a}{16 f \left(a +b \right)^{4} \left(1+\cos \left(f x +e \right)\right)}-\frac{9 b}{16 f \left(a +b \right)^{4} \left(1+\cos \left(f x +e \right)\right)}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) a^{2}}{16 f \left(a +b \right)^{5}}+\frac{15 \ln \left(1+\cos \left(f x +e \right)\right) a b}{8 f \left(a +b \right)^{5}}-\frac{15 \ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{16 f \left(a +b \right)^{5}}"," ",0,"-9/8/f*b/(a+b)^5/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3*a^3-3/4/f*b^2/(a+b)^5/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3*a^2+3/8/f*b^3/(a+b)^5/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)^3*a-7/8/f*b^2/(a+b)^5/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)*a^2-1/4/f*b^3/(a+b)^5/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)*a+5/8/f*b^4/(a+b)^5/(b+a*cos(f*x+e)^2)^2*cos(f*x+e)+15/8/f*b/(a+b)^5/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))*a^2-15/4/f*b^2/(a+b)^5/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))*a+3/8/f*b^3/(a+b)^5/(a*b)^(1/2)*arctan(a*cos(f*x+e)/(a*b)^(1/2))-1/16/f/(a+b)^3/(-1+cos(f*x+e))^2+3/16/f/(a+b)^4/(-1+cos(f*x+e))*a-9/16/f/(a+b)^4/(-1+cos(f*x+e))*b+3/16/f/(a+b)^5*ln(-1+cos(f*x+e))*a^2-15/8/f/(a+b)^5*ln(-1+cos(f*x+e))*a*b+15/16/f/(a+b)^5*ln(-1+cos(f*x+e))*b^2+1/16/f/(a+b)^3/(1+cos(f*x+e))^2+3/16/f/(a+b)^4/(1+cos(f*x+e))*a-9/16/f/(a+b)^4/(1+cos(f*x+e))*b-3/16/f/(a+b)^5*ln(1+cos(f*x+e))*a^2+15/8/f/(a+b)^5*ln(1+cos(f*x+e))*a*b-15/16/f/(a+b)^5*ln(1+cos(f*x+e))*b^2","B"
60,1,689,292,1.277000," ","int(sin(f*x+e)^6/(a+b*sec(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 +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{23 b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 b \tan \left(f x +e \right)}{8 a^{2} f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{17 b^{2} \tan \left(f x +e \right)}{4 f \,a^{3} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{41 b^{3} \tan \left(f x +e \right)}{8 f \,a^{4} \left(a +b +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{\left(a +b \right) b}}\right)}{8 f \,a^{3} \sqrt{\left(a +b \right) b}}-\frac{95 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f \,a^{4} \sqrt{\left(a +b \right) b}}-\frac{20 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{5} \sqrt{\left(a +b \right) b}}-\frac{2 b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{f \,a^{5} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{2 b^{4} \tan \left(f x +e \right)}{f \,a^{5} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{10 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{6} \sqrt{\left(a +b \right) b}}-\frac{27 \left(\tan^{5}\left(f x +e \right)\right) b}{8 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{3 \left(\tan^{5}\left(f x +e \right)\right) b^{2}}{f \,a^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{11 \left(\tan^{5}\left(f x +e \right)\right)}{16 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{6 \left(\tan^{3}\left(f x +e \right)\right) b}{f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{6 \left(\tan^{3}\left(f x +e \right)\right) b^{2}}{f \,a^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{6 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \tan \left(f x +e \right)}{16 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{21 \tan \left(f x +e \right) b}{8 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{3 \tan \left(f x +e \right) b^{2}}{f \,a^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{45 \arctan \left(\tan \left(f x +e \right)\right) b}{8 f \,a^{4}}+\frac{15 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f \,a^{5}}+\frac{10 \arctan \left(\tan \left(f x +e \right)\right) b^{3}}{f \,a^{6}}+\frac{5 \arctan \left(\tan \left(f x +e \right)\right)}{16 f \,a^{3}}"," ",0,"-7/8/f*b^2/a^3/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-23/8/f*b^3/a^4/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-9/8*b*tan(f*x+e)/a^2/f/(a+b+b*tan(f*x+e)^2)^2-17/4/f*b^2/a^3/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-41/8/f*b^3/a^4/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-15/8/f*b/a^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-95/8/f*b^2/a^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-20/f*b^3/a^5/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-2/f*b^4/a^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-2/f*b^4/a^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-10/f*b^4/a^6/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-27/8/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b-3/f/a^5/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b^2-11/16/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5-6/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b-6/f/a^5/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b^2-5/6/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3-5/16/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)-21/8/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b-3/f/a^5/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b^2+45/8/f/a^4*arctan(tan(f*x+e))*b+15/f/a^5*arctan(tan(f*x+e))*b^2+10/f/a^6*arctan(tan(f*x+e))*b^3+5/16/f/a^3*arctan(tan(f*x+e))","B"
61,1,423,218,1.176000," ","int(sin(f*x+e)^4/(a+b*sec(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 +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)}{2 f \,a^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 b \tan \left(f x +e \right)}{8 a^{2} f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{21 b^{2} \tan \left(f x +e \right)}{8 f \,a^{3} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{3 b^{3} \tan \left(f x +e \right)}{2 f \,a^{4} \left(a +b +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{\left(a +b \right) b}}\right)}{8 f \,a^{3} \sqrt{\left(a +b \right) b}}-\frac{15 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,a^{4} \sqrt{\left(a +b \right) b}}-\frac{6 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{5} \sqrt{\left(a +b \right) b}}-\frac{3 \left(\tan^{3}\left(f x +e \right)\right) b}{2 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \tan \left(f x +e \right)}{8 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \tan \left(f x +e \right) b}{2 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{9 \arctan \left(\tan \left(f x +e \right)\right) b}{2 f \,a^{4}}+\frac{6 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f \,a^{5}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right)}{8 f \,a^{3}}"," ",0,"-7/8/f*b^2/a^3/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-3/2/f*b^3/a^4/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-9/8*b*tan(f*x+e)/a^2/f/(a+b+b*tan(f*x+e)^2)^2-21/8/f*b^2/a^3/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-3/2/f*b^3/a^4/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-15/8/f*b/a^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-15/2/f*b^2/a^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-6/f*b^3/a^5/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-3/2/f/a^4/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3*b-5/8/f/a^3/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3-3/8/f/a^3/(tan(f*x+e)^2+1)^2*tan(f*x+e)-3/2/f/a^4/(tan(f*x+e)^2+1)^2*tan(f*x+e)*b+9/2/f/a^4*arctan(tan(f*x+e))*b+6/f/a^5*arctan(tan(f*x+e))*b^2+3/8/f/a^3*arctan(tan(f*x+e))","A"
62,1,314,166,0.960000," ","int(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}-\frac{b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{f \,a^{3} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}-\frac{9 b \tan \left(f x +e \right)}{8 a^{2} f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{2} \tan \left(f x +e \right)}{f \,a^{3} \left(a +b +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{\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{\tan \left(f x +e \right) b}{\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{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{4} \left(a +b \right) \sqrt{\left(a +b \right) b}}-\frac{\tan \left(f x +e \right)}{2 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{2 f \,a^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b}{f \,a^{4}}"," ",0,"-7/8/f/a^2*b^2/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)^3-1/f/a^3*b^3/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)^3-9/8*b*tan(f*x+e)/a^2/f/(a+b+b*tan(f*x+e)^2)^2-1/f*b^2/a^3/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-15/8/f/a^2*b/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-5/f/a^3*b^2/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-3/f/a^4*b^3/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/2/f/a^3*tan(f*x+e)/(tan(f*x+e)^2+1)+1/2/f/a^3*arctan(tan(f*x+e))+3/f/a^4*arctan(tan(f*x+e))*b","A"
63,1,321,130,0.968000," ","int(1/(a+b*sec(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f a \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{2 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{9 b \tan \left(f x +e \right)}{8 a \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{2} \tan \left(f x +e \right)}{2 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}-\frac{15 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\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{\tan \left(f x +e \right) b}{\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{\tan \left(f x +e \right) b}{\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{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"-7/8/f/a*b^2/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3-1/2/f/a^2*b^3/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3-9/8*b*tan(f*x+e)/a/(a+b)/f/(a+b+b*tan(f*x+e)^2)^2-1/2/f/a^2*b^2/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)-15/8/f/a*b/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-5/2/f/a^2*b^2/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a^3*b^3/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a^3*arctan(tan(f*x+e))","B"
64,1,157,108,1.071000," ","int(csc(f*x+e)^2/(a+b*sec(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 +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 a b \tan \left(f x +e \right)}{8 \left(a +b \right)^{3} f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 b^{2} \tan \left(f x +e \right)}{8 f \left(a +b \right)^{3} \left(a +b +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{\left(a +b \right) b}}\right)}{8 f \left(a +b \right)^{3} \sqrt{\left(a +b \right) b}}-\frac{1}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}"," ",0,"-7/8/f/(a+b)^3*b^2/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-9/8*a*b*tan(f*x+e)/(a+b)^3/f/(a+b+b*tan(f*x+e)^2)^2-9/8/f/(a+b)^3*b^2/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-15/8/f/(a+b)^3*b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/(a+b)^3/tan(f*x+e)","A"
65,1,306,148,1.231000," ","int(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right) a}{8 f \left(a +b \right)^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{2 f \left(a +b \right)^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{9 b \tan \left(f x +e \right) a^{2}}{8 f \left(a +b \right)^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{5 b^{2} \tan \left(f x +e \right) a}{8 f \left(a +b \right)^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{3} \tan \left(f x +e \right)}{2 f \left(a +b \right)^{4} \left(a +b +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{\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{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \left(a +b \right)^{4} \sqrt{\left(a +b \right) b}}-\frac{1}{3 f \left(a +b \right)^{3} \tan \left(f x +e \right)^{3}}-\frac{a}{f \left(a +b \right)^{4} \tan \left(f x +e \right)}+\frac{2 b}{f \left(a +b \right)^{4} \tan \left(f x +e \right)}"," ",0,"-7/8/f/(a+b)^4*b^2/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3*a+1/2/f/(a+b)^4*b^3/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-9/8/f/(a+b)^4*b/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)*a^2-5/8/f/(a+b)^4*b^2/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)*a+1/2/f/(a+b)^4*b^3/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-15/8/f/(a+b)^4*b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))*a+5/2/f/(a+b)^4*b^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/3/f/(a+b)^3/tan(f*x+e)^3-1/f/(a+b)^4/tan(f*x+e)*a+2/f/(a+b)^4/tan(f*x+e)*b","B"
66,1,411,222,1.178000," ","int(csc(f*x+e)^6/(a+b*sec(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 +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}{f \left(a +b \right)^{5} \left(a +b +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 +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{2} \tan \left(f x +e \right) a^{2}}{8 f \left(a +b \right)^{5} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{3} \tan \left(f x +e \right) a}{f \left(a +b \right)^{5} \left(a +b +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{\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{\tan \left(f x +e \right) b}{\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{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{5} \sqrt{\left(a +b \right) b}}-\frac{1}{5 f \left(a +b \right)^{3} \tan \left(f x +e \right)^{5}}-\frac{2 a}{3 f \left(a +b \right)^{4} \tan \left(f x +e \right)^{3}}+\frac{b}{3 f \left(a +b \right)^{4} \tan \left(f x +e \right)^{3}}-\frac{a^{2}}{f \left(a +b \right)^{5} \tan \left(f x +e \right)}+\frac{4 a b}{f \left(a +b \right)^{5} \tan \left(f x +e \right)}-\frac{b^{2}}{f \left(a +b \right)^{5} \tan \left(f x +e \right)}"," ",0,"-7/8/f*b^2/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3*a^2+1/f*b^3/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3*a-9/8/f*b/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)*a^3-1/8/f*b^2/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)*a^2+1/f*b^3/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)*a-15/8/f*b/(a+b)^5/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))*a^2+5/f*b^2/(a+b)^5/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))*a-1/f*b^3/(a+b)^5/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/5/f/(a+b)^3/tan(f*x+e)^5-2/3/f/(a+b)^4/tan(f*x+e)^3*a+1/3/f/(a+b)^4/tan(f*x+e)^3*b-1/f/(a+b)^5/tan(f*x+e)*a^2+4/f/(a+b)^5/tan(f*x+e)*a*b-1/f/(a+b)^5/tan(f*x+e)*b^2","A"
67,1,1840,123,4.584000," ","int(sin(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/30/f*(-1+cos(f*x+e))^2*(-4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*b^(3/2)*(a+b)^(3/2)+30*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*b^(1/2)*(a+b)^(3/2)*4^(1/2)*a^2+15*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(5/2)*4^(1/2)*a^2-15*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(5/2)*4^(1/2)*a^2+10*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*b^(1/2)*(a+b)^(3/2)*a+15*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(3/2)*4^(1/2)*a^3-15*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(3/2)*4^(1/2)*a^3-15*cos(f*x+e)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*(a+b)^(3/2)*4^(1/2)*a^2*b-4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^4*b^(3/2)*(a+b)^(3/2)-16*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^3*b^(3/2)*(a+b)^(3/2)-24*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^2*b^(3/2)*(a+b)^(3/2)-16*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)*b^(3/2)*(a+b)^(3/2)+16*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^4*b^(1/2)*(a+b)^(3/2)*a-56*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^3*b^(1/2)*(a+b)^(3/2)*a-84*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^2*b^(1/2)*(a+b)^(3/2)*a+15*cos(f*x+e)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(5/2)*4^(1/2)*a^2-15*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(5/2)*4^(1/2)*a^2-15*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)*(a+b)^(3/2)*4^(1/2)*a+15*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*(a+b)^(3/2)*4^(1/2)*a^2-20*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)*b^(1/2)*(a+b)^(3/2)*a+15*cos(f*x+e)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(3/2)*4^(1/2)*a^3-15*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(3/2)*4^(1/2)*a^3-15*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*(a+b)^(3/2)*4^(1/2)*a^2*b+6*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^6*b^(1/2)*(a+b)^(3/2)*a+24*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^5*b^(1/2)*(a+b)^(3/2)*a)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)/sin(f*x+e)^4/b^(1/2)/(a+b)^(3/2)/a^2","B"
68,1,1525,88,1.841000," ","int(sin(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(2 \left(\cos^{4}\left(f x +e \right)\right) \left(a +b \right)^{\frac{3}{2}} \sqrt{b}\, \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}}+8 \left(\cos^{3}\left(f x +e \right)\right) \left(a +b \right)^{\frac{3}{2}} \sqrt{b}\, \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}}+6 \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \right)^{\frac{3}{2}} \sqrt{b}\, \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}}+3 \cos \left(f x +e \right) \sqrt{4}\, b^{\frac{5}{2}} \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a -3 \cos \left(f x +e \right) \sqrt{4}\, b^{\frac{5}{2}} \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a -6 \cos \left(f x +e \right) \left(a +b \right)^{\frac{3}{2}} \sqrt{4}\, \sqrt{b}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a +3 \cos \left(f x +e \right) \left(a +b \right)^{\frac{3}{2}} \sqrt{4}\, \arctanh \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right) \sqrt{4}-2 \cos \left(f x +e \right)-\sqrt{4}-2\right) \sqrt{b}\, \sqrt{4}}{8 \sin \left(f x +e \right)^{2} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right) a b -4 \cos \left(f x +e \right) \left(a +b \right)^{\frac{3}{2}} \sqrt{b}\, \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}}+3 \cos \left(f x +e \right) \sqrt{4}\, b^{\frac{3}{2}} \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a^{2}-3 \cos \left(f x +e \right) \sqrt{4}\, b^{\frac{3}{2}} \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a^{2}+3 \left(a +b \right)^{\frac{3}{2}} \sqrt{4}\, b^{\frac{3}{2}} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+3 \sqrt{4}\, b^{\frac{5}{2}} \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a -3 \sqrt{4}\, b^{\frac{5}{2}} \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a -3 \left(a +b \right)^{\frac{3}{2}} \sqrt{4}\, \sqrt{b}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a +3 \left(a +b \right)^{\frac{3}{2}} \sqrt{4}\, \arctanh \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right) \sqrt{4}-2 \cos \left(f x +e \right)-\sqrt{4}-2\right) \sqrt{b}\, \sqrt{4}}{8 \sin \left(f x +e \right)^{2} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right) a b -4 \left(a +b \right)^{\frac{3}{2}} \sqrt{b}\, \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}}+3 \sqrt{4}\, b^{\frac{3}{2}} \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a^{2}-3 \sqrt{4}\, b^{\frac{3}{2}} \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a^{2}\right) \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}}{6 f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sin \left(f x +e \right)^{4} \sqrt{b}\, a \left(a +b \right)^{\frac{3}{2}}}"," ",0,"1/6/f*(-1+cos(f*x+e))^2*(2*cos(f*x+e)^4*(a+b)^(3/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)+8*cos(f*x+e)^3*(a+b)^(3/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)+6*cos(f*x+e)^2*(a+b)^(3/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)+3*cos(f*x+e)*4^(1/2)*b^(5/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-3*cos(f*x+e)*4^(1/2)*b^(5/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-6*cos(f*x+e)*(a+b)^(3/2)*4^(1/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+3*cos(f*x+e)*(a+b)^(3/2)*4^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a*b-4*cos(f*x+e)*(a+b)^(3/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)+3*cos(f*x+e)*4^(1/2)*b^(3/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2-3*cos(f*x+e)*4^(1/2)*b^(3/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2+3*(a+b)^(3/2)*4^(1/2)*b^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)+3*4^(1/2)*b^(5/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-3*4^(1/2)*b^(5/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-3*(a+b)^(3/2)*4^(1/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+3*(a+b)^(3/2)*4^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a*b-4*(a+b)^(3/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)+3*4^(1/2)*b^(3/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2-3*4^(1/2)*b^(3/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)/sin(f*x+e)^4/b^(1/2)/a/(a+b)^(3/2)","B"
69,1,93,58,0.528000," ","int(sin(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{f a \sec \left(f x +e \right)}+\frac{b \sec \left(f x +e \right) \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{f a}+\frac{\sqrt{b}\, \ln \left(\sec \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}\right)}{f}"," ",0,"-1/f/a/sec(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2)+1/f/a*b*sec(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2)+1/f*b^(1/2)*ln(sec(f*x+e)*b^(1/2)+(a+b*sec(f*x+e)^2)^(1/2))","A"
70,1,688,70,2.013000," ","int(csc(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{4}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\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{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right)+2 \arctanh \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right) \sqrt{4}-2 \cos \left(f x +e \right)-\sqrt{4}-2\right) \sqrt{b}\, \sqrt{4}}{8 \sin \left(f x +e \right)^{2} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}}\right) \sqrt{a +b}\, b -\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a \sqrt{b}-\ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) \sqrt{b}\, a -\ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) b^{\frac{3}{2}}\right) \left(-1+\cos \left(f x +e \right)\right)}{4 f \sin \left(f x +e \right)^{2} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{b}\, \sqrt{a +b}}"," ",0,"-1/4/f*4^(1/2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)*(ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(3/2)-2*b^(3/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))+2*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*(a+b)^(1/2)*b-ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b^(1/2)-ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^(1/2)*a-ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^(3/2))*(-1+cos(f*x+e))/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)/b^(1/2)/(a+b)^(1/2)","B"
71,1,3015,106,1.719000," ","int(csc(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/8/f*(-1+cos(f*x+e))*(-2*cos(f*x+e)*(a+b)^(3/2)*4^(1/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+4*cos(f*x+e)^2*(a+b)^(3/2)*4^(1/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a-4*cos(f*x+e)^2*(a+b)^(3/2)*4^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a*b-4^(1/2)*b^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3-5*4^(1/2)*b^(5/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a+4*(a+b)^(3/2)*4^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^2+4*cos(f*x+e)^2*4^(1/2)*b^(7/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))-2*cos(f*x+e)^2*4^(1/2)*b^(7/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))-4*4^(1/2)*b^(3/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2-4^(1/2)*b^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3-4*4^(1/2)*b^(7/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))-8*cos(f*x+e)^2*(a+b)^(3/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)-16*cos(f*x+e)*(a+b)^(3/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)+2*(a+b)^(3/2)*4^(1/2)*b^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)+3*4^(1/2)*b^(5/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-8*4^(1/2)*b^(5/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-4*4^(1/2)*b^(3/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2-8*(a+b)^(3/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)+2*cos(f*x+e)^2*4^(1/2)*b^(7/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))+5*cos(f*x+e)^2*4^(1/2)*b^(5/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a+8*cos(f*x+e)^2*4^(1/2)*b^(5/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-3*cos(f*x+e)^2*4^(1/2)*b^(5/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-4*cos(f*x+e)^2*(a+b)^(3/2)*4^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^2+4*cos(f*x+e)^2*4^(1/2)*b^(3/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2+4*cos(f*x+e)^2*4^(1/2)*b^(3/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2+cos(f*x+e)^2*4^(1/2)*b^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3+cos(f*x+e)^2*4^(1/2)*b^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3-2*cos(f*x+e)*(a+b)^(3/2)*4^(1/2)*b^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)+2*4^(1/2)*b^(7/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))-2*4^(1/2)*b^(7/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))-2*(a+b)^(3/2)*4^(1/2)*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+4*(a+b)^(3/2)*4^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a*b)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)/sin(f*x+e)^4/(a+b)^(5/2)/b^(1/2)","B"
72,1,9758,161,1.897000," ","int(csc(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
73,1,2665,214,3.356000," ","int(sin(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/48/f*(-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*sin(f*x+e)-10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b-40*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2+40*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a^2*b-14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)+10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3-26*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3+26*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3+33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^3-33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^3-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+90*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)+30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)-15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)-96*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e))*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*sin(f*x+e)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/a^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
74,1,1939,159,1.490000," ","int(sin(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\left(2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} \sin \left(f x +e \right)-12 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)+16 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}-5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2}+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b +5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}+5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) a \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/8/f*(2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)-12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)+16*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/a/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
75,1,1290,105,1.182000," ","int(sin(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\left(-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)-4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)+\left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a +\cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/2/f*(-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*sin(f*x+e)+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)+cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)*cos(f*x+e)*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
76,1,588,67,4.737000," ","int((a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{2}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a +\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b -2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b -2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \right) \cos \left(f x +e \right) \left(\sin^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}}{f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/f*2^(1/2)*(EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a+EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b-2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b-2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a)*cos(f*x+e)*sin(f*x+e)^2*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
77,1,1003,60,2.062000," ","int(csc(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, b -2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right) \cos \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right)}{f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \sin \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/f*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)*(EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*b-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)*cos(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)-cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/(b+a*cos(f*x+e)^2)/sin(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
78,1,3847,93,1.857000," ","int(csc(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"1/3/f*(-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a*b-3*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^3*sin(f*x+e)*a*b+6*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*a*b+6*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a*b+3*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2-6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)*sin(f*x+e)*a*b-6*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2+3*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)-6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*b^2*sin(f*x+e)-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+3*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(b+a*cos(f*x+e)^2)/sin(f*x+e)^3/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(a+b)","C"
79,1,8587,133,1.835000," ","int(csc(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
80,1,2537,172,1.773000," ","int((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^5,x)","\text{Expression too large to display}"," ",0,"1/60/f*(-1+cos(f*x+e))^3*(60*cos(f*x+e)^2*b^(13/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-60*cos(f*x+e)^2*b^(13/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a+45*cos(f*x+e)^2*b^(5/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^5-45*cos(f*x+e)^2*b^(5/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^5+6*cos(f*x+e)^2*b^(7/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)-15*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2)*(a+b)^(7/2)*a-15*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(3/2)*(a+b)^(7/2)*a^2+315*cos(f*x+e)^2*b^(9/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3+6*cos(f*x+e)^3*b^(7/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)+225*cos(f*x+e)^2*b^(11/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2-225*cos(f*x+e)^2*b^(11/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2-315*cos(f*x+e)^2*b^(9/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3+195*cos(f*x+e)^2*b^(7/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4-195*cos(f*x+e)^2*b^(7/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4-45*cos(f*x+e)^2*(a+b)^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a^3*b+15*cos(f*x+e)^2*(a+b)^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a^2*b^2+60*cos(f*x+e)^2*(a+b)^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a*b^3-8*cos(f*x+e)^5*b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2+12*cos(f*x+e)^4*b^(5/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a-20*a^3*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)^5-8*a^2*b^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)^4-74*b^(5/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)^3*a-20*cos(f*x+e)^4*b^(1/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^3-50*cos(f*x+e)^3*b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2-74*cos(f*x+e)^2*b^(5/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+30*cos(f*x+e)^3*b^(1/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^3-50*a^2*b^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)^2-15*b^(5/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)*a+30*cos(f*x+e)^2*b^(1/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^3-15*a^2*b^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)+6*a^2*b^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)^7+6*a^3*b^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)^7+6*a^2*b^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)^6+12*b^(5/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*cos(f*x+e)^5*a+6*cos(f*x+e)^6*b^(1/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^3)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*4^(1/2)/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)/sin(f*x+e)^6/a/b^(1/2)/(a+b)^(9/2)","B"
81,1,1913,142,1.430000," ","int((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^3,x)","\text{Expression too large to display}"," ",0,"-1/12/f*(-1+cos(f*x+e))^3*(-6*cos(f*x+e)^2*b^(13/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))-6*cos(f*x+e)^2*b^(7/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3+6*cos(f*x+e)^2*b^(7/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3+8*cos(f*x+e)^3*b^(5/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)+8*cos(f*x+e)^2*b^(5/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)+3*cos(f*x+e)*b^(5/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)+3*b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a-6*cos(f*x+e)^2*(a+b)^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^3-18*cos(f*x+e)^2*b^(11/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a+18*cos(f*x+e)^2*b^(11/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-18*cos(f*x+e)^2*b^(9/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2+18*cos(f*x+e)^2*b^(9/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2+6*cos(f*x+e)^2*b^(13/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))+3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2)*(a+b)^(7/2)+9*cos(f*x+e)^2*(a+b)^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a^2*b+3*cos(f*x+e)^2*(a+b)^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a*b^2+2*cos(f*x+e)^5*b^(1/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2+2*cos(f*x+e)^4*b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+2*cos(f*x+e)^4*b^(1/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2+2*cos(f*x+e)^3*b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a-6*cos(f*x+e)^3*b^(1/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2+2*cos(f*x+e)^2*b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a-6*cos(f*x+e)^2*b^(1/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2+3*cos(f*x+e)*b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+2*cos(f*x+e)^5*b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*4^(1/2)/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)/sin(f*x+e)^6/b^(1/2)/(a+b)^(9/2)","B"
82,1,121,86,0.355000," ","int((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e),x)","-\frac{\left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{\frac{5}{2}}}{f a \sec \left(f x +e \right)}+\frac{b \sec \left(f x +e \right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{f a}+\frac{3 b \sec \left(f x +e \right) \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{2 f}+\frac{3 a \sqrt{b}\, \ln \left(\sec \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}\right)}{2 f}"," ",0,"-1/f/a/sec(f*x+e)*(a+b*sec(f*x+e)^2)^(5/2)+1/f/a*b*sec(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2)+3/2*b*sec(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2)/f+3/2/f*a*b^(1/2)*ln(sec(f*x+e)*b^(1/2)+(a+b*sec(f*x+e)^2)^(1/2))","A"
83,1,2563,104,1.581000," ","int(csc(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/4/f*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*4^(1/2)*cos(f*x+e)*(-1+cos(f*x+e))^3*(-cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^(13/2)-15*cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^(9/2)*a^2-6*cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^(11/2)*a-cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^(1/2)*a^6-cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(1/2)*a^6-6*cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^(3/2)*a^5-6*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(3/2)*a^5-6*cos(f*x+e)^2*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(5/2)*a^4-15*cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^(5/2)*a^4-9*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^(5/2)*a^4-20*cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^(7/2)*a^3+cos(f*x+e)^2*b^(13/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))-20*cos(f*x+e)^2*b^(7/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3+cos(f*x+e)*b^(5/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)+b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+2*cos(f*x+e)^2*(a+b)^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*b^3+6*cos(f*x+e)^2*b^(11/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a-12*cos(f*x+e)^2*b^(11/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a+9*cos(f*x+e)^2*b^(9/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2-24*cos(f*x+e)^2*b^(9/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2-2*cos(f*x+e)^2*b^(13/2)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(5/2)*(a+b)^(7/2)+3*cos(f*x+e)^2*(a+b)^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a^2*b+5*cos(f*x+e)^2*(a+b)^(7/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*a*b^2+cos(f*x+e)*b^(3/2)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a)/sin(f*x+e)^6/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)/b^(1/2)/(a+b)^(9/2)","B"
84,1,5178,139,1.825000," ","int(csc(f*x+e)^3*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
85,1,10199,190,2.132000," ","int(csc(f*x+e)^5*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
86,1,3067,266,2.275000," ","int((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^6,x)","\text{output too large to display}"," ",0,"-1/48/f*(270*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^2*b+94*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b-68*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b+68*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2-24*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2-94*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b-26*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3+26*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3+33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3-33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^9*a^3-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^8*a^3+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*b^3-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*b^3-144*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*a^2*b+240*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b^2-63*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*b-75*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b^2-90*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a*b^2+24*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a*b^2-22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^2*b+22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^2*b+17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a*b^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*b^3-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*b^3+15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*sin(f*x+e)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/a/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
87,1,2309,189,1.796000," ","int((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^4,x)","\frac{\left(2 \left(\cos^{7}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}+6 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2}-36 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b +6 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}-3 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{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 \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b +9 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2}+24 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -24 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}-2 \left(\cos^{6}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}-5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}+7 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}-7 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b +5 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -5 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}+4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \cos \left(f x +e \right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\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(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/8/f*(2*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+6*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2-36*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b+6*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-3*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2+6*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+9*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+24*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*a*b-24*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-2*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2+7*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2-7*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+5*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-5*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*sin(f*x+e)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
88,1,1583,139,1.260000," ","int((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^2,x)","\frac{\left(6 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -2 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}+2 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2}-6 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b -\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2}+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \cos \left(f x +e \right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/2/f*(6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*a*b-2*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2+2*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2-6*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b-sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2+cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*sin(f*x+e)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
89,1,1557,100,1.471000," ","int((a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\left(6 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +2 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}-2 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2}-3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b -\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2}+4 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \cos \left(f x +e \right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/2/f*(6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*a*b+2*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-2*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2-3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+4*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*sin(f*x+e)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
90,1,2032,91,1.401000," ","int(csc(f*x+e)^2*(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \cos \left(f x +e \right) \left(6 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +6 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -3 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2}+6 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +6 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}-3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b -3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}+3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{2 f \sin \left(f x +e \right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/2/f*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)*(6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^3*sin(f*x+e)*a*b+6*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a*b-3*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*a*b+6*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2+3*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+3*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/sin(f*x+e)/(b+a*cos(f*x+e)^2)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
91,1,3925,152,1.570000," ","int(csc(f*x+e)^4*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"1/6/f*(-9*cos(f*x+e)^5*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a*b-15*cos(f*x+e)^5*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^2+18*cos(f*x+e)^5*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b+30*cos(f*x+e)^5*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^2-9*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a*b-15*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^2+18*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b+30*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^2+9*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a*b+15*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2-18*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^3*sin(f*x+e)*a*b-30*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2+4*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+15*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+9*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+15*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2-18*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*a*b-30*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2-16*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+15*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-20*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(b+a*cos(f*x+e)^2)^2/sin(f*x+e)^3/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
92,1,8726,185,2.443000," ","int(csc(f*x+e)^6*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
93,1,105,111,1.960000," ","int(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(3 \left(\cos^{4}\left(f x +e \right)\right) a^{2}-10 a^{2} \left(\cos^{2}\left(f x +e \right)\right)-4 \left(\cos^{2}\left(f x +e \right)\right) a b +15 a^{2}+20 a b +8 b^{2}\right)}{15 f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) a^{3}}"," ",0,"-1/15/f*(b+a*cos(f*x+e)^2)*(3*cos(f*x+e)^4*a^2-10*a^2*cos(f*x+e)^2-4*cos(f*x+e)^2*a*b+15*a^2+20*a*b+8*b^2)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/a^3","A"
94,1,69,66,1.494000," ","int(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(\cos^{2}\left(f x +e \right)\right)-3 a -2 b \right)}{3 f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) a^{2}}"," ",0,"1/3/f*(b+a*cos(f*x+e)^2)*(a*cos(f*x+e)^2-3*a-2*b)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/a^2","A"
95,1,31,28,0.360000," ","int(sin(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{f a \sec \left(f x +e \right)}"," ",0,"-1/f/a/sec(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2)","A"
96,1,280,37,1.741000," ","int(csc(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\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{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right)+\ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right)\right) \left(\sin^{2}\left(f x +e \right)\right)}{2 f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{a +b}}"," ",0,"1/2/f*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))+ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e))))*sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/(a+b)^(1/2)","B"
97,1,2199,75,1.860000," ","int(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/4/f*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^3*a^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^3*a*b+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^3*a^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^3*a*b+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^2*a^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^2*a*b+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*a^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*a*b-2*cos(f*x+e)^2*(a+b)^(3/2)*a-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*a^2-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*a*b-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a^2-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a*b-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a*b-2*(a+b)^(3/2)*b)*sin(f*x+e)^2/(-1+cos(f*x+e))^2/cos(f*x+e)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(1+cos(f*x+e))^2/(a+b)^(5/2)","B"
98,1,4983,122,1.919000," ","int(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"1/16/f*(-10*(a+b)^(5/2)*a*b-3*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^2-6*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b-3*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^2-6*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b-3*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^2-6*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b-3*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^2+12*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b+6*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^2+12*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b+6*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^2+12*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b+6*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^2+12*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b+6*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^2-6*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b-3*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^2-6*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b-3*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^2+6*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4-3*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4+6*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4+6*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4-3*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4-3*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4-3*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4-6*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b-3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^2-3*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4-6*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b-3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^2+2*(a+b)^(5/2)*cos(f*x+e)^2*a*b-3*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4+6*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4-3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4-6*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b-3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4+6*(a+b)^(5/2)*cos(f*x+e)^4*a^2-10*(a+b)^(5/2)*cos(f*x+e)^2*a^2-4*(a+b)^(5/2)*b^2)/(-1+cos(f*x+e))^2/cos(f*x+e)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(1+cos(f*x+e))^2/(a+b)^(9/2)","B"
99,1,2425,173,1.759000," ","int(sin(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \left(90 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \,b^{2} \sin \left(f x +e \right)-45 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} b \sin \left(f x +e \right)+33 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b +40 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}-33 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a^{2} b -40 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a \,b^{2}-8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{7}\left(f x +e \right)\right) a^{3}-33 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{3}+15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -26 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{3}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2} b -14 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2} b -5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a \,b^{2}+14 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b +5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}+8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{6}\left(f x +e \right)\right) a^{3}-15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{3}+26 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{3}+33 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{3}+30 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{3} \sin \left(f x +e \right)+30 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{3} \sin \left(f x +e \right)-15 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{3} \sin \left(f x +e \right)-15 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{3} \sin \left(f x +e \right)+90 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} b \sin \left(f x +e \right)-45 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \,b^{2} \sin \left(f x +e \right)\right)}{48 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}}"," ",0,"1/48/f*sin(f*x+e)*(30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*sin(f*x+e)-14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a^2*b-40*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b-45*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)+30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3-26*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3+26*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3-33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^3+33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^3-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3+33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+40*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*sin(f*x+e)-15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)+90*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)+90*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)-45*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^3","C"
100,1,1701,119,1.439000," ","int(sin(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \left(2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} \sin \left(f x +e \right)-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} \sin \left(f x +e \right)+12 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)-5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b +5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}+5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}}"," ",0,"1/8/f*sin(f*x+e)*(2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)+12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^2","C"
101,1,1055,73,1.562000," ","int(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sin \left(f x +e \right) \left(\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)+\left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a +\cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a}"," ",0,"-1/2/f*sin(f*x+e)*(2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)+cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a","C"
102,1,380,33,2.470000," ","int(1/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right)-2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right)\right) \left(\sin^{2}\left(f x +e \right)\right)}{f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/f*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*(EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)))*sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
103,1,48,31,1.699000," ","int(csc(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right)}{f \sin \left(f x +e \right) \left(a +b \right)}"," ",0,"-1/f*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)/sin(f*x+e)/(a+b)","A"
104,1,66,70,1.635000," ","int(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\left(2 a \left(\cos^{2}\left(f x +e \right)\right)-3 a -b \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right)}{3 f \sin \left(f x +e \right)^{3} \left(a +b \right)^{2}}"," ",0,"1/3/f*(2*a*cos(f*x+e)^2-3*a-b)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)/sin(f*x+e)^3/(a+b)^2","A"
105,1,101,120,1.681000," ","int(csc(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\left(8 \left(\cos^{4}\left(f x +e \right)\right) a^{2}-20 a^{2} \left(\cos^{2}\left(f x +e \right)\right)-4 \left(\cos^{2}\left(f x +e \right)\right) a b +15 a^{2}+10 a b +3 b^{2}\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right)}{15 f \sin \left(f x +e \right)^{5} \left(a +b \right)^{3}}"," ",0,"-1/15/f*(8*cos(f*x+e)^4*a^2-20*a^2*cos(f*x+e)^2-4*cos(f*x+e)^2*a*b+15*a^2+10*a*b+3*b^2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)/sin(f*x+e)^5/(a+b)^3","A"
106,1,35190,155,3.236000," ","int(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
107,1,12782,102,1.903000," ","int(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
108,1,59,58,0.290000," ","int(sin(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{-\frac{1}{a \sec \left(f x +e \right) \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}-\frac{2 b \sec \left(f x +e \right)}{a^{2} \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}}{f}"," ",0,"1/f*(-1/a/sec(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2)-2*b/a^2*sec(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2))","A"
109,1,1094,72,2.126000," ","int(csc(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) \cos \left(f x +e \right) a^{2}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) \cos \left(f x +e \right) a b +\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) \cos \left(f x +e \right) a^{2}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) \cos \left(f x +e \right) a b +\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a^{2}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a b +\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) a^{2}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) a b +2 \left(a +b \right)^{\frac{3}{2}} b \right)}{2 f \cos \left(f x +e \right)^{3} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(a +b \right)^{\frac{5}{2}} a}"," ",0,"-1/2/f*(b+a*cos(f*x+e)^2)*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*a^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*a*b+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a*b+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a*b+2*(a+b)^(3/2)*b)/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(a+b)^(5/2)/a","B"
110,1,3289,110,2.292000," ","int(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"1/4/f/(b+a*cos(f*x+e)^2)^2*(2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^3-2*cos(f*x+e)^2*(a+b)^(5/2)*a+4*cos(f*x+e)^2*(a+b)^(5/2)*b+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^3-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^3*a^3-2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^3*b^3+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^3*a^3-2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^3*b^3+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*a^3-2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*b^3+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^2*a^3-2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^2*b^3-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a^3+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*b^3-((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*a^3+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*b^3+3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a*b^2+3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b^2-3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^3*a*b^2-3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^3*a*b^2-3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)^2*a*b^2-3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)^2*a*b^2+3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a*b^2+3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*a*b^2-6*(a+b)^(5/2)*b)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^3/sin(f*x+e)^2/(a+b)^(9/2)","B"
111,1,8268,157,2.068000," ","int(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
112,1,2437,218,1.933000," ","int(sin(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-450 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \,b^{2} \sin \left(f x +e \right)+135 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} b \sin \left(f x +e \right)-81 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b -190 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}+81 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a^{2} b +190 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a \,b^{2}+8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{7}\left(f x +e \right)\right) a^{3}+33 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{3}-105 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}+14 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2} b +26 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{3}-14 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2} b +68 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2} b +35 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a \,b^{2}-68 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b -35 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{6}\left(f x +e \right)\right) a^{3}+105 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{3}-26 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{3}-33 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{3}-210 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{3} \sin \left(f x +e \right)-30 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{3} \sin \left(f x +e \right)+15 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{3} \sin \left(f x +e \right)+105 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{3} \sin \left(f x +e \right)-270 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} b \sin \left(f x +e \right)+225 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \,b^{2} \sin \left(f x +e \right)\right) \sin \left(f x +e \right)}{48 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{3} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{4}}"," ",0,"-1/48/f*(b+a*cos(f*x+e)^2)*(-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*sin(f*x+e)+68*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+35*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2+81*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a^2*b+190*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2-14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+225*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)-210*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)+14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b-68*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-35*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3+26*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3-26*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3+33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^3-33*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^3+105*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-81*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-190*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*sin(f*x+e)+105*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-270*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)-450*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)+135*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)-105*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^4","C"
113,1,1714,155,1.296000," ","int(sin(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} \sin \left(f x +e \right)+18 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b \sin \left(f x +e \right)+15 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} \sin \left(f x +e \right)-36 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)-30 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}+5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2}+5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}-5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +13 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a b +15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-13 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \sin \left(f x +e \right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{3} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}}"," ",0,"-1/8/f*(b+a*cos(f*x+e)^2)*(-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*sin(f*x+e)+18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)+15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)-36*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+13*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-13*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*sin(f*x+e)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/cos(f*x+e)^3/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^3","C"
114,1,1069,105,1.103000," ","int(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \sin \left(f x +e \right)+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)+\left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a +3 \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right) \sin \left(f x +e \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{3} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}}"," ",0,"-1/2/f*(b+a*cos(f*x+e)^2)*(-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*sin(f*x+e)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)+cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+3*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^2","C"
115,1,1007,69,1.839000," ","int(1/(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)+\cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right) \sin \left(f x +e \right)}{f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{3} \left(a +b \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a}"," ",0,"-1/f*(b+a*cos(f*x+e)^2)*(2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)+cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)*sin(f*x+e)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/cos(f*x+e)^3/(a+b)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a","C"
116,1,89,64,1.384000," ","int(csc(f*x+e)^2/(a+b*sec(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 +2 b \right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(f x +e \right)\right)}{f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sin \left(f x +e \right) \left(a +b \right)^{2}}"," ",0,"-1/f/(b+a*cos(f*x+e)^2)^2*(a*cos(f*x+e)^2-cos(f*x+e)^2*b+2*b)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^3/sin(f*x+e)/(a+b)^2","A"
117,1,137,111,1.697000," ","int(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\left(2 \left(\cos^{4}\left(f x +e \right)\right) a^{2}-6 \left(\cos^{4}\left(f x +e \right)\right) a b -3 a^{2} \left(\cos^{2}\left(f x +e \right)\right)+10 \left(\cos^{2}\left(f x +e \right)\right) a b -3 b^{2} \left(\cos^{2}\left(f x +e \right)\right)-6 a b +2 b^{2}\right) \left(\cos^{3}\left(f x +e \right)\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{3 f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sin \left(f x +e \right)^{3} \left(a +b \right)^{3}}"," ",0,"1/3/f/(b+a*cos(f*x+e)^2)^2*(2*cos(f*x+e)^4*a^2-6*cos(f*x+e)^4*a*b-3*a^2*cos(f*x+e)^2+10*cos(f*x+e)^2*a*b-3*b^2*cos(f*x+e)^2-6*a*b+2*b^2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/sin(f*x+e)^3/(a+b)^3","A"
118,1,204,167,2.111000," ","int(csc(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(8 \left(\cos^{6}\left(f x +e \right)\right) a^{3}-40 \left(\cos^{6}\left(f x +e \right)\right) a^{2} b -20 \left(\cos^{4}\left(f x +e \right)\right) a^{3}+104 \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -20 \left(\cos^{4}\left(f x +e \right)\right) a \,b^{2}+15 \left(\cos^{2}\left(f x +e \right)\right) a^{3}-85 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b +49 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}+5 \left(\cos^{2}\left(f x +e \right)\right) b^{3}+30 a^{2} b -20 b^{2} a -2 b^{3}\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(f x +e \right)\right)}{15 f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sin \left(f x +e \right)^{5} \left(a +b \right)^{4}}"," ",0,"-1/15/f/(b+a*cos(f*x+e)^2)^2*(8*cos(f*x+e)^6*a^3-40*cos(f*x+e)^6*a^2*b-20*cos(f*x+e)^4*a^3+104*cos(f*x+e)^4*a^2*b-20*cos(f*x+e)^4*a*b^2+15*cos(f*x+e)^2*a^3-85*a^2*cos(f*x+e)^2*b+49*cos(f*x+e)^2*a*b^2+5*cos(f*x+e)^2*b^3+30*a^2*b-20*b^2*a-2*b^3)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^3/sin(f*x+e)^5/(a+b)^4","A"
119,1,229,199,3.411000," ","int(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x)","\frac{\left(a +b \right)^{7} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(3 \left(\cos^{8}\left(f x +e \right)\right) a^{4}-10 \left(\cos^{6}\left(f x +e \right)\right) a^{4}-8 \left(\cos^{6}\left(f x +e \right)\right) a^{3} b +15 \left(\cos^{4}\left(f x +e \right)\right) a^{4}+60 \left(\cos^{4}\left(f x +e \right)\right) a^{3} b +48 \left(\cos^{4}\left(f x +e \right)\right) a^{2} b^{2}+60 \left(\cos^{2}\left(f x +e \right)\right) a^{3} b +240 \left(\cos^{2}\left(f x +e \right)\right) a^{2} b^{2}+192 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{3}+40 a^{2} b^{2}+160 a \,b^{3}+128 b^{4}\right) \sqrt{4}\, a^{2}}{30 f \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{5} \left(\sqrt{-a b}+a \right)^{7} \left(\sqrt{-a b}-a \right)^{7}}"," ",0,"1/30/f*(a+b)^7*(b+a*cos(f*x+e)^2)*(3*cos(f*x+e)^8*a^4-10*cos(f*x+e)^6*a^4-8*cos(f*x+e)^6*a^3*b+15*cos(f*x+e)^4*a^4+60*cos(f*x+e)^4*a^3*b+48*cos(f*x+e)^4*a^2*b^2+60*cos(f*x+e)^2*a^3*b+240*cos(f*x+e)^2*a^2*b^2+192*cos(f*x+e)^2*a*b^3+40*a^2*b^2+160*a*b^3+128*b^4)*4^(1/2)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5*a^2/((-a*b)^(1/2)+a)^7/((-a*b)^(1/2)-a)^7","A"
120,1,159,132,2.105000," ","int(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x)","-\frac{\left(a +b \right)^{5} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(\left(\cos^{6}\left(f x +e \right)\right) a^{3}-3 \left(\cos^{4}\left(f x +e \right)\right) a^{3}-6 \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -12 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b -24 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-8 b^{2} a -16 b^{3}\right) \sqrt{4}\, a}{6 f \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{5} \left(\sqrt{-a b}-a \right)^{5} \left(\sqrt{-a b}+a \right)^{5}}"," ",0,"-1/6/f*(a+b)^5*(b+a*cos(f*x+e)^2)*(cos(f*x+e)^6*a^3-3*cos(f*x+e)^4*a^3-6*cos(f*x+e)^4*a^2*b-12*a^2*cos(f*x+e)^2*b-24*cos(f*x+e)^2*a*b^2-8*b^2*a-16*b^3)*4^(1/2)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5*a/((-a*b)^(1/2)-a)^5/((-a*b)^(1/2)+a)^5","A"
121,1,90,87,0.303000," ","int(sin(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x)","\frac{-\frac{1}{a \sec \left(f x +e \right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}-\frac{4 b \left(\frac{\sec \left(f x +e \right)}{3 a \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{2 \sec \left(f x +e \right)}{3 a^{2} \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}\right)}{a}}{f}"," ",0,"1/f*(-1/a/sec(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2)-4*b/a*(1/3*sec(f*x+e)/a/(a+b*sec(f*x+e)^2)^(3/2)+2/3/a^2*sec(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2)))","A"
122,1,5056,113,2.136000," ","int(csc(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
123,1,11110,151,2.605000," ","int(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
124,1,15551,210,3.230000," ","int(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
125,1,4477,260,2.849000," ","int(sin(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"1/48/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(450*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*b+630*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^4+315*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4-315*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^4+630*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^3-225*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*b-525*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b^2-315*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^3+113*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2+33*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4+8*cos(f*x+e)^8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4+26*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4-26*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4-315*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4-33*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4+420*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3+30*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^4-15*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^4+30*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*b+450*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b^2+1050*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b^2-8*cos(f*x+e)^9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4+1050*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^3-15*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*b-225*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b^2-525*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^3+18*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b-18*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b-96*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b-63*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2+96*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b+63*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2-162*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b-574*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2-420*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3+162*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b+574*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2+420*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3-113*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2-420*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^5","C"
126,1,3223,203,2.125000," ","int(sin(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"-1/24/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(-180*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^2*b+78*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+140*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2+55*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2+21*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+90*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)-210*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)-21*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b-78*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-140*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2-210*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a*b^2+90*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*b+6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3-6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3+105*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-55*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+105*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b^2+105*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)-180*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)+9*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)-105*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3+9*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^4","C"
127,1,3158,147,1.713000," ","int(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"-1/6/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3+18*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*b+15*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b^2-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3-36*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^2*b-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)+15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)-36*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+18*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+20*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-18*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-20*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+13*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-13*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)/(a+b)/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/a^3/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
128,1,3024,111,2.205000," ","int(1/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"-1/3/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3+6*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*b+3*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b^2-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3-12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^2*b-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a*b^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)-12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)+6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5/(a^2+2*a*b+b^2)/a^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
129,1,146,96,1.610000," ","int(csc(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x)","-\frac{\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 -\left(\cos^{4}\left(f x +e \right)\right) b^{2}+12 \left(\cos^{2}\left(f x +e \right)\right) a b -4 b^{2} \left(\cos^{2}\left(f x +e \right)\right)+8 b^{2}\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \left(\cos^{5}\left(f x +e \right)\right)}{3 f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{4} \sin \left(f x +e \right) \left(a^{2}+2 a b +b^{2}\right) \left(a +b \right)}"," ",0,"-1/3/f/(b+a*cos(f*x+e)^2)^4*(3*cos(f*x+e)^4*a^2-6*cos(f*x+e)^4*a*b-cos(f*x+e)^4*b^2+12*cos(f*x+e)^2*a*b-4*b^2*cos(f*x+e)^2+8*b^2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)*cos(f*x+e)^5/sin(f*x+e)/(a^2+2*a*b+b^2)/(a+b)","A"
130,1,225,144,1.673000," ","int(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x)","\frac{\left(2 \left(\cos^{6}\left(f x +e \right)\right) a^{3}-12 \left(\cos^{6}\left(f x +e \right)\right) a^{2} b +2 \left(\cos^{6}\left(f x +e \right)\right) a \,b^{2}-3 \left(\cos^{4}\left(f x +e \right)\right) a^{3}+21 \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -21 \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 +24 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-12 \left(\cos^{2}\left(f x +e \right)\right) b^{3}-8 b^{2} a +8 b^{3}\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \left(\cos^{5}\left(f x +e \right)\right)}{3 f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{4} \sin \left(f x +e \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a +b \right)^{2}}"," ",0,"1/3/f/(b+a*cos(f*x+e)^2)^4*(2*cos(f*x+e)^6*a^3-12*cos(f*x+e)^6*a^2*b+2*cos(f*x+e)^6*a*b^2-3*cos(f*x+e)^4*a^3+21*cos(f*x+e)^4*a^2*b-21*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+24*cos(f*x+e)^2*a*b^2-12*cos(f*x+e)^2*b^3-8*b^2*a+8*b^3)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)*cos(f*x+e)^5/sin(f*x+e)^3/(a^2+2*a*b+b^2)/(a+b)^2","A"
131,1,324,206,1.745000," ","int(csc(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x)","-\frac{\left(8 \left(\cos^{8}\left(f x +e \right)\right) a^{4}-80 \left(\cos^{8}\left(f x +e \right)\right) a^{3} b +40 \left(\cos^{8}\left(f x +e \right)\right) a^{2} b^{2}-20 \left(\cos^{6}\left(f x +e \right)\right) a^{4}+212 \left(\cos^{6}\left(f x +e \right)\right) a^{3} b -220 \left(\cos^{6}\left(f x +e \right)\right) a^{2} b^{2}+60 \left(\cos^{6}\left(f x +e \right)\right) a \,b^{3}+15 \left(\cos^{4}\left(f x +e \right)\right) a^{4}-180 \left(\cos^{4}\left(f x +e \right)\right) a^{3} b +378 \left(\cos^{4}\left(f x +e \right)\right) a^{2} b^{2}-180 \left(\cos^{4}\left(f x +e \right)\right) a \,b^{3}+15 \left(\cos^{4}\left(f x +e \right)\right) b^{4}+60 \left(\cos^{2}\left(f x +e \right)\right) a^{3} b -220 \left(\cos^{2}\left(f x +e \right)\right) a^{2} b^{2}+212 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{3}-20 \left(\cos^{2}\left(f x +e \right)\right) b^{4}+40 a^{2} b^{2}-80 a \,b^{3}+8 b^{4}\right) \left(\cos^{5}\left(f x +e \right)\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}}}{15 f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{4} \sin \left(f x +e \right)^{5} \left(a^{2}+2 a b +b^{2}\right) \left(a +b \right)^{3}}"," ",0,"-1/15/f/(b+a*cos(f*x+e)^2)^4*(8*cos(f*x+e)^8*a^4-80*cos(f*x+e)^8*a^3*b+40*cos(f*x+e)^8*a^2*b^2-20*cos(f*x+e)^6*a^4+212*cos(f*x+e)^6*a^3*b-220*cos(f*x+e)^6*a^2*b^2+60*cos(f*x+e)^6*a*b^3+15*cos(f*x+e)^4*a^4-180*cos(f*x+e)^4*a^3*b+378*cos(f*x+e)^4*a^2*b^2-180*cos(f*x+e)^4*a*b^3+15*cos(f*x+e)^4*b^4+60*cos(f*x+e)^2*a^3*b-220*cos(f*x+e)^2*a^2*b^2+212*cos(f*x+e)^2*a*b^3-20*cos(f*x+e)^2*b^4+40*a^2*b^2-80*a*b^3+8*b^4)*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/sin(f*x+e)^5/(a^2+2*a*b+b^2)/(a+b)^3","A"
132,0,0,115,3.480000," ","int((a+b*sec(f*x+e)^2)^p*(d*sin(f*x+e))^m,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(d \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*(d*sin(f*x+e))^m,x)","F"
133,0,0,174,4.768000," ","int((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^5,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(\sin^{5}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^5,x)","F"
134,0,0,111,4.520000," ","int((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^3,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(\sin^{3}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^3,x)","F"
135,0,0,66,1.367000," ","int((a+b*sec(f*x+e)^2)^p*sin(f*x+e),x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \sin \left(f x +e \right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*sin(f*x+e),x)","F"
136,0,0,73,1.540000," ","int(csc(f*x+e)*(a+b*sec(f*x+e)^2)^p,x)","\int \csc \left(f x +e \right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)*(a+b*sec(f*x+e)^2)^p,x)","F"
137,0,0,75,1.561000," ","int(csc(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\csc^{3}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x)","F"
138,0,0,82,6.090000," ","int((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^4,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(\sin^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^4,x)","F"
139,0,0,82,4.441000," ","int((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^2,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(\sin^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^2,x)","F"
140,0,0,79,1.346000," ","int((a+b*sec(f*x+e)^2)^p,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p,x)","F"
141,0,0,71,1.834000," ","int(csc(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\csc^{2}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x)","F"
142,0,0,122,1.679000," ","int(csc(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\csc^{4}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x)","F"
143,0,0,184,1.749000," ","int(csc(f*x+e)^6*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\csc^{6}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^6*(a+b*sec(f*x+e)^2)^p,x)","F"
144,1,125,68,1.488000," ","int((a-a*sec(d*x+c)^2)^4,x)","\frac{-a^{4} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)+4 a^{4} \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)-6 a^{4} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)-4 a^{4} \tan \left(d x +c \right)+a^{4} \left(d x +c \right)}{d}"," ",0,"1/d*(-a^4*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c)+4*a^4*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)-6*a^4*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)-4*a^4*tan(d*x+c)+a^4*(d*x+c))","A"
145,1,81,52,1.262000," ","int((a-a*sec(d*x+c)^2)^3,x)","\frac{a^{3} \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)-3 a^{3} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)-3 a^{3} \tan \left(d x +c \right)+a^{3} \left(d x +c \right)}{d}"," ",0,"1/d*(a^3*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)-3*a^3*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)-3*a^3*tan(d*x+c)+a^3*(d*x+c))","A"
146,1,49,36,1.018000," ","int((a-a*sec(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^{2} \tan \left(d x +c \right)+a^{2} \left(d x +c \right)}{d}"," ",0,"1/d*(-a^2*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)-2*a^2*tan(d*x+c)+a^2*(d*x+c))","A"
147,1,17,16,0.779000," ","int(a-a*sec(d*x+c)^2,x)","a x -\frac{a \tan \left(d x +c \right)}{d}"," ",0,"a*x-a*tan(d*x+c)/d","A"
148,1,31,19,0.517000," ","int(1/(a-a*sec(d*x+c)^2),x)","\frac{1}{a d \tan \left(d x +c \right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{a d}"," ",0,"1/a/d/tan(d*x+c)+1/a/d*arctan(tan(d*x+c))","A"
149,1,47,35,0.681000," ","int(1/(a-a*sec(d*x+c)^2)^2,x)","-\frac{1}{3 d \,a^{2} \tan \left(d x +c \right)^{3}}+\frac{1}{d \,a^{2} \tan \left(d x +c \right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"-1/3/d/a^2/tan(d*x+c)^3+1/d/a^2/tan(d*x+c)+1/d/a^2*arctan(tan(d*x+c))","A"
150,1,63,51,0.895000," ","int(1/(a-a*sec(d*x+c)^2)^3,x)","-\frac{1}{3 d \,a^{3} \tan \left(d x +c \right)^{3}}+\frac{1}{5 d \,a^{3} \tan \left(d x +c \right)^{5}}+\frac{1}{d \,a^{3} \tan \left(d x +c \right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"-1/3/d/a^3/tan(d*x+c)^3+1/5/d/a^3/tan(d*x+c)^5+1/d/a^3/tan(d*x+c)+1/d/a^3*arctan(tan(d*x+c))","A"
151,1,79,67,0.786000," ","int(1/(a-a*sec(d*x+c)^2)^4,x)","-\frac{1}{7 d \,a^{4} \tan \left(d x +c \right)^{7}}-\frac{1}{3 d \,a^{4} \tan \left(d x +c \right)^{3}}+\frac{1}{5 d \,a^{4} \tan \left(d x +c \right)^{5}}+\frac{1}{d \,a^{4} \tan \left(d x +c \right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,a^{4}}"," ",0,"-1/7/d/a^4/tan(d*x+c)^7-1/3/d/a^4/tan(d*x+c)^3+1/5/d/a^4/tan(d*x+c)^5+1/d/a^4/tan(d*x+c)+1/d/a^4*arctan(tan(d*x+c))","A"
152,1,138,90,0.801000," ","int(sec(f*x+e)^5*(a+b*sec(f*x+e)^2),x)","\frac{a \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{3 a \tan \left(f x +e \right) \sec \left(f x +e \right)}{8 f}+\frac{3 a \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{b \left(\sec^{5}\left(f x +e \right)\right) \tan \left(f x +e \right)}{6 f}+\frac{5 b \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{24 f}+\frac{5 b \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}+\frac{5 b \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}"," ",0,"1/4/f*a*tan(f*x+e)*sec(f*x+e)^3+3/8/f*a*tan(f*x+e)*sec(f*x+e)+3/8/f*a*ln(sec(f*x+e)+tan(f*x+e))+1/6*b*sec(f*x+e)^5*tan(f*x+e)/f+5/24*b*sec(f*x+e)^3*tan(f*x+e)/f+5/16*b*sec(f*x+e)*tan(f*x+e)/f+5/16/f*b*ln(sec(f*x+e)+tan(f*x+e))","A"
153,1,98,64,1.027000," ","int(sec(f*x+e)^3*(a+b*sec(f*x+e)^2),x)","\frac{a \tan \left(f x +e \right) \sec \left(f x +e \right)}{2 f}+\frac{a \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{b \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{4 f}+\frac{3 b \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{3 b \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}"," ",0,"1/2/f*a*tan(f*x+e)*sec(f*x+e)+1/2/f*a*ln(sec(f*x+e)+tan(f*x+e))+1/4*b*sec(f*x+e)^3*tan(f*x+e)/f+3/8*b*sec(f*x+e)*tan(f*x+e)/f+3/8/f*b*ln(sec(f*x+e)+tan(f*x+e))","A"
154,1,59,36,0.794000," ","int(sec(f*x+e)*(a+b*sec(f*x+e)^2),x)","\frac{a \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{b \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{b \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}"," ",0,"1/f*a*ln(sec(f*x+e)+tan(f*x+e))+1/2*b*sec(f*x+e)*tan(f*x+e)/f+1/2/f*b*ln(sec(f*x+e)+tan(f*x+e))","A"
155,1,32,24,0.671000," ","int(cos(f*x+e)*(a+b*sec(f*x+e)^2),x)","\frac{a \sin \left(f x +e \right)}{f}+\frac{b \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}"," ",0,"a*sin(f*x+e)/f+1/f*b*ln(sec(f*x+e)+tan(f*x+e))","A"
156,1,33,28,1.485000," ","int(cos(f*x+e)^3*(a+b*sec(f*x+e)^2),x)","\frac{\frac{a \left(2+\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)}{3}+b \sin \left(f x +e \right)}{f}"," ",0,"1/f*(1/3*a*(2+cos(f*x+e)^2)*sin(f*x+e)+b*sin(f*x+e))","A"
157,1,54,46,1.880000," ","int(cos(f*x+e)^5*(a+b*sec(f*x+e)^2),x)","\frac{\frac{a \left(\frac{8}{3}+\cos^{4}\left(f x +e \right)+\frac{4 \left(\cos^{2}\left(f x +e \right)\right)}{3}\right) \sin \left(f x +e \right)}{5}+\frac{b \left(2+\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(1/5*a*(8/3+cos(f*x+e)^4+4/3*cos(f*x+e)^2)*sin(f*x+e)+1/3*b*(2+cos(f*x+e)^2)*sin(f*x+e))","A"
158,1,78,79,1.044000," ","int(sec(f*x+e)^6*(a+b*sec(f*x+e)^2),x)","\frac{-a \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(f x +e \right)\right)}{15}\right) \tan \left(f x +e \right)-b \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(f x +e \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(f x +e \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(f x +e \right)\right)}{35}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(-a*(-8/15-1/5*sec(f*x+e)^4-4/15*sec(f*x+e)^2)*tan(f*x+e)-b*(-16/35-1/7*sec(f*x+e)^6-6/35*sec(f*x+e)^4-8/35*sec(f*x+e)^2)*tan(f*x+e))","A"
159,1,58,59,1.055000," ","int(sec(f*x+e)^4*(a+b*sec(f*x+e)^2),x)","\frac{-a \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)-b \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(f x +e \right)\right)}{15}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(-a*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e)-b*(-8/15-1/5*sec(f*x+e)^4-4/15*sec(f*x+e)^2)*tan(f*x+e))","A"
160,1,35,39,0.964000," ","int(sec(f*x+e)^2*(a+b*sec(f*x+e)^2),x)","\frac{a \tan \left(f x +e \right)-b \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*tan(f*x+e)-b*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e))","A"
161,1,16,15,0.752000," ","int(a+b*sec(f*x+e)^2,x)","a x +\frac{b \tan \left(f x +e \right)}{f}"," ",0,"a*x+b*tan(f*x+e)/f","A"
162,1,37,27,0.687000," ","int(cos(f*x+e)^2*(a+b*sec(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)+\left(f x +e \right) b}{f}"," ",0,"1/f*(a*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+(f*x+e)*b)","A"
163,1,65,55,1.293000," ","int(cos(f*x+e)^4*(a+b*sec(f*x+e)^2),x)","\frac{a \left(\frac{\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+b \left(\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}"," ",0,"1/f*(a*(1/4*(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+3/8*f*x+3/8*e)+b*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
164,1,86,81,1.680000," ","int(cos(f*x+e)^6*(a+b*sec(f*x+e)^2),x)","\frac{a \left(\frac{\left(\cos^{5}\left(f x +e \right)+\frac{5 \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{15 \cos \left(f x +e \right)}{8}\right) \sin \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+b \left(\frac{\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)}{f}"," ",0,"1/f*(a*(1/6*(cos(f*x+e)^5+5/4*cos(f*x+e)^3+15/8*cos(f*x+e))*sin(f*x+e)+5/16*f*x+5/16*e)+b*(1/4*(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+3/8*f*x+3/8*e))","A"
165,1,256,155,1.287000," ","int(sec(f*x+e)^5*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{3 a^{2} \tan \left(f x +e \right) \sec \left(f x +e \right)}{8 f}+\frac{3 a^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{a b \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{3 f}+\frac{5 a b \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{12 f}+\frac{5 a b \tan \left(f x +e \right) \sec \left(f x +e \right)}{8 f}+\frac{5 a b \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{b^{2} \tan \left(f x +e \right) \left(\sec^{7}\left(f x +e \right)\right)}{8 f}+\frac{7 b^{2} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{48 f}+\frac{35 b^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{192 f}+\frac{35 b^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{128 f}+\frac{35 b^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{128 f}"," ",0,"1/4/f*a^2*tan(f*x+e)*sec(f*x+e)^3+3/8/f*a^2*tan(f*x+e)*sec(f*x+e)+3/8/f*a^2*ln(sec(f*x+e)+tan(f*x+e))+1/3/f*a*b*tan(f*x+e)*sec(f*x+e)^5+5/12/f*a*b*tan(f*x+e)*sec(f*x+e)^3+5/8/f*a*b*tan(f*x+e)*sec(f*x+e)+5/8/f*a*b*ln(sec(f*x+e)+tan(f*x+e))+1/8/f*b^2*tan(f*x+e)*sec(f*x+e)^7+7/48/f*b^2*tan(f*x+e)*sec(f*x+e)^5+35/192/f*b^2*tan(f*x+e)*sec(f*x+e)^3+35/128*b^2*sec(f*x+e)*tan(f*x+e)/f+35/128/f*b^2*ln(sec(f*x+e)+tan(f*x+e))","A"
166,1,191,121,1.313000," ","int(sec(f*x+e)^3*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \tan \left(f x +e \right) \sec \left(f x +e \right)}{2 f}+\frac{a^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{a b \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{2 f}+\frac{3 a b \tan \left(f x +e \right) \sec \left(f x +e \right)}{4 f}+\frac{3 a b \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{4 f}+\frac{b^{2} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{6 f}+\frac{5 b^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{24 f}+\frac{5 b^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}+\frac{5 b^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}"," ",0,"1/2/f*a^2*tan(f*x+e)*sec(f*x+e)+1/2/f*a^2*ln(sec(f*x+e)+tan(f*x+e))+1/2/f*a*b*tan(f*x+e)*sec(f*x+e)^3+3/4/f*a*b*tan(f*x+e)*sec(f*x+e)+3/4/f*a*b*ln(sec(f*x+e)+tan(f*x+e))+1/6/f*b^2*tan(f*x+e)*sec(f*x+e)^5+5/24/f*b^2*tan(f*x+e)*sec(f*x+e)^3+5/16*b^2*sec(f*x+e)*tan(f*x+e)/f+5/16/f*b^2*ln(sec(f*x+e)+tan(f*x+e))","A"
167,1,125,85,1.154000," ","int(sec(f*x+e)*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{a b \tan \left(f x +e \right) \sec \left(f x +e \right)}{f}+\frac{a b \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{b^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{3 b^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{3 b^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}"," ",0,"1/f*a^2*ln(sec(f*x+e)+tan(f*x+e))+1/f*a*b*tan(f*x+e)*sec(f*x+e)+1/f*a*b*ln(sec(f*x+e)+tan(f*x+e))+1/4/f*b^2*tan(f*x+e)*sec(f*x+e)^3+3/8*b^2*sec(f*x+e)*tan(f*x+e)/f+3/8/f*b^2*ln(sec(f*x+e)+tan(f*x+e))","A"
168,1,78,52,1.061000," ","int(cos(f*x+e)*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \sin \left(f x +e \right)}{f}+\frac{2 a b \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{b^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{b^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}"," ",0,"a^2*sin(f*x+e)/f+2/f*a*b*ln(sec(f*x+e)+tan(f*x+e))+1/2*b^2*sec(f*x+e)*tan(f*x+e)/f+1/2/f*b^2*ln(sec(f*x+e)+tan(f*x+e))","A"
169,1,72,47,1.039000," ","int(cos(f*x+e)^3*(a+b*sec(f*x+e)^2)^2,x)","\frac{\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) a^{2}}{3 f}+\frac{2 a^{2} \sin \left(f x +e \right)}{3 f}+\frac{2 \sin \left(f x +e \right) a b}{f}+\frac{b^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}"," ",0,"1/3/f*sin(f*x+e)*cos(f*x+e)^2*a^2+2/3*a^2*sin(f*x+e)/f+2/f*sin(f*x+e)*a*b+1/f*b^2*ln(sec(f*x+e)+tan(f*x+e))","A"
170,1,67,49,1.598000," ","int(cos(f*x+e)^5*(a+b*sec(f*x+e)^2)^2,x)","\frac{\frac{a^{2} \left(\frac{8}{3}+\cos^{4}\left(f x +e \right)+\frac{4 \left(\cos^{2}\left(f x +e \right)\right)}{3}\right) \sin \left(f x +e \right)}{5}+\frac{2 a b \left(2+\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)}{3}+b^{2} \sin \left(f x +e \right)}{f}"," ",0,"1/f*(1/5*a^2*(8/3+cos(f*x+e)^4+4/3*cos(f*x+e)^2)*sin(f*x+e)+2/3*a*b*(2+cos(f*x+e)^2)*sin(f*x+e)+b^2*sin(f*x+e))","A"
171,1,134,98,1.260000," ","int(sec(f*x+e)^6*(a+b*sec(f*x+e)^2)^2,x)","\frac{-a^{2} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(f x +e \right)\right)}{15}\right) \tan \left(f x +e \right)-2 a b \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(f x +e \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(f x +e \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(f x +e \right)\right)}{35}\right) \tan \left(f x +e \right)-b^{2} \left(-\frac{128}{315}-\frac{\left(\sec^{8}\left(f x +e \right)\right)}{9}-\frac{8 \left(\sec^{6}\left(f x +e \right)\right)}{63}-\frac{16 \left(\sec^{4}\left(f x +e \right)\right)}{105}-\frac{64 \left(\sec^{2}\left(f x +e \right)\right)}{315}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(-a^2*(-8/15-1/5*sec(f*x+e)^4-4/15*sec(f*x+e)^2)*tan(f*x+e)-2*a*b*(-16/35-1/7*sec(f*x+e)^6-6/35*sec(f*x+e)^4-8/35*sec(f*x+e)^2)*tan(f*x+e)-b^2*(-128/315-1/9*sec(f*x+e)^8-8/63*sec(f*x+e)^6-16/105*sec(f*x+e)^4-64/315*sec(f*x+e)^2)*tan(f*x+e))","A"
172,1,104,74,1.253000," ","int(sec(f*x+e)^4*(a+b*sec(f*x+e)^2)^2,x)","\frac{-a^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)-2 a b \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(f x +e \right)\right)}{15}\right) \tan \left(f x +e \right)-b^{2} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(f x +e \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(f x +e \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(f x +e \right)\right)}{35}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(-a^2*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e)-2*a*b*(-8/15-1/5*sec(f*x+e)^4-4/15*sec(f*x+e)^2)*tan(f*x+e)-b^2*(-16/35-1/7*sec(f*x+e)^6-6/35*sec(f*x+e)^4-8/35*sec(f*x+e)^2)*tan(f*x+e))","A"
173,1,71,49,1.521000," ","int(sec(f*x+e)^2*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \tan \left(f x +e \right)-2 a b \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)-b^{2} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(f x +e \right)\right)}{15}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(a^2*tan(f*x+e)-2*a*b*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e)-b^2*(-8/15-1/5*sec(f*x+e)^4-4/15*sec(f*x+e)^2)*tan(f*x+e))","A"
174,1,48,38,1.280000," ","int((a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \left(f x +e \right)+2 a b \tan \left(f x +e \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*(f*x+e)+2*a*b*tan(f*x+e)-b^2*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e))","A"
175,1,51,43,1.217000," ","int(cos(f*x+e)^2*(a+b*sec(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(f x +e \right)+b^{2} \tan \left(f x +e \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*(f*x+e)+b^2*tan(f*x+e))","A"
176,1,78,75,1.226000," ","int(cos(f*x+e)^4*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \left(\frac{\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+2 a b \left(\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+b^{2} \left(f x +e \right)}{f}"," ",0,"1/f*(a^2*(1/4*(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+3/8*f*x+3/8*e)+2*a*b*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+b^2*(f*x+e))","A"
177,1,116,111,1.615000," ","int(cos(f*x+e)^6*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \left(\frac{\left(\cos^{5}\left(f x +e \right)+\frac{5 \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{15 \cos \left(f x +e \right)}{8}\right) \sin \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+2 a b \left(\frac{\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+b^{2} \left(\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}"," ",0,"1/f*(a^2*(1/6*(cos(f*x+e)^5+5/4*cos(f*x+e)^3+15/8*cos(f*x+e))*sin(f*x+e)+5/16*f*x+5/16*e)+2*a*b*(1/4*(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+3/8*f*x+3/8*e)+b^2*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
178,1,84,69,1.249000," ","int((a+b*sec(d*x+c)^2)^3,x)","\frac{a^{3} \left(d x +c \right)+3 a^{2} b \tan \left(d x +c \right)-3 b^{2} a \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)-b^{3} \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*(a^3*(d*x+c)+3*a^2*b*tan(d*x+c)-3*b^2*a*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)-b^3*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","A"
179,1,130,105,1.479000," ","int((a+b*sec(d*x+c)^2)^4,x)","\frac{a^{4} \left(d x +c \right)+4 a^{3} b \tan \left(d x +c \right)-6 a^{2} b^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)-4 a \,b^{3} \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)-b^{4} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^4*(d*x+c)+4*a^3*b*tan(d*x+c)-6*a^2*b^2*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)-4*a*b^3*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)-b^4*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c))","A"
180,1,141,74,0.640000," ","int(sec(f*x+e)^5/(a+b*sec(f*x+e)^2),x)","\frac{a^{2} \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{f \,b^{2} \sqrt{\left(a +b \right) a}}-\frac{1}{4 f b \left(-1+\sin \left(f x +e \right)\right)}+\frac{\ln \left(-1+\sin \left(f x +e \right)\right) a}{2 f \,b^{2}}-\frac{\ln \left(-1+\sin \left(f x +e \right)\right)}{4 f b}-\frac{1}{4 f b \left(1+\sin \left(f x +e \right)\right)}-\frac{\ln \left(1+\sin \left(f x +e \right)\right) a}{2 f \,b^{2}}+\frac{\ln \left(1+\sin \left(f x +e \right)\right)}{4 f b}"," ",0,"1/f/b^2*a^2/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))-1/4/f/b/(-1+sin(f*x+e))+1/2/f/b^2*ln(-1+sin(f*x+e))*a-1/4/f/b*ln(-1+sin(f*x+e))-1/4/f/b/(1+sin(f*x+e))-1/2/f/b^2*ln(1+sin(f*x+e))*a+1/4/f/b*ln(1+sin(f*x+e))","A"
181,1,68,47,0.619000," ","int(sec(f*x+e)^3/(a+b*sec(f*x+e)^2),x)","-\frac{a \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{f b \sqrt{\left(a +b \right) a}}-\frac{\ln \left(-1+\sin \left(f x +e \right)\right)}{2 f b}+\frac{\ln \left(1+\sin \left(f x +e \right)\right)}{2 f b}"," ",0,"-1/f/b*a/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))-1/2/f/b*ln(-1+sin(f*x+e))+1/2/f/b*ln(1+sin(f*x+e))","A"
182,1,28,28,0.888000," ","int(sec(f*x+e)/(a+b*sec(f*x+e)^2),x)","\frac{\arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{f \sqrt{\left(a +b \right) a}}"," ",0,"1/f/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))","A"
183,1,45,44,1.397000," ","int(cos(f*x+e)/(a+b*sec(f*x+e)^2),x)","\frac{\frac{\sin \left(f x +e \right)}{a}-\frac{b \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{a \sqrt{\left(a +b \right) a}}}{f}"," ",0,"1/f*(1/a*sin(f*x+e)-1/a*b/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2)))","A"
184,1,70,66,1.479000," ","int(cos(f*x+e)^3/(a+b*sec(f*x+e)^2),x)","\frac{-\frac{\frac{a \left(\sin^{3}\left(f x +e \right)\right)}{3}-a \sin \left(f x +e \right)+b \sin \left(f x +e \right)}{a^{2}}+\frac{b^{2} \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{a^{2} \sqrt{\left(a +b \right) a}}}{f}"," ",0,"1/f*(-1/a^2*(1/3*a*sin(f*x+e)^3-a*sin(f*x+e)+b*sin(f*x+e))+b^2/a^2/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2)))","A"
185,1,110,96,1.394000," ","int(cos(f*x+e)^5/(a+b*sec(f*x+e)^2),x)","\frac{\frac{\frac{\left(\sin^{5}\left(f x +e \right)\right) a^{2}}{5}-\frac{2 \left(\sin^{3}\left(f x +e \right)\right) a^{2}}{3}+\frac{\left(\sin^{3}\left(f x +e \right)\right) a b}{3}+a^{2} \sin \left(f x +e \right)-\sin \left(f x +e \right) a b +b^{2} \sin \left(f x +e \right)}{a^{3}}-\frac{b^{3} \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{a^{3} \sqrt{\left(a +b \right) a}}}{f}"," ",0,"1/f*(1/a^3*(1/5*sin(f*x+e)^5*a^2-2/3*sin(f*x+e)^3*a^2+1/3*sin(f*x+e)^3*a*b+a^2*sin(f*x+e)-sin(f*x+e)*a*b+b^2*sin(f*x+e))-b^3/a^3/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2)))","A"
186,1,79,67,0.580000," ","int(sec(f*x+e)^6/(a+b*sec(f*x+e)^2),x)","\frac{\tan^{3}\left(f x +e \right)}{3 b f}-\frac{\tan \left(f x +e \right) a}{f \,b^{2}}+\frac{\tan \left(f x +e \right)}{b f}+\frac{a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,b^{2} \sqrt{\left(a +b \right) b}}"," ",0,"1/3*tan(f*x+e)^3/b/f-1/f/b^2*tan(f*x+e)*a+tan(f*x+e)/b/f+1/f/b^2*a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))","A"
187,1,47,44,0.431000," ","int(sec(f*x+e)^4/(a+b*sec(f*x+e)^2),x)","\frac{\tan \left(f x +e \right)}{b f}-\frac{a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f b \sqrt{\left(a +b \right) b}}"," ",0,"tan(f*x+e)/b/f-1/f/b*a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))","A"
188,1,28,28,0.551000," ","int(sec(f*x+e)^2/(a+b*sec(f*x+e)^2),x)","\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \sqrt{\left(a +b \right) b}}"," ",0,"1/f/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))","A"
189,1,48,37,0.776000," ","int(1/(a+b*sec(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f a \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f a}"," ",0,"-1/f/a*b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a*arctan(tan(f*x+e))","A"
190,1,92,63,1.564000," ","int(cos(f*x+e)^2/(a+b*sec(f*x+e)^2),x)","\frac{b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \sqrt{\left(a +b \right) b}}+\frac{\tan \left(f x +e \right)}{2 f a \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{2 f a}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b}{f \,a^{2}}"," ",0,"1/f*b^2/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/2/f/a*tan(f*x+e)/(tan(f*x+e)^2+1)+1/2/f/a*arctan(tan(f*x+e))-1/f/a^2*arctan(tan(f*x+e))*b","A"
191,1,194,103,1.753000," ","int(cos(f*x+e)^4/(a+b*sec(f*x+e)^2),x)","-\frac{b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \sqrt{\left(a +b \right) b}}+\frac{3 \left(\tan^{3}\left(f x +e \right)\right)}{8 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b}{2 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{\tan \left(f x +e \right) b}{2 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{5 \tan \left(f x +e \right)}{8 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f \,a^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right)}{8 f a}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b}{2 f \,a^{2}}"," ",0,"-1/f*b^3/a^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+3/8/f/a/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3-1/2/f/a^2/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3*b-1/2/f/a^2/(tan(f*x+e)^2+1)^2*tan(f*x+e)*b+5/8/f/a/(tan(f*x+e)^2+1)^2*tan(f*x+e)+1/f/a^3*arctan(tan(f*x+e))*b^2+3/8/f/a*arctan(tan(f*x+e))-1/2/f/a^2*arctan(tan(f*x+e))*b","A"
192,1,359,147,1.654000," ","int(cos(f*x+e)^6/(a+b*sec(f*x+e)^2),x)","\frac{b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{4} \sqrt{\left(a +b \right) b}}+\frac{5 \left(\tan^{5}\left(f x +e \right)\right)}{16 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{3 \left(\tan^{5}\left(f x +e \right)\right) b}{8 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{\left(\tan^{5}\left(f x +e \right)\right) b^{2}}{2 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{\left(\tan^{3}\left(f x +e \right)\right) b^{2}}{f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{6 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b}{f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \tan \left(f x +e \right) b}{8 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{\tan \left(f x +e \right) b^{2}}{2 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{11 \tan \left(f x +e \right)}{16 f a \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{3}}{f \,a^{4}}+\frac{5 \arctan \left(\tan \left(f x +e \right)\right)}{16 f a}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b}{8 f \,a^{2}}+\frac{\arctan \left(\tan \left(f x +e \right)\right) b^{2}}{2 f \,a^{3}}"," ",0,"1/f/a^4*b^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+5/16/f/a/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5-3/8/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b+1/2/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b^2+1/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b^2+5/6/f/a/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3-1/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b-5/8/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b+1/2/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b^2+11/16/f/a/(tan(f*x+e)^2+1)^3*tan(f*x+e)-1/f/a^4*arctan(tan(f*x+e))*b^3+5/16/f/a*arctan(tan(f*x+e))-3/8/f/a^2*arctan(tan(f*x+e))*b+1/2/f/a^3*arctan(tan(f*x+e))*b^2","B"
193,1,151,90,0.559000," ","int(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x)","\frac{a \sin \left(f x +e \right)}{2 f b \left(a +b \right) \left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)}-\frac{a^{2} \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{f \,b^{2} \left(a +b \right) \sqrt{\left(a +b \right) a}}-\frac{3 a \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{2 f b \left(a +b \right) \sqrt{\left(a +b \right) a}}-\frac{\ln \left(-1+\sin \left(f x +e \right)\right)}{2 f \,b^{2}}+\frac{\ln \left(1+\sin \left(f x +e \right)\right)}{2 f \,b^{2}}"," ",0,"1/2/f*a/b/(a+b)*sin(f*x+e)/(-a-b+a*sin(f*x+e)^2)-1/f*a^2/b^2/(a+b)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))-3/2/f*a/b/(a+b)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))-1/2/f/b^2*ln(-1+sin(f*x+e))+1/2/f/b^2*ln(1+sin(f*x+e))","A"
194,1,68,62,0.638000," ","int(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x)","\frac{-\frac{\sin \left(f x +e \right)}{2 \left(a +b \right) \left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)}+\frac{\arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{2 \left(a +b \right) \sqrt{\left(a +b \right) a}}}{f}"," ",0,"1/f*(-1/2*sin(f*x+e)/(a+b)/(-a-b+a*sin(f*x+e)^2)+1/2/(a+b)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2)))","A"
195,1,80,71,0.839000," ","int(sec(f*x+e)/(a+b*sec(f*x+e)^2)^2,x)","\frac{\frac{b \sin \left(f x +e \right)}{2 \left(a +b \right) a \left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)}+\frac{\left(2 a +b \right) \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{2 \left(a +b \right) a \sqrt{\left(a +b \right) a}}}{f}"," ",0,"1/f*(1/2*b/(a+b)/a*sin(f*x+e)/(-a-b+a*sin(f*x+e)^2)+1/2*(2*a+b)/(a+b)/a/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2)))","A"
196,1,92,89,1.155000," ","int(cos(f*x+e)/(a+b*sec(f*x+e)^2)^2,x)","\frac{\frac{\sin \left(f x +e \right)}{a^{2}}+\frac{b \left(-\frac{b \sin \left(f x +e \right)}{2 \left(a +b \right) \left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)}-\frac{\left(4 a +3 b \right) \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{2 \left(a +b \right) \sqrt{\left(a +b \right) a}}\right)}{a^{2}}}{f}"," ",0,"1/f*(1/a^2*sin(f*x+e)+b/a^2*(-1/2*b/(a+b)*sin(f*x+e)/(-a-b+a*sin(f*x+e)^2)-1/2*(4*a+3*b)/(a+b)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))))","A"
197,1,120,112,1.400000," ","int(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x)","\frac{-\frac{\frac{a \left(\sin^{3}\left(f x +e \right)\right)}{3}-a \sin \left(f x +e \right)+2 b \sin \left(f x +e \right)}{a^{3}}-\frac{b^{2} \left(-\frac{b \sin \left(f x +e \right)}{2 \left(a +b \right) \left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)}-\frac{\left(6 a +5 b \right) \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{2 \left(a +b \right) \sqrt{\left(a +b \right) a}}\right)}{a^{3}}}{f}"," ",0,"1/f*(-1/a^3*(1/3*a*sin(f*x+e)^3-a*sin(f*x+e)+2*b*sin(f*x+e))-b^2/a^3*(-1/2*b/(a+b)*sin(f*x+e)/(-a-b+a*sin(f*x+e)^2)-1/2*(6*a+5*b)/(a+b)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))))","A"
198,1,158,141,1.850000," ","int(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x)","\frac{\frac{\frac{\left(\sin^{5}\left(f x +e \right)\right) a^{2}}{5}-\frac{2 \left(\sin^{3}\left(f x +e \right)\right) a^{2}}{3}+\frac{2 \left(\sin^{3}\left(f x +e \right)\right) a b}{3}+a^{2} \sin \left(f x +e \right)-2 \sin \left(f x +e \right) a b +3 b^{2} \sin \left(f x +e \right)}{a^{4}}+\frac{b^{3} \left(-\frac{b \sin \left(f x +e \right)}{2 \left(a +b \right) \left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)}-\frac{\left(8 a +7 b \right) \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{2 \left(a +b \right) \sqrt{\left(a +b \right) a}}\right)}{a^{4}}}{f}"," ",0,"1/f*(1/a^4*(1/5*sin(f*x+e)^5*a^2-2/3*sin(f*x+e)^3*a^2+2/3*sin(f*x+e)^3*a*b+a^2*sin(f*x+e)-2*sin(f*x+e)*a*b+3*b^2*sin(f*x+e))+b^3/a^4*(-1/2*b/(a+b)*sin(f*x+e)/(-a-b+a*sin(f*x+e)^2)-1/2*(8*a+7*b)/(a+b)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))))","A"
199,1,128,88,0.701000," ","int(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x)","\frac{\tan \left(f x +e \right)}{b^{2} f}+\frac{a^{2} \tan \left(f x +e \right)}{2 b^{2} \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,b^{2} \left(a +b \right) \sqrt{\left(a +b \right) b}}-\frac{2 a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f b \left(a +b \right) \sqrt{\left(a +b \right) b}}"," ",0,"tan(f*x+e)/b^2/f+1/2*a^2*tan(f*x+e)/b^2/(a+b)/f/(a+b+b*tan(f*x+e)^2)-3/2/f*a^2/b^2/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-2/f*a/b/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))","A"
200,1,106,70,0.694000," ","int(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x)","-\frac{a \tan \left(f x +e \right)}{2 b \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f b \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right) \sqrt{\left(a +b \right) b}}"," ",0,"-1/2*a*tan(f*x+e)/b/(a+b)/f/(a+b+b*tan(f*x+e)^2)+1/2/f*a/b/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))","A"
201,1,66,61,0.566000," ","int(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x)","\frac{\tan \left(f x +e \right)}{2 \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \left(a +b \right) \sqrt{\left(a +b \right) b}}"," ",0,"1/2*tan(f*x+e)/(a+b)/f/(a+b+b*tan(f*x+e)^2)+1/2/f/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))","A"
202,1,127,80,0.868000," ","int(1/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 a \left(a +b \right) f \left(a +b +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{\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{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"-1/2*b*tan(f*x+e)/a/(a+b)/f/(a+b+b*tan(f*x+e)^2)-3/2/f*b/a/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f*b^2/a^2/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a^2*arctan(tan(f*x+e))","A"
203,1,174,126,1.244000," ","int(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x)","\frac{b^{2} \tan \left(f x +e \right)}{2 f \,a^{2} \left(a +b \right) \left(a +b +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{\left(a +b \right) b}}\right)}{2 f \,a^{2} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{2 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{\tan \left(f x +e \right)}{2 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{2 f \,a^{2}}-\frac{2 \arctan \left(\tan \left(f x +e \right)\right) b}{f \,a^{3}}"," ",0,"1/2/f*b^2/a^2/(a+b)*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)+5/2/f*b^2/a^2/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+2/f*b^3/a^3/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/2/f/a^2*tan(f*x+e)/(tan(f*x+e)^2+1)+1/2/f/a^2*arctan(tan(f*x+e))-2/f/a^3*arctan(tan(f*x+e))*b","A"
204,1,276,185,1.322000," ","int(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b^{3} \tan \left(f x +e \right)}{2 f \,a^{3} \left(a +b \right) \left(a +b +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{\left(a +b \right) b}}\right)}{2 f \,a^{3} \left(a +b \right) \sqrt{\left(a +b \right) b}}-\frac{3 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{4} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{3 \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{\left(\tan^{3}\left(f x +e \right)\right) b}{f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{\tan \left(f x +e \right) b}{f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{5 \tan \left(f x +e \right)}{8 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f \,a^{4}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right)}{8 f \,a^{2}}-\frac{\arctan \left(\tan \left(f x +e \right)\right) b}{f \,a^{3}}"," ",0,"-1/2/f*b^3/a^3/(a+b)*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)-7/2/f*b^3/a^3/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-3/f*b^4/a^4/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+3/8/f/a^2/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3-1/f/a^3/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3*b-1/f/a^3/(tan(f*x+e)^2+1)^2*tan(f*x+e)*b+5/8/f/a^2/(tan(f*x+e)^2+1)^2*tan(f*x+e)+3/f/a^4*arctan(tan(f*x+e))*b^2+3/8/f/a^2*arctan(tan(f*x+e))-1/f/a^3*arctan(tan(f*x+e))*b","A"
205,1,442,258,1.531000," ","int(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x)","\frac{b^{4} \tan \left(f x +e \right)}{2 f \,a^{4} \left(a +b \right) \left(a +b +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{\left(a +b \right) b}}\right)}{2 f \,a^{4} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{4 b^{5} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{5} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{5 \left(\tan^{5}\left(f x +e \right)\right)}{16 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{3 \left(\tan^{5}\left(f x +e \right)\right) b}{4 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{3 \left(\tan^{5}\left(f x +e \right)\right) b^{2}}{2 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{3 \left(\tan^{3}\left(f x +e \right)\right) b^{2}}{f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{6 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{2 \left(\tan^{3}\left(f x +e \right)\right) b}{f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{5 \tan \left(f x +e \right) b}{4 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{3 \tan \left(f x +e \right) b^{2}}{2 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{11 \tan \left(f x +e \right)}{16 f \,a^{2} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{4 \arctan \left(\tan \left(f x +e \right)\right) b^{3}}{f \,a^{5}}+\frac{5 \arctan \left(\tan \left(f x +e \right)\right)}{16 f \,a^{2}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b}{4 f \,a^{3}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{2 f \,a^{4}}"," ",0,"1/2/f/a^4*b^4/(a+b)*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)+9/2/f*b^4/a^4/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+4/f/a^5*b^5/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+5/16/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5-3/4/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b+3/2/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b^2+3/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b^2+5/6/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3-2/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b-5/4/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b+3/2/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b^2+11/16/f/a^2/(tan(f*x+e)^2+1)^3*tan(f*x+e)-4/f/a^5*arctan(tan(f*x+e))*b^3+5/16/f/a^2*arctan(tan(f*x+e))-3/4/f/a^3*arctan(tan(f*x+e))*b+3/2/f/a^4*arctan(tan(f*x+e))*b^2","A"
206,1,108,94,0.901000," ","int(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x)","\frac{\frac{\sin \left(f x +e \right)}{4 \left(a +b \right) \left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{-\frac{3 \sin \left(f x +e \right)}{8 \left(a +b \right) \left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)}+\frac{3 \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{8 \left(a +b \right) \sqrt{\left(a +b \right) a}}}{a +b}}{f}"," ",0,"1/f*(1/4*sin(f*x+e)/(a+b)/(-a-b+a*sin(f*x+e)^2)^2+3/4/(a+b)*(-1/2*sin(f*x+e)/(a+b)/(-a-b+a*sin(f*x+e)^2)+1/2/(a+b)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))))","A"
207,1,124,111,0.930000," ","int(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x)","\frac{\frac{-\frac{\left(4 a +b \right) \left(\sin^{3}\left(f x +e \right)\right)}{8 \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(4 a -b \right) \sin \left(f x +e \right)}{8 \left(a +b \right) a}}{\left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{\left(4 a +b \right) \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{8 \left(a^{2}+2 a b +b^{2}\right) a \sqrt{\left(a +b \right) a}}}{f}"," ",0,"1/f*((-1/8*(4*a+b)/(a^2+2*a*b+b^2)*sin(f*x+e)^3+1/8*(4*a-b)/(a+b)/a*sin(f*x+e))/(-a-b+a*sin(f*x+e)^2)^2+1/8*(4*a+b)/(a^2+2*a*b+b^2)/a/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2)))","A"
208,1,142,130,0.962000," ","int(sec(f*x+e)/(a+b*sec(f*x+e)^2)^3,x)","\frac{-\frac{-\frac{b \left(8 a +5 b \right) \left(\sin^{3}\left(f x +e \right)\right)}{8 a \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(8 a +3 b \right) b \sin \left(f x +e \right)}{8 a^{2} \left(a +b \right)}}{\left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{\left(8 a^{2}+8 a b +3 b^{2}\right) \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{8 \left(a^{2}+2 a b +b^{2}\right) a^{2} \sqrt{\left(a +b \right) a}}}{f}"," ",0,"1/f*(-(-1/8*b*(8*a+5*b)/a/(a^2+2*a*b+b^2)*sin(f*x+e)^3+1/8*(8*a+3*b)/a^2*b/(a+b)*sin(f*x+e))/(-a-b+a*sin(f*x+e)^2)^2+1/8*(8*a^2+8*a*b+3*b^2)/(a^2+2*a*b+b^2)/a^2/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2)))","A"
209,1,149,142,1.405000," ","int(cos(f*x+e)/(a+b*sec(f*x+e)^2)^3,x)","\frac{\frac{\sin \left(f x +e \right)}{a^{3}}+\frac{b \left(\frac{-\frac{3 a b \left(4 a +3 b \right) \left(\sin^{3}\left(f x +e \right)\right)}{8 \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(12 a +7 b \right) b \sin \left(f x +e \right)}{8 a +8 b}}{\left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{3 \left(8 a^{2}+12 a b +5 b^{2}\right) \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{8 \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) a}}\right)}{a^{3}}}{f}"," ",0,"1/f*(1/a^3*sin(f*x+e)+1/a^3*b*((-3/8*a*b*(4*a+3*b)/(a^2+2*a*b+b^2)*sin(f*x+e)^3+1/8*(12*a+7*b)*b/(a+b)*sin(f*x+e))/(-a-b+a*sin(f*x+e)^2)^2-3/8*(8*a^2+12*a*b+5*b^2)/(a^2+2*a*b+b^2)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))))","A"
210,1,177,165,1.236000," ","int(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x)","\frac{-\frac{\frac{a \left(\sin^{3}\left(f x +e \right)\right)}{3}-a \sin \left(f x +e \right)+3 b \sin \left(f x +e \right)}{a^{4}}-\frac{b^{2} \left(\frac{-\frac{a b \left(16 a +13 b \right) \left(\sin^{3}\left(f x +e \right)\right)}{8 \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(16 a +11 b \right) b \sin \left(f x +e \right)}{8 a +8 b}}{\left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{\left(48 a^{2}+80 a b +35 b^{2}\right) \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{8 \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) a}}\right)}{a^{4}}}{f}"," ",0,"1/f*(-1/a^4*(1/3*a*sin(f*x+e)^3-a*sin(f*x+e)+3*b*sin(f*x+e))-b^2/a^4*((-1/8*a*b*(16*a+13*b)/(a^2+2*a*b+b^2)*sin(f*x+e)^3+1/8*(16*a+11*b)*b/(a+b)*sin(f*x+e))/(-a-b+a*sin(f*x+e)^2)^2-1/8*(48*a^2+80*a*b+35*b^2)/(a^2+2*a*b+b^2)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))))","A"
211,1,214,196,1.320000," ","int(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x)","\frac{\frac{\frac{\left(\sin^{5}\left(f x +e \right)\right) a^{2}}{5}-\frac{2 \left(\sin^{3}\left(f x +e \right)\right) a^{2}}{3}+\left(\sin^{3}\left(f x +e \right)\right) a b +a^{2} \sin \left(f x +e \right)-3 \sin \left(f x +e \right) a b +6 b^{2} \sin \left(f x +e \right)}{a^{5}}+\frac{b^{3} \left(\frac{-\frac{a b \left(20 a +17 b \right) \left(\sin^{3}\left(f x +e \right)\right)}{8 \left(a^{2}+2 a b +b^{2}\right)}+\frac{5 \left(4 a +3 b \right) b \sin \left(f x +e \right)}{8 \left(a +b \right)}}{\left(-a -b +a \left(\sin^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{\left(80 a^{2}+140 a b +63 b^{2}\right) \arctanh \left(\frac{a \sin \left(f x +e \right)}{\sqrt{\left(a +b \right) a}}\right)}{8 \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) a}}\right)}{a^{5}}}{f}"," ",0,"1/f*(1/a^5*(1/5*sin(f*x+e)^5*a^2-2/3*sin(f*x+e)^3*a^2+sin(f*x+e)^3*a*b+a^2*sin(f*x+e)-3*sin(f*x+e)*a*b+6*b^2*sin(f*x+e))+b^3/a^5*((-1/8*a*b*(20*a+17*b)/(a^2+2*a*b+b^2)*sin(f*x+e)^3+5/8*(4*a+3*b)*b/(a+b)*sin(f*x+e))/(-a-b+a*sin(f*x+e)^2)^2-1/8*(80*a^2+140*a*b+63*b^2)/(a^2+2*a*b+b^2)/((a+b)*a)^(1/2)*arctanh(a*sin(f*x+e)/((a+b)*a)^(1/2))))","A"
212,1,294,128,0.638000," ","int(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x)","-\frac{5 a^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b \left(a^{2}+2 a b +b^{2}\right)}-\frac{a \left(\tan^{3}\left(f x +e \right)\right)}{f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{3 a^{2} \tan \left(f x +e \right)}{8 f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b^{2} \left(a +b \right)}-\frac{a \tan \left(f x +e \right)}{b \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right) a^{2}}{8 f \left(a^{2}+2 a b +b^{2}\right) b^{2} \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right) a}{f \left(a^{2}+2 a b +b^{2}\right) b \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}"," ",0,"-5/8/f/(a+b+b*tan(f*x+e)^2)^2*a^2/b/(a^2+2*a*b+b^2)*tan(f*x+e)^3-1/f/(a+b+b*tan(f*x+e)^2)^2*a/(a^2+2*a*b+b^2)*tan(f*x+e)^3-3/8/f/(a+b+b*tan(f*x+e)^2)^2*a^2/b^2/(a+b)*tan(f*x+e)-a*tan(f*x+e)/b/(a+b)/f/(a+b+b*tan(f*x+e)^2)^2+3/8/f/(a^2+2*a*b+b^2)/b^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))*a^2+1/f/(a^2+2*a*b+b^2)/b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))*a+1/f/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))","B"
213,1,238,109,0.618000," ","int(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x)","\frac{a \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(\tan^{3}\left(f x +e \right)\right) b}{2 f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{a \tan \left(f x +e \right)}{8 b \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{\tan \left(f x +e \right)}{2 \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right) a}{8 f \left(a^{2}+2 a b +b^{2}\right) b \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}"," ",0,"1/8/f/(a+b+b*tan(f*x+e)^2)^2*a/(a^2+2*a*b+b^2)*tan(f*x+e)^3+1/2/f/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3*b-1/8*a*tan(f*x+e)/b/(a+b)/f/(a+b+b*tan(f*x+e)^2)^2+1/2*tan(f*x+e)/(a+b)/f/(a+b+b*tan(f*x+e)^2)^2+1/8/f/(a^2+2*a*b+b^2)/b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))*a+1/2/f/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))","B"
214,1,97,92,0.791000," ","int(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x)","\frac{\tan \left(f x +e \right)}{4 \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 \tan \left(f x +e \right)}{8 \left(a +b \right)^{2} f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{3 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f \left(a +b \right)^{2} \sqrt{\left(a +b \right) b}}"," ",0,"1/4*tan(f*x+e)/(a+b)/f/(a+b+b*tan(f*x+e)^2)^2+3/8*tan(f*x+e)/(a+b)^2/f/(a+b+b*tan(f*x+e)^2)+3/8/f/(a+b)^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))","A"
215,1,321,130,1.115000," ","int(1/(a+b*sec(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f a \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{2 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{9 b \tan \left(f x +e \right)}{8 a \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{2} \tan \left(f x +e \right)}{2 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}-\frac{15 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\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{\tan \left(f x +e \right) b}{\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{\tan \left(f x +e \right) b}{\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{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"-7/8/f/a*b^2/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3-1/2/f/a^2*b^3/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3-9/8*b*tan(f*x+e)/a/(a+b)/f/(a+b+b*tan(f*x+e)^2)^2-1/2/f/a^2*b^2/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)-15/8/f/a*b/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-5/2/f/a^2*b^2/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a^3*b^3/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a^3*arctan(tan(f*x+e))","B"
216,1,366,183,1.606000," ","int(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x)","\frac{11 b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{f \,a^{3} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{13 b^{2} \tan \left(f x +e \right)}{8 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}+\frac{b^{3} \tan \left(f x +e \right)}{f \,a^{3} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}+\frac{35 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f \,a^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}+\frac{7 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\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{3 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{4} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}+\frac{\tan \left(f x +e \right)}{2 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{2 f \,a^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b}{f \,a^{4}}"," ",0,"11/8/f/a^2*b^3/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3+1/f/a^3*b^4/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3+13/8/f/a^2*b^2/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)+1/f/a^3*b^3/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)+35/8/f/a^2*b^2/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+7/f/a^3*b^3/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+3/f/a^4*b^4/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/2/f/a^3*tan(f*x+e)/(tan(f*x+e)^2+1)+1/2/f/a^3*arctan(tan(f*x+e))-3/f/a^4*arctan(tan(f*x+e))*b","A"
217,1,470,249,1.668000," ","int(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x)","-\frac{15 b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{3 b^{5} \left(\tan^{3}\left(f x +e \right)\right)}{2 f \,a^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{17 b^{3} \tan \left(f x +e \right)}{8 f \,a^{3} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}-\frac{3 b^{4} \tan \left(f x +e \right)}{2 f \,a^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}-\frac{63 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f \,a^{3} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}-\frac{27 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,a^{4} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}-\frac{6 b^{5} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{5} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}+\frac{3 \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \left(\tan^{3}\left(f x +e \right)\right) b}{2 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}-\frac{3 \tan \left(f x +e \right) b}{2 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{5 \tan \left(f x +e \right)}{8 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{2}}+\frac{6 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f \,a^{5}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right)}{8 f \,a^{3}}-\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b}{2 f \,a^{4}}"," ",0,"-15/8/f/a^3*b^4/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3-3/2/f/a^4*b^5/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3-17/8/f/a^3*b^3/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)-3/2/f/a^4*b^4/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)-63/8/f/a^3*b^3/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-27/2/f/a^4*b^4/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-6/f/a^5*b^5/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+3/8/f/a^3/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3-3/2/f/a^4/(tan(f*x+e)^2+1)^2*tan(f*x+e)^3*b-3/2/f/a^4/(tan(f*x+e)^2+1)^2*tan(f*x+e)*b+5/8/f/a^3/(tan(f*x+e)^2+1)^2*tan(f*x+e)+6/f/a^5*arctan(tan(f*x+e))*b^2+3/8/f/a^3*arctan(tan(f*x+e))-3/2/f/a^4*arctan(tan(f*x+e))*b","A"
218,1,636,330,1.595000," ","int(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x)","\frac{19 b^{5} \left(\tan^{3}\left(f x +e \right)\right)}{8 f \,a^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 b^{6} \left(\tan^{3}\left(f x +e \right)\right)}{f \,a^{5} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{21 b^{4} \tan \left(f x +e \right)}{8 f \,a^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}+\frac{2 b^{5} \tan \left(f x +e \right)}{f \,a^{5} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}+\frac{99 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f \,a^{4} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}+\frac{22 b^{5} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{5} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}+\frac{10 b^{6} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{6} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}+\frac{5 \left(\tan^{5}\left(f x +e \right)\right)}{16 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{9 \left(\tan^{5}\left(f x +e \right)\right) b}{8 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{3 \left(\tan^{5}\left(f x +e \right)\right) b^{2}}{f \,a^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{6 \left(\tan^{3}\left(f x +e \right)\right) b^{2}}{f \,a^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{6 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{3 \left(\tan^{3}\left(f x +e \right)\right) b}{f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{15 \tan \left(f x +e \right) b}{8 f \,a^{4} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{3 \tan \left(f x +e \right) b^{2}}{f \,a^{5} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}+\frac{11 \tan \left(f x +e \right)}{16 f \,a^{3} \left(1+\tan^{2}\left(f x +e \right)\right)^{3}}-\frac{10 \arctan \left(\tan \left(f x +e \right)\right) b^{3}}{f \,a^{6}}+\frac{5 \arctan \left(\tan \left(f x +e \right)\right)}{16 f \,a^{3}}-\frac{9 \arctan \left(\tan \left(f x +e \right)\right) b}{8 f \,a^{4}}+\frac{3 \arctan \left(\tan \left(f x +e \right)\right) b^{2}}{f \,a^{5}}"," ",0,"19/8/f/a^4*b^5/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3+2/f*b^6/a^5/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3+21/8/f/a^4*b^4/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)+2/f*b^5/a^5/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)+99/8/f/a^4*b^4/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+22/f/a^5*b^5/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+10/f*b^6/a^6/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+5/16/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5-9/8/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b+3/f/a^5/(tan(f*x+e)^2+1)^3*tan(f*x+e)^5*b^2+6/f/a^5/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b^2+5/6/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3-3/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)^3*b-15/8/f/a^4/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b+3/f/a^5/(tan(f*x+e)^2+1)^3*tan(f*x+e)*b^2+11/16/f/a^3/(tan(f*x+e)^2+1)^3*tan(f*x+e)-10/f/a^6*arctan(tan(f*x+e))*b^3+5/16/f/a^3*arctan(tan(f*x+e))-9/8/f/a^4*arctan(tan(f*x+e))*b+3/f/a^5*arctan(tan(f*x+e))*b^2","A"
219,1,649,188,0.819000," ","int(1/(a+b*sec(d*x+c)^2)^4,x)","-\frac{19 b^{3} \left(\tan^{5}\left(d x +c \right)\right)}{16 d a \left(a +b +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{3} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{11 b^{4} \left(\tan^{5}\left(d x +c \right)\right)}{8 d \,a^{2} \left(a +b +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{3} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{b^{5} \left(\tan^{5}\left(d x +c \right)\right)}{2 d \,a^{3} \left(a +b +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{3} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{17 b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{6 d a \left(a +b +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{3} \left(a^{2}+2 a b +b^{2}\right)}-\frac{3 b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{d \,a^{2} \left(a +b +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{3} \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{d \,a^{3} \left(a +b +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{3} \left(a^{2}+2 a b +b^{2}\right)}-\frac{29 b \tan \left(d x +c \right)}{16 a \left(a +b \right) d \left(a +b +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{3}}-\frac{13 b^{2} \tan \left(d x +c \right)}{8 d \,a^{2} \left(a +b +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{3} \left(a +b \right)}-\frac{b^{3} \tan \left(d x +c \right)}{2 d \,a^{3} \left(a +b +b \left(\tan^{2}\left(d x +c \right)\right)\right)^{3} \left(a +b \right)}-\frac{35 b \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{16 d a \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right) \sqrt{\left(a +b \right) b}}-\frac{35 b^{2} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 d \,a^{2} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right) \sqrt{\left(a +b \right) b}}-\frac{7 b^{3} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 d \,a^{3} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right) \sqrt{\left(a +b \right) b}}-\frac{b^{4} \arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{d \,a^{4} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right) \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,a^{4}}"," ",0,"-19/16/d/a*b^3/(a+b+b*tan(d*x+c)^2)^3/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)^5-11/8/d/a^2*b^4/(a+b+b*tan(d*x+c)^2)^3/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)^5-1/2/d/a^3*b^5/(a+b+b*tan(d*x+c)^2)^3/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)^5-17/6/d/a*b^2/(a+b+b*tan(d*x+c)^2)^3/(a^2+2*a*b+b^2)*tan(d*x+c)^3-3/d/a^2*b^3/(a+b+b*tan(d*x+c)^2)^3/(a^2+2*a*b+b^2)*tan(d*x+c)^3-1/d/a^3*b^4/(a+b+b*tan(d*x+c)^2)^3/(a^2+2*a*b+b^2)*tan(d*x+c)^3-29/16*b*tan(d*x+c)/a/(a+b)/d/(a+b+b*tan(d*x+c)^2)^3-13/8/d/a^2*b^2/(a+b+b*tan(d*x+c)^2)^3/(a+b)*tan(d*x+c)-1/2/d/a^3*b^3/(a+b+b*tan(d*x+c)^2)^3/(a+b)*tan(d*x+c)-35/16/d/a*b/(a^3+3*a^2*b+3*a*b^2+b^3)/((a+b)*b)^(1/2)*arctan(tan(d*x+c)*b/((a+b)*b)^(1/2))-35/8/d/a^2*b^2/(a^3+3*a^2*b+3*a*b^2+b^3)/((a+b)*b)^(1/2)*arctan(tan(d*x+c)*b/((a+b)*b)^(1/2))-7/2/d/a^3*b^3/(a^3+3*a^2*b+3*a*b^2+b^3)/((a+b)*b)^(1/2)*arctan(tan(d*x+c)*b/((a+b)*b)^(1/2))-1/d/a^4*b^4/(a^3+3*a^2*b+3*a*b^2+b^3)/((a+b)*b)^(1/2)*arctan(tan(d*x+c)*b/((a+b)*b)^(1/2))+1/d/a^4*arctan(tan(d*x+c))","B"
220,1,168,120,2.327000," ","int((a-a*sec(d*x+c)^2)^(7/2),x)","\frac{\left(12 \left(\cos^{6}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-12 \left(\cos^{6}\left(d x +c \right)\right) \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right)+12 \left(\cos^{6}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-11 \left(\cos^{6}\left(d x +c \right)\right)+18 \left(\cos^{4}\left(d x +c \right)\right)-9 \left(\cos^{2}\left(d x +c \right)\right)+2\right) \cos \left(d x +c \right) \left(-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{2}}\right)^{\frac{7}{2}}}{12 d \sin \left(d x +c \right)^{7}}"," ",0,"1/12/d*(12*cos(d*x+c)^6*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-12*cos(d*x+c)^6*ln(2/(1+cos(d*x+c)))+12*cos(d*x+c)^6*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-11*cos(d*x+c)^6+18*cos(d*x+c)^4-9*cos(d*x+c)^2+2)*cos(d*x+c)*(-a*sin(d*x+c)^2/cos(d*x+c)^2)^(7/2)/sin(d*x+c)^7","A"
221,1,158,91,1.990000," ","int((a-a*sec(d*x+c)^2)^(5/2),x)","-\frac{\left(4 \left(\cos^{4}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+4 \left(\cos^{4}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-4 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right)-3 \left(\cos^{4}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \cos \left(d x +c \right) \left(-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{2}}\right)^{\frac{5}{2}}}{4 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/4/d*(4*cos(d*x+c)^4*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))+4*cos(d*x+c)^4*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-4*ln(2/(1+cos(d*x+c)))*cos(d*x+c)^4-3*cos(d*x+c)^4+4*cos(d*x+c)^2-1)*cos(d*x+c)*(-a*sin(d*x+c)^2/cos(d*x+c)^2)^(5/2)/sin(d*x+c)^5","A"
222,1,148,58,2.340000," ","int((a-a*sec(d*x+c)^2)^(3/2),x)","\frac{\left(2 \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+2 \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-2 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)-\left(\cos^{2}\left(d x +c \right)\right)+1\right) \cos \left(d x +c \right) \left(-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{2}}\right)^{\frac{3}{2}}}{2 d \sin \left(d x +c \right)^{3}}"," ",0,"1/2/d*(2*cos(d*x+c)^2*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))+2*cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-2*ln(2/(1+cos(d*x+c)))*cos(d*x+c)^2-cos(d*x+c)^2+1)*cos(d*x+c)*(-a*sin(d*x+c)^2/cos(d*x+c)^2)^(3/2)/sin(d*x+c)^3","B"
223,1,109,31,3.072000," ","int((a-a*sec(d*x+c)^2)^(1/2),x)","-\frac{\left(\ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+\ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right)\right) \cos \left(d x +c \right) \sqrt{-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{2}}}}{d \sin \left(d x +c \right)}"," ",0,"-1/d*(ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-ln(2/(1+cos(d*x+c))))*cos(d*x+c)*(-a*sin(d*x+c)^2/cos(d*x+c)^2)^(1/2)/sin(d*x+c)","B"
224,1,76,30,1.959000," ","int(1/(a-a*sec(d*x+c)^2)^(1/2),x)","-\frac{\left(-\ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+\ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right)\right) \sin \left(d x +c \right)}{d \sqrt{-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{2}}}\, \cos \left(d x +c \right)}"," ",0,"-1/d*(-ln(-(-1+cos(d*x+c))/sin(d*x+c))+ln(2/(1+cos(d*x+c))))*sin(d*x+c)/(-a*sin(d*x+c)^2/cos(d*x+c)^2)^(1/2)/cos(d*x+c)","B"
225,1,141,61,1.664000," ","int(1/(a-a*sec(d*x+c)^2)^(3/2),x)","\frac{\left(4 \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-4 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)-\left(\cos^{2}\left(d x +c \right)\right)-4 \ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+4 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right)-1\right) \sin \left(d x +c \right)}{4 d \cos \left(d x +c \right)^{3} \left(-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/4/d*(4*cos(d*x+c)^2*ln(-(-1+cos(d*x+c))/sin(d*x+c))-4*ln(2/(1+cos(d*x+c)))*cos(d*x+c)^2-cos(d*x+c)^2-4*ln(-(-1+cos(d*x+c))/sin(d*x+c))+4*ln(2/(1+cos(d*x+c)))-1)*sin(d*x+c)/cos(d*x+c)^3/(-a*sin(d*x+c)^2/cos(d*x+c)^2)^(3/2)","B"
226,1,203,90,1.778000," ","int(1/(a-a*sec(d*x+c)^2)^(5/2),x)","\frac{\left(32 \left(\cos^{4}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-32 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right)-13 \left(\cos^{4}\left(d x +c \right)\right)-64 \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+64 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)-6 \left(\cos^{2}\left(d x +c \right)\right)+32 \ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-32 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right)+11\right) \sin \left(d x +c \right)}{32 d \cos \left(d x +c \right)^{5} \left(-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{2}}\right)^{\frac{5}{2}}}"," ",0,"1/32/d*(32*cos(d*x+c)^4*ln(-(-1+cos(d*x+c))/sin(d*x+c))-32*ln(2/(1+cos(d*x+c)))*cos(d*x+c)^4-13*cos(d*x+c)^4-64*cos(d*x+c)^2*ln(-(-1+cos(d*x+c))/sin(d*x+c))+64*ln(2/(1+cos(d*x+c)))*cos(d*x+c)^2-6*cos(d*x+c)^2+32*ln(-(-1+cos(d*x+c))/sin(d*x+c))-32*ln(2/(1+cos(d*x+c)))+11)*sin(d*x+c)/cos(d*x+c)^5/(-a*sin(d*x+c)^2/cos(d*x+c)^2)^(5/2)","B"
227,1,265,119,1.834000," ","int(1/(a-a*sec(d*x+c)^2)^(7/2),x)","-\frac{\left(48 \left(\cos^{6}\left(d x +c \right)\right) \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right)-48 \ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{6}\left(d x +c \right)\right)+25 \left(\cos^{6}\left(d x +c \right)\right)-144 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right)+144 \left(\cos^{4}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-3 \left(\cos^{4}\left(d x +c \right)\right)+144 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)-144 \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-33 \left(\cos^{2}\left(d x +c \right)\right)-48 \ln \left(\frac{2}{1+\cos \left(d x +c \right)}\right)+48 \ln \left(-\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+19\right) \sin \left(d x +c \right)}{48 d \left(-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{2}}\right)^{\frac{7}{2}} \cos \left(d x +c \right)^{7}}"," ",0,"-1/48/d*(48*cos(d*x+c)^6*ln(2/(1+cos(d*x+c)))-48*ln(-(-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^6+25*cos(d*x+c)^6-144*ln(2/(1+cos(d*x+c)))*cos(d*x+c)^4+144*cos(d*x+c)^4*ln(-(-1+cos(d*x+c))/sin(d*x+c))-3*cos(d*x+c)^4+144*ln(2/(1+cos(d*x+c)))*cos(d*x+c)^2-144*cos(d*x+c)^2*ln(-(-1+cos(d*x+c))/sin(d*x+c))-33*cos(d*x+c)^2-48*ln(2/(1+cos(d*x+c)))+48*ln(-(-1+cos(d*x+c))/sin(d*x+c))+19)*sin(d*x+c)/(-a*sin(d*x+c)^2/cos(d*x+c)^2)^(7/2)/cos(d*x+c)^7","B"
228,1,6562,346,2.288000," ","int(sec(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
229,1,4739,266,1.503000," ","int(sec(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"1/6/f*(6*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b-8*I*cos(f*x+e)^5*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)^4*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*cos(f*x+e)^3*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-8*I*cos(f*x+e)^3*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)^2*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+8*I*cos(f*x+e)^2*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)^4*a^(5/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*cos(f*x+e)^5*a^(5/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+2*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-4*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+6*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-4*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b-5*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2+6*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b+6*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-4*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b-5*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3+4*I*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3-4*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+2*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3-2*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3-sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3-2*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+2*I*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(5/2)*b^(1/2)-2*I*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(3/2)*b^(3/2)-4*I*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(1/2)*b^(5/2)+2*I*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(5/2)*b^(1/2)-2*I*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(3/2)*b^(3/2)-4*I*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(1/2)*b^(5/2))*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(b+a*cos(f*x+e)^2)/cos(f*x+e)^2/sin(f*x+e)/b/(2*I*a^(1/2)*b^(1/2)-a+b)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
230,1,3454,206,1.483000," ","int(sec(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/2/f*(2*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-2*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+2*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b-4*I*a^(1/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2+sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2-2*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2+sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2+sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+2*I*sin(f*x+e)*cos(f*x+e)^2*a^(3/2)*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*I*sin(f*x+e)*cos(f*x+e)^2*a^(1/2)*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*I*sin(f*x+e)*cos(f*x+e)*a^(3/2)*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*I*sin(f*x+e)*cos(f*x+e)*a^(1/2)*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-2*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-2*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2+4*I*cos(f*x+e)^3*a^(3/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)*a^(1/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*cos(f*x+e)^2*a^(3/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(b+a*cos(f*x+e)^2)/sin(f*x+e)/(2*I*a^(1/2)*b^(1/2)-a+b)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
231,1,3408,75,2.017000," ","int(cos(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/2/f*(2*I*sin(f*x+e)*a^(3/2)*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)-EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*sin(f*x+e)+2*I*sin(f*x+e)*a^(1/2)*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)*b^2-2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)+2*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-2*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b-4*I*a^(1/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2-sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+2*I*sin(f*x+e)*cos(f*x+e)*a^(3/2)*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*I*sin(f*x+e)*cos(f*x+e)*a^(1/2)*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*b^2*sin(f*x+e)+4*I*cos(f*x+e)^3*a^(3/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)*a^(1/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*cos(f*x+e)^2*a^(3/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(b+a*cos(f*x+e)^2)/sin(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(2*I*a^(1/2)*b^(1/2)-a+b)","C"
232,1,4623,228,2.331000," ","int(cos(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/6/f*(6*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a^3-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)+6*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-5*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a^2*b-4*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a*b^2+4*I*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(5/2)*b^(1/2)*sin(f*x+e)+2*I*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(3/2)*b^(3/2)*sin(f*x+e)-2*I*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(1/2)*b^(5/2)*sin(f*x+e)-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)+4*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-2*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2-2*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-8*I*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+4*I*cos(f*x+e)*a^(5/2)*b^(1/2)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*I*cos(f*x+e)*a^(3/2)*b^(3/2)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*I*cos(f*x+e)*a^(1/2)*b^(5/2)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-5*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)-4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a*b^2-2*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a^3-cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^3+4*I*cos(f*x+e)^5*a^(5/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)^3*a^(5/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+8*I*cos(f*x+e)^3*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-8*I*cos(f*x+e)^2*a^(5/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*cos(f*x+e)^2*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(b+a*cos(f*x+e)^2)/sin(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(2*I*a^(1/2)*b^(1/2)-a+b)/a","C"
233,1,6394,316,2.535000," ","int(cos(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
234,1,2518,166,2.119000," ","int(sec(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/48/f*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*(-18*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2-10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+14*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-14*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-3*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b+9*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2+6*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-10*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+10*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-4*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-15*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+4*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+15*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-15*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+15*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-6*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3-30*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3+3*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3+15*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/cos(f*x+e)^5/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/b^2","C"
235,1,1769,106,1.716000," ","int(sec(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \left(-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}+3 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}-3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b +3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \cos \left(f x +e \right)^{3} b \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/8/f*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*(-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a^2+4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a*b+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^4*sin(f*x+e)*b^2+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a^2-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a*b-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*b^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2+3*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2-3*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+3*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-3*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/cos(f*x+e)^3/b/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
236,1,1098,64,1.362000," ","int(sec(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \left(-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) a -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) b +2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) a +2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/2/f*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*(-cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a-cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b+2*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*a+2*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/cos(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
237,1,588,67,2.385000," ","int((a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{2}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a +\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b -2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b -2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \right) \cos \left(f x +e \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\sin^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}}{f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/f*2^(1/2)*(EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a+EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b-2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b-2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a)*cos(f*x+e)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)^2*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
238,1,1064,70,1.762000," ","int(cos(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\left(\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/2/f*(2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)*cos(f*x+e)*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
239,1,1713,124,2.309000," ","int(cos(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\left(-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} \sin \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} \sin \left(f x +e \right)-4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) a \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/8/f*(-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*sin(f*x+e)+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)-4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/a/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
240,1,2436,176,2.463000," ","int(cos(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\left(-4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a \,b^{2}+14 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b +6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \,b^{2} \sin \left(f x +e \right)-10 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2} b +15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b +4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \,b^{2} \sin \left(f x +e \right)-18 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} b \sin \left(f x +e \right)-15 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}+15 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}-15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a^{2} b -8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{7}\left(f x +e \right)\right) a^{3}+10 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2} b +10 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{3}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-14 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2} b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a \,b^{2}+8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{6}\left(f x +e \right)\right) a^{3}-10 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{3}+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{3}+9 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} b \sin \left(f x +e \right)-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{3} \sin \left(f x +e \right)+15 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{3} \sin \left(f x +e \right)-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}-30 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{3} \sin \left(f x +e \right)+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{3} \sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}}{48 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) a^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/48/f*(-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*sin(f*x+e)-14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2-10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)+15*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-15*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3+10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3+10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3-15*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3-10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)+9*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*sin(f*x+e))*cos(f*x+e)*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/a^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
241,1,7996,420,2.831000," ","int(sec(f*x+e)^5*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
242,1,6562,345,1.816000," ","int(sec(f*x+e)^3*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
243,1,5185,268,1.468000," ","int(sec(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
244,1,3632,212,1.546000," ","int(cos(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"-1/2/f*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^2*(-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2-sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*a^2*b+sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*a*b^2-cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a^2*b+cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a*b^2+2*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3+2*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-4*I*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*b^3-sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*a^3+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a^3+cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^3+2*I*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*a^(5/2)*b^(1/2)+4*I*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*a^(3/2)*b^(3/2)+2*I*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*a^(1/2)*b^(5/2)+2*I*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*a^(5/2)*b^(1/2)+4*I*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*a^(3/2)*b^(3/2)+2*I*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*a^(1/2)*b^(5/2)+4*I*cos(f*x+e)*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)^4*a^(5/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^(5/2)*b^(1/2)+4*I*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^(3/2)*b^(3/2)-4*I*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a^(3/2)*b^(3/2))/sin(f*x+e)/(b+a*cos(f*x+e)^2)^2/(2*I*a^(1/2)*b^(1/2)-a+b)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
245,1,5069,223,1.707000," ","int(cos(f*x+e)^3*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
246,1,6396,297,2.095000," ","int(cos(f*x+e)^5*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
247,1,3343,219,2.801000," ","int(sec(f*x+e)^6*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"1/384/f*sin(f*x+e)*(-24*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*b+70*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*b^4-70*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*b^4-56*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*b^4+18*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^4+210*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^4-9*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^4-105*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^4+48*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^4-148*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a*b^3-120*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^3+148*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a*b^3+215*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a*b^3+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3*b-107*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^2*b^2-215*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a*b^3-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3*b+107*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^2*b^2+78*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b^2-78*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b^2+120*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^3-9*cos(f*x+e)^9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4+9*cos(f*x+e)^8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4+105*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4-105*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4+56*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4+108*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b^2+360*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^3+12*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*b-54*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b^2-180*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^3-48*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4+15*cos(f*x+e)^9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b+145*cos(f*x+e)^9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2+105*cos(f*x+e)^9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3-15*cos(f*x+e)^8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b-145*cos(f*x+e)^8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2-105*cos(f*x+e)^8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/cos(f*x+e)^5/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/b^2","C"
248,1,2519,145,2.318000," ","int(sec(f*x+e)^4*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/48/f*sin(f*x+e)*(-54*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2-22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+32*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-32*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+9*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b+27*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-18*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-10*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+10*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-22*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-15*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+22*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+15*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-15*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+15*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+6*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3-30*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3-3*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3+15*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/cos(f*x+e)^3/b/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
249,1,1768,95,1.502000," ","int(sec(f*x+e)^2*(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\sin \left(f x +e \right) \left(6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+12 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}+5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}+3 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}-3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +7 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b +3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}-7 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/8/f*sin(f*x+e)*(6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a^2+12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a*b+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^4*sin(f*x+e)*b^2-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a^2-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a*b-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*b^2+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2+3*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2-3*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+3*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-3*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/cos(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
250,1,1557,100,1.346000," ","int((a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\left(6 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +2 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}-2 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2}-3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b -\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2}+4 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \cos \left(f x +e \right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/2/f*(6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*a*b+2*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-2*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2-3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+4*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*sin(f*x+e)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
251,1,1512,106,1.448000," ","int(cos(f*x+e)^2*(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\sin \left(f x +e \right) \left(4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b \right) \left(\cos^{3}\left(f x +e \right)\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/2/f*sin(f*x+e)*(4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
252,1,1713,109,1.723000," ","int(cos(f*x+e)^4*(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\sin \left(f x +e \right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(f x +e \right)\right) \left(2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} \sin \left(f x +e \right)+12 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} \sin \left(f x +e \right)-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2}+7 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}-7 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a b +5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/8/f*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^3*(2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)+12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2+7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
253,1,2439,173,2.075000," ","int(cos(f*x+e)^6*(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\sin \left(f x +e \right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(f x +e \right)\right) \left(-22 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a \,b^{2}+32 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b -22 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2} b +15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b +22 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}+9 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \,b^{2} \sin \left(f x +e \right)-15 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}+15 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}-10 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{3}-8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{7}\left(f x +e \right)\right) a^{3}+22 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -15 \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b +10 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{3}+17 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-32 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2} b -17 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a \,b^{2}+8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{6}\left(f x +e \right)\right) a^{3}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{3}+15 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{3} \sin \left(f x +e \right)-54 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} b \sin \left(f x +e \right)-18 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \,b^{2} \sin \left(f x +e \right)+27 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} b \sin \left(f x +e \right)+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{3} \sin \left(f x +e \right)-30 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{3} \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{3} \sin \left(f x +e \right)\right)}{48 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} a \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/48/f*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^3*(-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*sin(f*x+e)-32*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b-17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2-22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+9*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)+15*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-15*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3+22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+32*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b+17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3+10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3-15*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3-10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-54*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)-18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)+27*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*sin(f*x+e))/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/a/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
254,1,2231,144,1.804000," ","int((a+b*sec(d*x+c)^2)^(5/2),x)","\frac{\left(16 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(d x +c \right)+b}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(d x +c \right)-b \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(d x +c \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{3}+30 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(d x +c \right)+b}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(d x +c \right)-b \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} b +20 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(d x +c \right)+b}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(d x +c \right)-b \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \,b^{2}+6 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(d x +c \right)+b}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(d x +c \right)-b \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{3}-8 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(d x +c \right)+b}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(d x +c \right)-b \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{3}-15 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(d x +c \right)+b}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(d x +c \right)-b \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} b -10 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(d x +c \right)+b}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(d x +c \right)-b \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \,b^{2}-3 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(d x +c \right)+b}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(d x +c \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(d x +c \right)-b \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{3}+9 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b +3 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}-9 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b -3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}+11 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}+3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}-11 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}-3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}+2 \cos \left(d x +c \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}\right) \cos \left(d x +c \right) \left(\frac{a \left(\cos^{2}\left(d x +c \right)\right)+b}{\cos \left(d x +c \right)^{2}}\right)^{\frac{5}{2}} \sin \left(d x +c \right)}{8 d \left(-1+\cos \left(d x +c \right)\right) \left(a \left(\cos^{2}\left(d x +c \right)\right)+b \right)^{3} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/8/d*(16*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)+a*cos(d*x+c)+b)/(1+cos(d*x+c))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)-a*cos(d*x+c)-b)/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(d*x+c),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3+30*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)+a*cos(d*x+c)+b)/(1+cos(d*x+c))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)-a*cos(d*x+c)-b)/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(d*x+c),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b+20*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)+a*cos(d*x+c)+b)/(1+cos(d*x+c))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)-a*cos(d*x+c)-b)/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(d*x+c),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2+6*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)+a*cos(d*x+c)+b)/(1+cos(d*x+c))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)-a*cos(d*x+c)-b)/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(d*x+c),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3-8*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)+a*cos(d*x+c)+b)/(1+cos(d*x+c))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)-a*cos(d*x+c)-b)/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(d*x+c),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3-15*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)+a*cos(d*x+c)+b)/(1+cos(d*x+c))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)-a*cos(d*x+c)-b)/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(d*x+c),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b-10*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)+a*cos(d*x+c)+b)/(1+cos(d*x+c))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)-a*cos(d*x+c)-b)/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(d*x+c),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-3*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)+a*cos(d*x+c)+b)/(1+cos(d*x+c))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(d*x+c)-I*a^(1/2)*b^(1/2)-a*cos(d*x+c)-b)/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(d*x+c),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3+9*cos(d*x+c)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+3*cos(d*x+c)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-9*cos(d*x+c)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-3*cos(d*x+c)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+11*cos(d*x+c)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+3*cos(d*x+c)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-11*cos(d*x+c)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-3*cos(d*x+c)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+2*cos(d*x+c)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)*cos(d*x+c)*((a*cos(d*x+c)^2+b)/cos(d*x+c)^2)^(5/2)*sin(d*x+c)/(-1+cos(d*x+c))/(a*cos(d*x+c)^2+b)^3/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
255,1,429,35,1.510000," ","int((1+sec(x)^2)^(3/2),x)","\frac{\left(-\frac{1}{4}+\frac{i}{4}\right) \left(8 \sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \left(-1\right)^{\frac{3}{4}} \sqrt{\frac{i \cos \left(x \right)+1-i+\cos \left(x \right)}{\cos \left(x \right)+1}}\, \sqrt{-\frac{i \cos \left(x \right)-\cos \left(x \right)-1-i}{\cos \left(x \right)+1}}\, \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -i, i\right)+4 \sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \left(-1\right)^{\frac{3}{4}} \sqrt{\frac{i \cos \left(x \right)+1-i+\cos \left(x \right)}{\cos \left(x \right)+1}}\, \sqrt{-\frac{i \cos \left(x \right)-\cos \left(x \right)-1-i}{\cos \left(x \right)+1}}\, \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i, i\right)+6 \sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \sqrt{2}\, \sqrt{\frac{i \cos \left(x \right)+1-i+\cos \left(x \right)}{\cos \left(x \right)+1}}\, \sqrt{-\frac{i \cos \left(x \right)-\cos \left(x \right)-1-i}{\cos \left(x \right)+1}}\, \EllipticF \left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right)-8 \sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \left(-1\right)^{\frac{1}{4}} \sqrt{\frac{i \cos \left(x \right)+1-i+\cos \left(x \right)}{\cos \left(x \right)+1}}\, \sqrt{-\frac{i \cos \left(x \right)-\cos \left(x \right)-1-i}{\cos \left(x \right)+1}}\, \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -i, i\right)-4 \sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \left(-1\right)^{\frac{1}{4}} \sqrt{\frac{i \cos \left(x \right)+1-i+\cos \left(x \right)}{\cos \left(x \right)+1}}\, \sqrt{-\frac{i \cos \left(x \right)-\cos \left(x \right)-1-i}{\cos \left(x \right)+1}}\, \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i, i\right)-i \left(\cos^{3}\left(x \right)\right)-\left(\cos^{3}\left(x \right)\right)+i \left(\cos^{2}\left(x \right)\right)+\cos^{2}\left(x \right)-i \cos \left(x \right)-\cos \left(x \right)+1+i\right) \sin \left(x \right) \cos \left(x \right) \left(\frac{1+\cos^{2}\left(x \right)}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}{\left(-1+\cos \left(x \right)\right) \left(1+\cos^{2}\left(x \right)\right)^{2}}"," ",0,"(-1/4+1/4*I)*(8*sin(x)*cos(x)^2*(-1)^(3/4)*((I*cos(x)+1-I+cos(x))/(cos(x)+1))^(1/2)*(-(I*cos(x)-cos(x)-1-I)/(cos(x)+1))^(1/2)*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),-I,I)+4*sin(x)*cos(x)^2*(-1)^(3/4)*((I*cos(x)+1-I+cos(x))/(cos(x)+1))^(1/2)*(-(I*cos(x)-cos(x)-1-I)/(cos(x)+1))^(1/2)*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),I,I)+6*sin(x)*cos(x)^2*2^(1/2)*((I*cos(x)+1-I+cos(x))/(cos(x)+1))^(1/2)*(-(I*cos(x)-cos(x)-1-I)/(cos(x)+1))^(1/2)*EllipticF((1/2+1/2*I)*2^(1/2)*(-1+cos(x))/sin(x),I)-8*sin(x)*cos(x)^2*(-1)^(1/4)*((I*cos(x)+1-I+cos(x))/(cos(x)+1))^(1/2)*(-(I*cos(x)-cos(x)-1-I)/(cos(x)+1))^(1/2)*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),-I,I)-4*sin(x)*cos(x)^2*(-1)^(1/4)*((I*cos(x)+1-I+cos(x))/(cos(x)+1))^(1/2)*(-(I*cos(x)-cos(x)-1-I)/(cos(x)+1))^(1/2)*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),I,I)-I*cos(x)^3-cos(x)^3+I*cos(x)^2+cos(x)^2-I*cos(x)-cos(x)+1+I)*sin(x)*cos(x)*((1+cos(x)^2)/cos(x)^2)^(3/2)/(-1+cos(x))/(1+cos(x)^2)^2","C"
256,1,190,21,2.704000," ","int((1+sec(x)^2)^(1/2),x)","\frac{\left(-1+i\right) \left(\left(-1\right)^{\frac{3}{4}} \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -i, i\right)+\left(-1\right)^{\frac{3}{4}} \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i, i\right)+\sqrt{2}\, \EllipticF \left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right)-\left(-1\right)^{\frac{1}{4}} \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -i, i\right)-\left(-1\right)^{\frac{1}{4}} \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i, i\right)\right) \cos \left(x \right) \left(\sin^{2}\left(x \right)\right) \sqrt{\frac{1+\cos^{2}\left(x \right)}{\cos \left(x \right)^{2}}}\, \sqrt{\frac{i \cos \left(x \right)+1-i+\cos \left(x \right)}{\cos \left(x \right)+1}}\, \sqrt{-\frac{i \cos \left(x \right)-\cos \left(x \right)-1-i}{\cos \left(x \right)+1}}}{\left(-1+\cos \left(x \right)\right) \left(1+\cos^{2}\left(x \right)\right)}"," ",0,"(-1+I)*((-1)^(3/4)*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),-I,I)+(-1)^(3/4)*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),I,I)+2^(1/2)*EllipticF((1/2+1/2*I)*2^(1/2)*(-1+cos(x))/sin(x),I)-(-1)^(1/4)*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),-I,I)-(-1)^(1/4)*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),I,I))*cos(x)*sin(x)^2*((1+cos(x)^2)/cos(x)^2)^(1/2)*((I*cos(x)+1-I+cos(x))/(cos(x)+1))^(1/2)*(-(I*cos(x)-cos(x)-1-I)/(cos(x)+1))^(1/2)/(-1+cos(x))/(1+cos(x)^2)","C"
257,1,4753,308,2.163000," ","int(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"1/3/f*(-3*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b-4*I*cos(f*x+e)^5*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*cos(f*x+e)^4*a^(5/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+2*I*cos(f*x+e)^4*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*cos(f*x+e)^3*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-2*I*cos(f*x+e)^2*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+2*I*cos(f*x+e)^2*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+3*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2+sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b-sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-3*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b+3*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2+sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b-sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2+2*I*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-2*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3-2*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3-sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3+sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3-sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-2*I*cos(f*x+e)^4*a^(5/2)*b^(1/2)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*I*cos(f*x+e)^4*a^(3/2)*b^(3/2)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*I*cos(f*x+e)^4*a^(1/2)*b^(5/2)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*I*cos(f*x+e)^3*a^(5/2)*b^(1/2)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+2*I*cos(f*x+e)^3*a^(3/2)*b^(3/2)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*I*cos(f*x+e)^3*a^(1/2)*b^(5/2)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+4*I*cos(f*x+e)^5*a^(5/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^(3/2)*b^(3/2))/cos(f*x+e)^4/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/sin(f*x+e)/b^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(2*I*a^(1/2)*b^(1/2)-a+b)","C"
258,1,3029,155,1.719000," ","int(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/2/f*(4*I*cos(f*x+e)^3*a^(3/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)*a^(1/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+2*I*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(1/2)*b^(3/2)-2*I*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(3/2)*b^(1/2)-2*I*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(3/2)*b^(1/2)-4*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+cos(f*x+e)^2*sin(f*x+e)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2+2*cos(f*x+e)^2*sin(f*x+e)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b+cos(f*x+e)^2*sin(f*x+e)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*b^2-4*I*cos(f*x+e)^2*a^(3/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2+2*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+2*I*sin(f*x+e)*cos(f*x+e)*a^(1/2)*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-4*I*a^(1/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)^2/sin(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/b/(2*I*a^(1/2)*b^(1/2)-a+b)","C"
259,1,269,75,1.553000," ","int(sec(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\left(\sin^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right)}{f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/f*sin(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
260,1,2985,92,1.729000," ","int(cos(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/2/f*(2*I*sin(f*x+e)*a^(3/2)*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-4*I*cos(f*x+e)^2*a^(3/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)^3*a^(3/2)*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+2*I*sin(f*x+e)*cos(f*x+e)*a^(3/2)*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*I*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^(1/2)*b^(3/2)+4*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2-2*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2-4*I*a^(1/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)-EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*sin(f*x+e)-2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*b^2*sin(f*x+e)+4*I*cos(f*x+e)*a^(1/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-2*I*a^(1/2)*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/cos(f*x+e)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/sin(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a/(2*I*a^(1/2)*b^(1/2)-a+b)","C"
261,1,4640,237,2.051000," ","int(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/3/f*(3*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a^3+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)-3*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a^2*b+cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a*b^2+4*I*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)+2*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2-4*I*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^(3/2)*b^(3/2)+2*I*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(5/2)*b^(1/2)*sin(f*x+e)+2*I*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(1/2)*b^(5/2)*sin(f*x+e)-cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-2*I*a^(3/2)*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)-2*I*cos(f*x+e)^3*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*I*cos(f*x+e)^2*a^(3/2)*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-4*I*cos(f*x+e)*a^(1/2)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a*b^2-cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*a^3+cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^3+2*I*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*a^(5/2)*b^(1/2)+2*I*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*a^(1/2)*b^(5/2)-2*I*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^(3/2)*b^(3/2)*sin(f*x+e)-4*I*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^(5/2)*b^(1/2)+2*I*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^(5/2)*b^(1/2)+2*I*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^(5/2)*b^(1/2)+2*I*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^(3/2)*b^(3/2))/cos(f*x+e)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/sin(f*x+e)/a^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(2*I*a^(1/2)*b^(1/2)-a+b)","C"
262,1,6382,323,2.485000," ","int(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
263,1,1756,121,2.199000," ","int(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sin \left(f x +e \right) \left(-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}-3 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}+3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{5} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}}"," ",0,"-1/8/f*sin(f*x+e)*(-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a^2+4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a*b-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^4*sin(f*x+e)*b^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a^2-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*a*b+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^4*sin(f*x+e)*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2-3*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2+3*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-3*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+3*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/b^2","C"
264,1,1086,69,2.040000," ","int(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \left(\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) a -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) b -2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) a +2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{3} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, b \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/2/f*sin(f*x+e)*(2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*b-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^2*sin(f*x+e)*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/b/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
265,1,379,33,1.597000," ","int(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right)-2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right)\right) \left(\sin^{2}\left(f x +e \right)\right)}{f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/f*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*(EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)))*sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
266,1,380,33,1.630000," ","int(1/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right)-2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right)\right) \left(\sin^{2}\left(f x +e \right)\right)}{f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/f*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*(EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)))*sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
267,1,1056,75,1.983000," ","int(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \left(2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a}"," ",0,"1/2/f*sin(f*x+e)*(2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/(-1+cos(f*x+e))/cos(f*x+e)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a","C"
268,1,1701,127,2.366000," ","int(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \left(2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2}-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} \sin \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} \sin \left(f x +e \right)-4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}}"," ",0,"1/8/f*sin(f*x+e)*(2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*sin(f*x+e)+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)-4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/(-1+cos(f*x+e))/cos(f*x+e)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^2","C"
269,1,2425,184,2.511000," ","int(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \left(-14 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a \,b^{2}+4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b -2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2} b -15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b +14 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}+15 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}-15 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}+10 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{3}+8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{7}\left(f x +e \right)\right) a^{3}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2} b +15 \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b -10 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{3}-5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2} b +5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a \,b^{2}+15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{3}-8 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{6}\left(f x +e \right)\right) a^{3}-15 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{3} \sin \left(f x +e \right)+9 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} b \sin \left(f x +e \right)-15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}+15 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{3} \sin \left(f x +e \right)-18 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} b \sin \left(f x +e \right)+18 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \,b^{2} \sin \left(f x +e \right)-9 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \,b^{2} \sin \left(f x +e \right)+30 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{3} \sin \left(f x +e \right)-30 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{3} \sin \left(f x +e \right)\right)}{48 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}}"," ",0,"1/48/f*sin(f*x+e)*(30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*sin(f*x+e)-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b-9*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)-15*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3+15*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3-10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3+15*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3+10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)+18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)+9*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*sin(f*x+e))/(-1+cos(f*x+e))/cos(f*x+e)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^3","C"
270,1,12510,275,2.218000," ","int(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
271,1,6601,143,1.950000," ","int(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
272,1,6593,217,2.250000," ","int(sec(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
273,1,8684,228,2.504000," ","int(cos(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
274,1,11939,315,2.506000," ","int(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
275,1,15199,412,2.756000," ","int(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
276,1,4338,124,1.881000," ","int(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"1/4/f*(-2*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(5/2)*a+13*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-2*b^(7/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)+4*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(3/2)*a^2-8*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(3/2)*a^2+2*cos(f*x+e)*b^(7/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)-13*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+2*cos(f*x+e)^5*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+6*cos(f*x+e)^5*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-2*cos(f*x+e)^4*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+4*cos(f*x+e)^3*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-6*cos(f*x+e)^4*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3+8*cos(f*x+e)^3*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2-4*cos(f*x+e)^2*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-8*cos(f*x+e)^2*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+2*cos(f*x+e)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-2*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+6*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(1/2)*a^3-12*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(1/2)*a^3+4*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(5/2)*a+4*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(5/2)*a-8*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(5/2)*a+6*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(3/2)*a^2-12*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(3/2)*a^2+13*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-13*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+13*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+13*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-13*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-13*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-2*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(7/2)+4*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(7/2))*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/b^(5/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(a+b)","C"
277,1,3068,69,1.825000," ","int(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"-1/2/f*(2*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a-4*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a+2*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2-4*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2+2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^(5/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)-4*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^(5/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)+2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a-4*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a+cos(f*x+e)^2*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2+cos(f*x+e)^2*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b-cos(f*x+e)^2*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2-cos(f*x+e)^2*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b+2*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(1/2)*a^2-2*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(1/2)*a^2+2*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(3/2)*a+sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b+sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^2-sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b-sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(3/2)*a)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/b^(3/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(a+b)","C"
278,1,59,30,1.449000," ","int(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \sin \left(f x +e \right)}{f \cos \left(f x +e \right)^{3} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(a +b \right)}"," ",0,"1/f*(b+a*cos(f*x+e)^2)*sin(f*x+e)/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(a+b)","A"
279,1,1007,69,1.910000," ","int(1/(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right) \sin \left(f x +e \right)}{f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{3} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(a +b \right) a \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/f*(b+a*cos(f*x+e)^2)*(2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(a+b)/a/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
280,1,1645,115,2.392000," ","int(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} \sin \left(f x +e \right)+4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \sin \left(f x +e \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{3} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} a^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(a +b \right)}"," ",0,"-1/2/f*(b+a*cos(f*x+e)^2)*(2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)+4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/a^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(a+b)","C"
281,1,2372,174,2.341000," ","int(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{3}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{5}\left(f x +e \right)\right) a^{2} b +6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{3} \sin \left(f x +e \right)-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} b \sin \left(f x +e \right)+18 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \,b^{2} \sin \left(f x +e \right)+30 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{3} \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{3} \sin \left(f x +e \right)+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} b \sin \left(f x +e \right)-9 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a \,b^{2} \sin \left(f x +e \right)-15 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{3} \sin \left(f x +e \right)-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{3}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2} b +3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2} b -5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a \,b^{2}-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b +5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}+3 \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b -4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a \,b^{2}-15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{3}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b +4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}+15 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}\right) \sin \left(f x +e \right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{3} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(a +b \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{3}}"," ",0,"1/8/f*(b+a*cos(f*x+e)^2)*(2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)+18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)+30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*sin(f*x+e)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)-9*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)-15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b+3*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-3*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+3*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(a+b)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^3","C"
282,1,3171,247,2.756000," ","int(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"1/48/f*(b+a*cos(f*x+e)^2)*(-210*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^4*sin(f*x+e)-10*a^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4+30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^4*sin(f*x+e)+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^4+10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^4+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^4-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^4+105*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^4+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3*b-13*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b^2-35*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^3-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3*b+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3*b-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3*b-14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b^2+14*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b^2-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^4-15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^4*sin(f*x+e)+105*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^4*sin(f*x+e)-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b+17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2-7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^3*b+13*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b^2+35*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^3+7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^3*b+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a^3*b-17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a^2*b^2+25*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^3-25*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3+12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*b*sin(f*x+e)-18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b^2*sin(f*x+e)-24*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*b*sin(f*x+e)-120*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^3*sin(f*x+e)+36*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b^2*sin(f*x+e)-105*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4+60*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^3*sin(f*x+e))*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^4/(a+b)","C"
283,1,14353,299,2.393000," ","int(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
284,1,10271,297,2.103000," ","int(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
285,1,14353,305,2.085000," ","int(sec(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
286,1,17502,327,2.613000," ","int(cos(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
287,1,20922,415,3.525000," ","int(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
288,1,26983,529,5.251000," ","int(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
289,1,3018,119,2.097000," ","int(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"-1/3/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3+6*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*b+3*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b^2-6*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3-12*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b-6*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-6*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b-12*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2-6*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3+3*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b-3*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b+4*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2)/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/(a^2+2*a*b+b^2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/b^2","C"
290,1,76,71,1.964000," ","int(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x)","\frac{\sin \left(f x +e \right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(2 a \left(\cos^{2}\left(f x +e \right)\right)+a +3 b \right)}{3 f \cos \left(f x +e \right)^{5} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \left(a +b \right)^{2}}"," ",0,"1/3/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(2*a*cos(f*x+e)^2+a+3*b)/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/(a+b)^2","A"
291,1,85,63,1.607000," ","int(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x)","\frac{\sin \left(f x +e \right) \left(3 a \left(\cos^{2}\left(f x +e \right)\right)+\left(\cos^{2}\left(f x +e \right)\right) b +2 b \right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{3 f \cos \left(f x +e \right)^{5} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \left(a +b \right)^{2}}"," ",0,"1/3/f*sin(f*x+e)*(3*a*cos(f*x+e)^2+cos(f*x+e)^2*b+2*b)*(b+a*cos(f*x+e)^2)/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/(a+b)^2","A"
292,1,3024,111,1.788000," ","int(1/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"-1/3/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3+6*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*b+3*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b^2-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3-12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^2*b-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a*b^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)-12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)+6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5/(a^2+2*a*b+b^2)/a^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
293,1,4270,167,2.407000," ","int(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"1/6/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(-18*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*b-30*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^4*sin(f*x+e)-3*a^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4-54*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b^2-30*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^3+15*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^3+9*2^(1/2)*a^3*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*b+27*2^(1/2)*a^2*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^4+15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^4+6*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^4-3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^4-6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^3*b-30*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b^2-20*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^3+6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^3*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b^2+15*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^4*sin(f*x+e)-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2+6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^3*b+30*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b^2+20*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^3-6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^3*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a^2*b^2+22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^3-22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*b*sin(f*x+e)+9*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b^2*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*b*sin(f*x+e)-54*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^3*sin(f*x+e)-18*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b^2*sin(f*x+e)-15*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4+27*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^3*sin(f*x+e))/(a+b)^2/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^3","C"
294,1,5600,237,2.936000," ","int(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
295,1,6934,304,3.751000," ","int(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
296,1,6116,161,2.643000," ","int(1/(a+b*sec(d*x+c)^2)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
297,1,142,12,1.096000," ","int(1/(1+sec(x)^2)^(1/2),x)","\frac{\left(-\frac{1}{2}+\frac{i}{2}\right) \left(\sin^{2}\left(x \right)\right) \sqrt{\frac{i \cos \left(x \right)+1-i+\cos \left(x \right)}{\cos \left(x \right)+1}}\, \sqrt{-\frac{i \cos \left(x \right)-\cos \left(x \right)-1-i}{\cos \left(x \right)+1}}\, \left(2 \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i, i\right) \left(-1\right)^{\frac{3}{4}}+\sqrt{2}\, \EllipticF \left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right)-2 \EllipticPi \left(\frac{\left(-1\right)^{\frac{1}{4}} \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i, i\right) \left(-1\right)^{\frac{1}{4}}\right)}{\sqrt{\frac{1+\cos^{2}\left(x \right)}{\cos \left(x \right)^{2}}}\, \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}"," ",0,"(-1/2+1/2*I)*sin(x)^2*((I*cos(x)+1-I+cos(x))/(cos(x)+1))^(1/2)*(-(I*cos(x)-cos(x)-1-I)/(cos(x)+1))^(1/2)*(2*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),I,I)*(-1)^(3/4)+EllipticF((1/2+1/2*I)*2^(1/2)*(-1+cos(x))/sin(x),I)*2^(1/2)-2*EllipticPi((-1)^(1/4)*(-1+cos(x))/sin(x),I,I)*(-1)^(1/4))/((1+cos(x)^2)/cos(x)^2)^(1/2)/cos(x)/(-1+cos(x))","C"
298,0,0,111,4.431000," ","int((d*sec(f*x+e))^m*(a+b*sec(f*x+e)^2)^p,x)","\int \left(d \sec \left(f x +e \right)\right)^{m} \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*sec(f*x+e))^m*(a+b*sec(f*x+e)^2)^p,x)","F"
299,0,0,99,1.556000," ","int(sec(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\sec^{3}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x)","F"
300,0,0,99,1.449000," ","int(sec(f*x+e)*(a+b*sec(f*x+e)^2)^p,x)","\int \sec \left(f x +e \right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)*(a+b*sec(f*x+e)^2)^p,x)","F"
301,0,0,97,1.907000," ","int(cos(f*x+e)*(a+b*sec(f*x+e)^2)^p,x)","\int \cos \left(f x +e \right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)*(a+b*sec(f*x+e)^2)^p,x)","F"
302,0,0,99,5.567000," ","int(cos(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\cos^{3}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x)","F"
303,0,0,99,6.060000," ","int(cos(f*x+e)^5*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\cos^{5}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^5*(a+b*sec(f*x+e)^2)^p,x)","F"
304,0,0,210,2.477000," ","int(sec(f*x+e)^6*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\sec^{6}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^6*(a+b*sec(f*x+e)^2)^p,x)","F"
305,0,0,127,1.736000," ","int(sec(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x)","F"
306,0,0,70,1.308000," ","int(sec(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x)","F"
307,0,0,79,0.046000," ","int((a+b*sec(f*x+e)^2)^p,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p,x)","F"
308,0,0,79,2.594000," ","int(cos(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x)","F"
309,0,0,79,3.015000," ","int(cos(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x)","F"
310,0,0,79,3.746000," ","int(cos(f*x+e)^6*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\cos^{6}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^6*(a+b*sec(f*x+e)^2)^p,x)","F"
311,1,65,66,0.625000," ","int((a+b*sec(f*x+e)^2)*tan(f*x+e)^5,x)","\frac{\left(\tan^{4}\left(f x +e \right)\right) a}{4 f}-\frac{a \left(\tan^{2}\left(f x +e \right)\right)}{2 f}-\frac{a \ln \left(\cos \left(f x +e \right)\right)}{f}+\frac{b \left(\sin^{6}\left(f x +e \right)\right)}{6 f \cos \left(f x +e \right)^{6}}"," ",0,"1/4/f*tan(f*x+e)^4*a-1/2/f*a*tan(f*x+e)^2-a*ln(cos(f*x+e))/f+1/6/f*b*sin(f*x+e)^6/cos(f*x+e)^6","A"
312,1,50,45,0.533000," ","int((a+b*sec(f*x+e)^2)*tan(f*x+e)^3,x)","\frac{a \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{a \ln \left(\cos \left(f x +e \right)\right)}{f}+\frac{b \left(\sin^{4}\left(f x +e \right)\right)}{4 f \cos \left(f x +e \right)^{4}}"," ",0,"1/2/f*a*tan(f*x+e)^2+a*ln(cos(f*x+e))/f+1/4/f*b*sin(f*x+e)^4/cos(f*x+e)^4","A"
313,1,28,28,0.226000," ","int((a+b*sec(f*x+e)^2)*tan(f*x+e),x)","\frac{b \left(\sec^{2}\left(f x +e \right)\right)}{2 f}+\frac{a \ln \left(\sec \left(f x +e \right)\right)}{f}"," ",0,"1/2*b*sec(f*x+e)^2/f+1/f*a*ln(sec(f*x+e))","A"
314,1,26,28,0.597000," ","int(cot(f*x+e)*(a+b*sec(f*x+e)^2),x)","\frac{b \ln \left(\tan \left(f x +e \right)\right)}{f}+\frac{a \ln \left(\sin \left(f x +e \right)\right)}{f}"," ",0,"1/f*b*ln(tan(f*x+e))+a*ln(sin(f*x+e))/f","A"
315,1,43,30,0.738000," ","int(cot(f*x+e)^3*(a+b*sec(f*x+e)^2),x)","-\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}-\frac{b}{2 f \sin \left(f x +e \right)^{2}}"," ",0,"-1/2*a*cot(f*x+e)^2/f-a*ln(sin(f*x+e))/f-1/2/f*b/sin(f*x+e)^2","A"
316,1,64,47,0.668000," ","int(cot(f*x+e)^5*(a+b*sec(f*x+e)^2),x)","-\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}-\frac{b \left(\cos^{4}\left(f x +e \right)\right)}{4 f \sin \left(f x +e \right)^{4}}"," ",0,"-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-1/4/f*b/sin(f*x+e)^4*cos(f*x+e)^4","A"
317,1,61,58,0.582000," ","int((a+b*sec(f*x+e)^2)*tan(f*x+e)^6,x)","\frac{a \left(\frac{\left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}+\tan \left(f x +e \right)-f x -e \right)+\frac{b \left(\sin^{7}\left(f x +e \right)\right)}{7 \cos \left(f x +e \right)^{7}}}{f}"," ",0,"1/f*(a*(1/5*tan(f*x+e)^5-1/3*tan(f*x+e)^3+tan(f*x+e)-f*x-e)+1/7*b*sin(f*x+e)^7/cos(f*x+e)^7)","A"
318,1,50,44,0.580000," ","int((a+b*sec(f*x+e)^2)*tan(f*x+e)^4,x)","\frac{a \left(\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}-\tan \left(f x +e \right)+f x +e \right)+\frac{b \left(\sin^{5}\left(f x +e \right)\right)}{5 \cos \left(f x +e \right)^{5}}}{f}"," ",0,"1/f*(a*(1/3*tan(f*x+e)^3-tan(f*x+e)+f*x+e)+1/5*b*sin(f*x+e)^5/cos(f*x+e)^5)","A"
319,1,41,30,0.633000," ","int((a+b*sec(f*x+e)^2)*tan(f*x+e)^2,x)","\frac{a \left(\tan \left(f x +e \right)-f x -e \right)+\frac{b \left(\sin^{3}\left(f x +e \right)\right)}{3 \cos \left(f x +e \right)^{3}}}{f}"," ",0,"1/f*(a*(tan(f*x+e)-f*x-e)+1/3*b*sin(f*x+e)^3/cos(f*x+e)^3)","A"
320,1,16,15,0.874000," ","int(a+b*sec(f*x+e)^2,x)","a x +\frac{b \tan \left(f x +e \right)}{f}"," ",0,"a*x+b*tan(f*x+e)/f","A"
321,1,33,19,0.886000," ","int(cot(f*x+e)^2*(a+b*sec(f*x+e)^2),x)","\frac{a \left(-\cot \left(f x +e \right)-f x -e \right)-b \cot \left(f x +e \right)}{f}"," ",0,"1/f*(a*(-cot(f*x+e)-f*x-e)-b*cot(f*x+e))","A"
322,1,48,31,0.741000," ","int(cot(f*x+e)^4*(a+b*sec(f*x+e)^2),x)","\frac{a \left(-\frac{\left(\cot^{3}\left(f x +e \right)\right)}{3}+\cot \left(f x +e \right)+f x +e \right)-\frac{b \left(\cos^{3}\left(f x +e \right)\right)}{3 \sin \left(f x +e \right)^{3}}}{f}"," ",0,"1/f*(a*(-1/3*cot(f*x+e)^3+cot(f*x+e)+f*x+e)-1/3*b/sin(f*x+e)^3*cos(f*x+e)^3)","A"
323,1,63,47,0.835000," ","int(cot(f*x+e)^6*(a+b*sec(f*x+e)^2),x)","\frac{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)-\frac{b \left(\cos^{5}\left(f x +e \right)\right)}{5 \sin \left(f x +e \right)^{5}}}{f}"," ",0,"1/f*(a*(-1/5*cot(f*x+e)^5+1/3*cot(f*x+e)^3-cot(f*x+e)-f*x-e)-1/5*b/sin(f*x+e)^5*cos(f*x+e)^5)","A"
324,1,120,94,0.692000," ","int((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^5,x)","\frac{\left(\tan^{4}\left(f x +e \right)\right) a^{2}}{4 f}-\frac{a^{2} \left(\tan^{2}\left(f x +e \right)\right)}{2 f}-\frac{a^{2} \ln \left(\cos \left(f x +e \right)\right)}{f}+\frac{a b \left(\sin^{6}\left(f x +e \right)\right)}{3 f \cos \left(f x +e \right)^{6}}+\frac{b^{2} \left(\sin^{6}\left(f x +e \right)\right)}{8 f \cos \left(f x +e \right)^{8}}+\frac{b^{2} \left(\sin^{6}\left(f x +e \right)\right)}{24 f \cos \left(f x +e \right)^{6}}"," ",0,"1/4/f*tan(f*x+e)^4*a^2-1/2/f*a^2*tan(f*x+e)^2-a^2*ln(cos(f*x+e))/f+1/3/f*a*b*sin(f*x+e)^6/cos(f*x+e)^6+1/8/f*b^2*sin(f*x+e)^6/cos(f*x+e)^8+1/24/f*b^2*sin(f*x+e)^6/cos(f*x+e)^6","A"
325,1,103,71,0.625000," ","int((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^3,x)","\frac{a^{2} \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{a^{2} \ln \left(\cos \left(f x +e \right)\right)}{f}+\frac{a b \left(\sin^{4}\left(f x +e \right)\right)}{2 f \cos \left(f x +e \right)^{4}}+\frac{b^{2} \left(\sin^{4}\left(f x +e \right)\right)}{6 f \cos \left(f x +e \right)^{6}}+\frac{b^{2} \left(\sin^{4}\left(f x +e \right)\right)}{12 f \cos \left(f x +e \right)^{4}}"," ",0,"1/2/f*a^2*tan(f*x+e)^2+a^2*ln(cos(f*x+e))/f+1/2/f*a*b*sin(f*x+e)^4/cos(f*x+e)^4+1/6/f*b^2*sin(f*x+e)^4/cos(f*x+e)^6+1/12/f*b^2*sin(f*x+e)^4/cos(f*x+e)^4","A"
326,1,46,46,0.337000," ","int((a+b*sec(f*x+e)^2)^2*tan(f*x+e),x)","\frac{b^{2} \left(\sec^{4}\left(f x +e \right)\right)}{4 f}+\frac{a b \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{a^{2} \ln \left(\sec \left(f x +e \right)\right)}{f}"," ",0,"1/4*b^2*sec(f*x+e)^4/f+a*b*sec(f*x+e)^2/f+1/f*a^2*ln(sec(f*x+e))","A"
327,1,60,51,0.935000," ","int(cot(f*x+e)*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \ln \left(\sin \left(f x +e \right)\right)}{f}+\frac{2 a b \ln \left(\tan \left(f x +e \right)\right)}{f}+\frac{b^{2}}{2 f \cos \left(f x +e \right)^{2}}+\frac{b^{2} \ln \left(\tan \left(f x +e \right)\right)}{f}"," ",0,"a^2*ln(sin(f*x+e))/f+2/f*a*b*ln(tan(f*x+e))+1/2/f*b^2/cos(f*x+e)^2+1/f*b^2*ln(tan(f*x+e))","A"
328,1,78,55,1.182000," ","int(cot(f*x+e)^3*(a+b*sec(f*x+e)^2)^2,x)","-\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}-\frac{a b}{f \sin \left(f x +e \right)^{2}}-\frac{b^{2}}{2 f \sin \left(f x +e \right)^{2}}+\frac{b^{2} \ln \left(\tan \left(f x +e \right)\right)}{f}"," ",0,"-1/2*a^2*cot(f*x+e)^2/f-a^2*ln(sin(f*x+e))/f-1/f*a*b/sin(f*x+e)^2-1/2/f*b^2/sin(f*x+e)^2+1/f*b^2*ln(tan(f*x+e))","A"
329,1,87,49,0.845000," ","int(cot(f*x+e)^5*(a+b*sec(f*x+e)^2)^2,x)","-\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}-\frac{a b \left(\cos^{4}\left(f x +e \right)\right)}{2 f \sin \left(f x +e \right)^{4}}-\frac{b^{2}}{4 f \sin \left(f x +e \right)^{4}}"," ",0,"-1/4*a^2*cot(f*x+e)^4/f+1/2*a^2*cot(f*x+e)^2/f+a^2*ln(sin(f*x+e))/f-1/2/f*a*b/sin(f*x+e)^4*cos(f*x+e)^4-1/4/f*b^2/sin(f*x+e)^4","A"
330,1,105,87,0.770000," ","int((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^6,x)","\frac{a^{2} \left(\frac{\left(\tan^{5}\left(f x +e \right)\right)}{5}-\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}+\tan \left(f x +e \right)-f x -e \right)+\frac{2 a b \left(\sin^{7}\left(f x +e \right)\right)}{7 \cos \left(f x +e \right)^{7}}+b^{2} \left(\frac{\sin^{7}\left(f x +e \right)}{9 \cos \left(f x +e \right)^{9}}+\frac{2 \left(\sin^{7}\left(f x +e \right)\right)}{63 \cos \left(f x +e \right)^{7}}\right)}{f}"," ",0,"1/f*(a^2*(1/5*tan(f*x+e)^5-1/3*tan(f*x+e)^3+tan(f*x+e)-f*x-e)+2/7*a*b*sin(f*x+e)^7/cos(f*x+e)^7+b^2*(1/9*sin(f*x+e)^7/cos(f*x+e)^9+2/63*sin(f*x+e)^7/cos(f*x+e)^7))","A"
331,1,94,71,0.596000," ","int((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^4,x)","\frac{a^{2} \left(\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}-\tan \left(f x +e \right)+f x +e \right)+\frac{2 a b \left(\sin^{5}\left(f x +e \right)\right)}{5 \cos \left(f x +e \right)^{5}}+b^{2} \left(\frac{\sin^{5}\left(f x +e \right)}{7 \cos \left(f x +e \right)^{7}}+\frac{2 \left(\sin^{5}\left(f x +e \right)\right)}{35 \cos \left(f x +e \right)^{5}}\right)}{f}"," ",0,"1/f*(a^2*(1/3*tan(f*x+e)^3-tan(f*x+e)+f*x+e)+2/5*a*b*sin(f*x+e)^5/cos(f*x+e)^5+b^2*(1/7*sin(f*x+e)^5/cos(f*x+e)^7+2/35*sin(f*x+e)^5/cos(f*x+e)^5))","A"
332,1,85,55,0.586000," ","int((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^2,x)","\frac{a^{2} \left(\tan \left(f x +e \right)-f x -e \right)+\frac{2 a b \left(\sin^{3}\left(f x +e \right)\right)}{3 \cos \left(f x +e \right)^{3}}+b^{2} \left(\frac{\sin^{3}\left(f x +e \right)}{5 \cos \left(f x +e \right)^{5}}+\frac{2 \left(\sin^{3}\left(f x +e \right)\right)}{15 \cos \left(f x +e \right)^{3}}\right)}{f}"," ",0,"1/f*(a^2*(tan(f*x+e)-f*x-e)+2/3*a*b*sin(f*x+e)^3/cos(f*x+e)^3+b^2*(1/5*sin(f*x+e)^3/cos(f*x+e)^5+2/15*sin(f*x+e)^3/cos(f*x+e)^3))","A"
333,1,48,38,1.033000," ","int((a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \left(f x +e \right)+2 a b \tan \left(f x +e \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*(f*x+e)+2*a*b*tan(f*x+e)-b^2*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e))","A"
334,1,66,36,0.928000," ","int(cot(f*x+e)^2*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \left(-\cot \left(f x +e \right)-f x -e \right)-2 a b \cot \left(f x +e \right)+b^{2} \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*(-cot(f*x+e)-f*x-e)-2*a*b*cot(f*x+e)+b^2*(1/sin(f*x+e)/cos(f*x+e)-2*cot(f*x+e)))","A"
335,1,73,43,1.284000," ","int(cot(f*x+e)^4*(a+b*sec(f*x+e)^2)^2,x)","\frac{a^{2} \left(-\frac{\left(\cot^{3}\left(f x +e \right)\right)}{3}+\cot \left(f x +e \right)+f x +e \right)-\frac{2 a b \left(\cos^{3}\left(f x +e \right)\right)}{3 \sin \left(f x +e \right)^{3}}+b^{2} \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(f x +e \right)\right)}{3}\right) \cot \left(f x +e \right)}{f}"," ",0,"1/f*(a^2*(-1/3*cot(f*x+e)^3+cot(f*x+e)+f*x+e)-2/3*a*b/sin(f*x+e)^3*cos(f*x+e)^3+b^2*(-2/3-1/3*csc(f*x+e)^2)*cot(f*x+e))","A"
336,1,107,61,1.165000," ","int(cot(f*x+e)^6*(a+b*sec(f*x+e)^2)^2,x)","\frac{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)-\frac{2 a b \left(\cos^{5}\left(f x +e \right)\right)}{5 \sin \left(f x +e \right)^{5}}+b^{2} \left(-\frac{\cos^{3}\left(f x +e \right)}{5 \sin \left(f x +e \right)^{5}}-\frac{2 \left(\cos^{3}\left(f x +e \right)\right)}{15 \sin \left(f x +e \right)^{3}}\right)}{f}"," ",0,"1/f*(a^2*(-1/5*cot(f*x+e)^5+1/3*cot(f*x+e)^3-cot(f*x+e)-f*x-e)-2/5*a*b/sin(f*x+e)^5*cos(f*x+e)^5+b^2*(-1/5/sin(f*x+e)^5*cos(f*x+e)^3-2/15/sin(f*x+e)^3*cos(f*x+e)^3))","A"
337,1,112,65,0.731000," ","int(tan(f*x+e)^5/(a+b*sec(f*x+e)^2),x)","-\frac{a \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \,b^{2}}-\frac{\ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{f b}-\frac{\ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 a f}+\frac{\ln \left(\cos \left(f x +e \right)\right) a}{f \,b^{2}}+\frac{2 \ln \left(\cos \left(f x +e \right)\right)}{b f}+\frac{1}{2 f b \cos \left(f x +e \right)^{2}}"," ",0,"-1/2/f/b^2*a*ln(b+a*cos(f*x+e)^2)-1/f/b*ln(b+a*cos(f*x+e)^2)-1/2*ln(b+a*cos(f*x+e)^2)/a/f+1/f/b^2*ln(cos(f*x+e))*a+2*ln(cos(f*x+e))/b/f+1/2/f/b/cos(f*x+e)^2","A"
338,1,59,43,0.640000," ","int(tan(f*x+e)^3/(a+b*sec(f*x+e)^2),x)","\frac{\ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f b}+\frac{\ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 a f}-\frac{\ln \left(\cos \left(f x +e \right)\right)}{b f}"," ",0,"1/2/f/b*ln(b+a*cos(f*x+e)^2)+1/2*ln(b+a*cos(f*x+e)^2)/a/f-ln(cos(f*x+e))/b/f","A"
339,1,37,21,0.227000," ","int(tan(f*x+e)/(a+b*sec(f*x+e)^2),x)","-\frac{\ln \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)}{2 f a}+\frac{\ln \left(\sec \left(f x +e \right)\right)}{f a}"," ",0,"-1/2/f/a*ln(a+b*sec(f*x+e)^2)+1/f/a*ln(sec(f*x+e))","A"
340,1,73,44,0.748000," ","int(cot(f*x+e)/(a+b*sec(f*x+e)^2),x)","\frac{b \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 a \left(a +b \right) f}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{f \left(2 a +2 b \right)}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{f \left(2 a +2 b \right)}"," ",0,"1/2*b*ln(b+a*cos(f*x+e)^2)/a/(a+b)/f+1/f/(2*a+2*b)*ln(-1+cos(f*x+e))+1/f/(2*a+2*b)*ln(1+cos(f*x+e))","A"
341,1,158,70,1.028000," ","int(cot(f*x+e)^3/(a+b*sec(f*x+e)^2),x)","-\frac{b^{2} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 a \left(a +b \right)^{2} f}+\frac{1}{f \left(4 a +4 b \right) \left(-1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a}{2 f \left(a +b \right)^{2}}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) b}{f \left(a +b \right)^{2}}-\frac{1}{f \left(4 a +4 b \right) \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) a}{2 f \left(a +b \right)^{2}}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) b}{f \left(a +b \right)^{2}}"," ",0,"-1/2*b^2*ln(b+a*cos(f*x+e)^2)/a/(a+b)^2/f+1/f/(4*a+4*b)/(-1+cos(f*x+e))-1/2/f/(a+b)^2*ln(-1+cos(f*x+e))*a-1/f/(a+b)^2*ln(-1+cos(f*x+e))*b-1/f/(4*a+4*b)/(1+cos(f*x+e))-1/2/f/(a+b)^2*ln(1+cos(f*x+e))*a-1/f/(a+b)^2*ln(1+cos(f*x+e))*b","B"
342,1,293,102,1.042000," ","int(cot(f*x+e)^5/(a+b*sec(f*x+e)^2),x)","\frac{b^{3} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 a \left(a +b \right)^{3} f}-\frac{1}{2 f \left(8 a +8 b \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}-\frac{7 a}{16 f \left(a +b \right)^{2} \left(-1+\cos \left(f x +e \right)\right)}-\frac{11 b}{16 f \left(a +b \right)^{2} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a^{2}}{2 f \left(a +b \right)^{3}}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) a b}{2 f \left(a +b \right)^{3}}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{2 f \left(a +b \right)^{3}}-\frac{1}{2 f \left(8 a +8 b \right) \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{7 a}{16 f \left(a +b \right)^{2} \left(1+\cos \left(f x +e \right)\right)}+\frac{11 b}{16 f \left(a +b \right)^{2} \left(1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) a^{2}}{2 f \left(a +b \right)^{3}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) a b}{2 f \left(a +b \right)^{3}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{2 f \left(a +b \right)^{3}}"," ",0,"1/2*b^3*ln(b+a*cos(f*x+e)^2)/a/(a+b)^3/f-1/2/f/(8*a+8*b)/(-1+cos(f*x+e))^2-7/16/f/(a+b)^2/(-1+cos(f*x+e))*a-11/16/f/(a+b)^2/(-1+cos(f*x+e))*b+1/2/f/(a+b)^3*ln(-1+cos(f*x+e))*a^2+3/2/f/(a+b)^3*ln(-1+cos(f*x+e))*a*b+3/2/f/(a+b)^3*ln(-1+cos(f*x+e))*b^2-1/2/f/(8*a+8*b)/(1+cos(f*x+e))^2+7/16/f/(a+b)^2/(1+cos(f*x+e))*a+11/16/f/(a+b)^2/(1+cos(f*x+e))*b+1/2/f/(a+b)^3*ln(1+cos(f*x+e))*a^2+3/2/f/(a+b)^3*ln(1+cos(f*x+e))*a*b+3/2/f/(a+b)^3*ln(1+cos(f*x+e))*b^2","B"
343,1,186,73,0.839000," ","int(tan(f*x+e)^6/(a+b*sec(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{2 \tan \left(f x +e \right)}{b f}+\frac{a^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,b^{2} \sqrt{\left(a +b \right) b}}+\frac{3 a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f b \sqrt{\left(a +b \right) b}}+\frac{3 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \sqrt{\left(a +b \right) b}}+\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f a \sqrt{\left(a +b \right) b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f a}"," ",0,"1/3*tan(f*x+e)^3/b/f-1/f/b^2*a*tan(f*x+e)-2*tan(f*x+e)/b/f+1/f/b^2*a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+3/f/b*a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+3/f/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f*b/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a*arctan(tan(f*x+e))","B"
344,1,121,51,0.679000," ","int(tan(f*x+e)^4/(a+b*sec(f*x+e)^2),x)","\frac{\tan \left(f x +e \right)}{b f}-\frac{a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f b \sqrt{\left(a +b \right) b}}-\frac{2 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \sqrt{\left(a +b \right) b}}-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f a \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f a}"," ",0,"tan(f*x+e)/b/f-1/f/b*a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-2/f/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f*b/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a*arctan(tan(f*x+e))","B"
345,1,75,38,0.717000," ","int(tan(f*x+e)^2/(a+b*sec(f*x+e)^2),x)","\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \sqrt{\left(a +b \right) b}}+\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f a \sqrt{\left(a +b \right) b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f a}"," ",0,"1/f/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f*b/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a*arctan(tan(f*x+e))","A"
346,1,48,37,0.581000," ","int(1/(a+b*sec(f*x+e)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f a \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f a}"," ",0,"-1/f*b/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a*arctan(tan(f*x+e))","A"
347,1,73,54,0.739000," ","int(cot(f*x+e)^2/(a+b*sec(f*x+e)^2),x)","\frac{b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right) a \sqrt{\left(a +b \right) b}}-\frac{1}{f \left(a +b \right) \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f a}"," ",0,"1/f/(a+b)*b^2/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/(a+b)/tan(f*x+e)-1/f/a*arctan(tan(f*x+e))","A"
348,1,110,76,1.059000," ","int(cot(f*x+e)^4/(a+b*sec(f*x+e)^2),x)","-\frac{b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{2} a \sqrt{\left(a +b \right) b}}-\frac{1}{3 f \left(a +b \right) \tan \left(f x +e \right)^{3}}+\frac{a}{f \left(a +b \right)^{2} \tan \left(f x +e \right)}+\frac{2 b}{f \left(a +b \right)^{2} \tan \left(f x +e \right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f a}"," ",0,"-1/f/(a+b)^2*b^3/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/3/f/(a+b)/tan(f*x+e)^3+1/f/(a+b)^2/tan(f*x+e)*a+2/f/(a+b)^2/tan(f*x+e)*b+1/f/a*arctan(tan(f*x+e))","A"
349,1,173,108,1.252000," ","int(cot(f*x+e)^6/(a+b*sec(f*x+e)^2),x)","\frac{b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{3} a \sqrt{\left(a +b \right) b}}-\frac{1}{5 f \left(a +b \right) \tan \left(f x +e \right)^{5}}+\frac{a}{3 f \left(a +b \right)^{2} \tan \left(f x +e \right)^{3}}+\frac{2 b}{3 f \left(a +b \right)^{2} \tan \left(f x +e \right)^{3}}-\frac{a^{2}}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}-\frac{3 a b}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}-\frac{3 b^{2}}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f a}"," ",0,"1/f/(a+b)^3*b^4/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/5/f/(a+b)/tan(f*x+e)^5+1/3/f/(a+b)^2/tan(f*x+e)^3*a+2/3/f/(a+b)^2/tan(f*x+e)^3*b-1/f/(a+b)^3/tan(f*x+e)*a^2-3/f/(a+b)^3/tan(f*x+e)*a*b-3/f/(a+b)^3/tan(f*x+e)*b^2-1/f/a*arctan(tan(f*x+e))","A"
350,1,126,73,1.025000," ","int(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x)","\frac{\ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \,b^{2}}-\frac{1}{2 f b \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{1}{f a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{\ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 a^{2} f}-\frac{b}{2 a^{2} f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{\ln \left(\cos \left(f x +e \right)\right)}{b^{2} f}"," ",0,"1/2/f/b^2*ln(b+a*cos(f*x+e)^2)-1/2/f/b/(b+a*cos(f*x+e)^2)-1/f/a/(b+a*cos(f*x+e)^2)-1/2*ln(b+a*cos(f*x+e)^2)/a^2/f-1/2*b/a^2/f/(b+a*cos(f*x+e)^2)-ln(cos(f*x+e))/b^2/f","A"
351,1,68,47,0.999000," ","int(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x)","\frac{\ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 a^{2} f}+\frac{1}{2 f a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{b}{2 a^{2} f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}"," ",0,"1/2*ln(b+a*cos(f*x+e)^2)/a^2/f+1/2/f/a/(b+a*cos(f*x+e)^2)+1/2*b/a^2/f/(b+a*cos(f*x+e)^2)","A"
352,1,59,45,0.327000," ","int(tan(f*x+e)/(a+b*sec(f*x+e)^2)^2,x)","-\frac{\ln \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)}{2 f \,a^{2}}+\frac{1}{2 f a \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)}+\frac{\ln \left(\sec \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"-1/2/f/a^2*ln(a+b*sec(f*x+e)^2)+1/2/f/a/(a+b*sec(f*x+e)^2)+1/f/a^2*ln(sec(f*x+e))","A"
353,1,155,79,1.092000," ","int(cot(f*x+e)/(a+b*sec(f*x+e)^2)^2,x)","\frac{b \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{f \left(a +b \right)^{2} a}+\frac{b^{2} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{2} a^{2}}+\frac{b^{2}}{2 f \left(a +b \right)^{2} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{b^{3}}{2 a^{2} \left(a +b \right)^{2} f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \left(a +b \right)^{2}}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \left(a +b \right)^{2}}"," ",0,"1/f*b/(a+b)^2/a*ln(b+a*cos(f*x+e)^2)+1/2/f*b^2/(a+b)^2/a^2*ln(b+a*cos(f*x+e)^2)+1/2/f*b^2/(a+b)^2/a/(b+a*cos(f*x+e)^2)+1/2*b^3/a^2/(a+b)^2/f/(b+a*cos(f*x+e)^2)+1/2/f/(a+b)^2*ln(-1+cos(f*x+e))+1/2/f/(a+b)^2*ln(1+cos(f*x+e))","A"
354,1,240,105,1.273000," ","int(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x)","-\frac{3 b^{2} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{3} a}-\frac{b^{3} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{3} a^{2}}-\frac{b^{3}}{2 f \left(a +b \right)^{3} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{b^{4}}{2 a^{2} \left(a +b \right)^{3} f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{1}{4 f \left(a +b \right)^{2} \left(-1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a}{2 f \left(a +b \right)^{3}}-\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b}{2 f \left(a +b \right)^{3}}-\frac{1}{4 f \left(a +b \right)^{2} \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) a}{2 f \left(a +b \right)^{3}}-\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b}{2 f \left(a +b \right)^{3}}"," ",0,"-3/2/f*b^2/(a+b)^3/a*ln(b+a*cos(f*x+e)^2)-1/2/f*b^3/(a+b)^3/a^2*ln(b+a*cos(f*x+e)^2)-1/2/f*b^3/(a+b)^3/a/(b+a*cos(f*x+e)^2)-1/2*b^4/a^2/(a+b)^3/f/(b+a*cos(f*x+e)^2)+1/4/f/(a+b)^2/(-1+cos(f*x+e))-1/2/f/(a+b)^3*ln(-1+cos(f*x+e))*a-3/2/f/(a+b)^3*ln(-1+cos(f*x+e))*b-1/4/f/(a+b)^2/(1+cos(f*x+e))-1/2/f/(a+b)^3*ln(1+cos(f*x+e))*a-3/2/f/(a+b)^3*ln(1+cos(f*x+e))*b","B"
355,1,374,134,1.224000," ","int(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x)","\frac{2 b^{3} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{f \left(a +b \right)^{4} a}+\frac{b^{4} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{4} a^{2}}+\frac{b^{4}}{2 f \left(a +b \right)^{4} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{b^{5}}{2 f \left(a +b \right)^{4} a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{1}{16 f \left(a +b \right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2}}-\frac{7 a}{16 f \left(a +b \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}-\frac{15 b}{16 f \left(a +b \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a^{2}}{2 f \left(a +b \right)^{4}}+\frac{2 \ln \left(-1+\cos \left(f x +e \right)\right) a b}{f \left(a +b \right)^{4}}+\frac{3 \ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{f \left(a +b \right)^{4}}-\frac{1}{16 f \left(a +b \right)^{2} \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{7 a}{16 f \left(a +b \right)^{3} \left(1+\cos \left(f x +e \right)\right)}+\frac{15 b}{16 f \left(a +b \right)^{3} \left(1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) a^{2}}{2 f \left(a +b \right)^{4}}+\frac{2 \ln \left(1+\cos \left(f x +e \right)\right) a b}{f \left(a +b \right)^{4}}+\frac{3 \ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{f \left(a +b \right)^{4}}"," ",0,"2/f*b^3/(a+b)^4/a*ln(b+a*cos(f*x+e)^2)+1/2/f*b^4/(a+b)^4/a^2*ln(b+a*cos(f*x+e)^2)+1/2/f*b^4/(a+b)^4/a/(b+a*cos(f*x+e)^2)+1/2/f*b^5/(a+b)^4/a^2/(b+a*cos(f*x+e)^2)-1/16/f/(a+b)^2/(-1+cos(f*x+e))^2-7/16/f/(a+b)^3/(-1+cos(f*x+e))*a-15/16/f/(a+b)^3/(-1+cos(f*x+e))*b+1/2/f/(a+b)^4*ln(-1+cos(f*x+e))*a^2+2/f/(a+b)^4*ln(-1+cos(f*x+e))*a*b+3/f/(a+b)^4*ln(-1+cos(f*x+e))*b^2-1/16/f/(a+b)^2/(1+cos(f*x+e))^2+7/16/f/(a+b)^3/(1+cos(f*x+e))*a+15/16/f/(a+b)^3/(1+cos(f*x+e))*b+1/2/f/(a+b)^4*ln(1+cos(f*x+e))*a^2+2/f/(a+b)^4*ln(1+cos(f*x+e))*a*b+3/f/(a+b)^4*ln(1+cos(f*x+e))*b^2","B"
356,1,242,105,0.768000," ","int(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x)","\frac{\tan \left(f x +e \right)}{b^{2} f}+\frac{a \tan \left(f x +e \right)}{2 f \,b^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{\tan \left(f x +e \right)}{f b \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{\tan \left(f x +e \right)}{2 a f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{3 a \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,b^{2} \sqrt{\left(a +b \right) b}}-\frac{2 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f b \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f a \sqrt{\left(a +b \right) b}}+\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \sqrt{\left(a +b \right) b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"tan(f*x+e)/b^2/f+1/2/f*a/b^2*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)+1/f/b*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)+1/2*tan(f*x+e)/a/f/(a+b+b*tan(f*x+e)^2)-3/2/f*a/b^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-2/f/b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/2/f/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f*b/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a^2*arctan(tan(f*x+e))","B"
357,1,168,78,0.897000," ","int(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x)","-\frac{\tan \left(f x +e \right)}{2 f b \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f b \sqrt{\left(a +b \right) b}}-\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f a \sqrt{\left(a +b \right) b}}-\frac{\tan \left(f x +e \right)}{2 a f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"-1/2/f/b*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)+1/2/f/b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/2/f/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/2*tan(f*x+e)/a/f/(a+b+b*tan(f*x+e)^2)-1/f*b/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a^2*arctan(tan(f*x+e))","B"
358,1,108,73,0.953000," ","int(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x)","\frac{\tan \left(f x +e \right)}{2 a f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f a \sqrt{\left(a +b \right) b}}+\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \sqrt{\left(a +b \right) b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"1/2*tan(f*x+e)/a/f/(a+b+b*tan(f*x+e)^2)+1/2/f/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f*b/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a^2*arctan(tan(f*x+e))","A"
359,1,127,80,0.917000," ","int(1/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b \tan \left(f x +e \right)}{2 a \left(a +b \right) f \left(a +b +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{\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{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"-1/2*b*tan(f*x+e)/a/(a+b)/f/(a+b+b*tan(f*x+e)^2)-3/2/f*b/a/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f*b^2/a^2/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a^2*arctan(tan(f*x+e))","A"
360,1,149,107,1.063000," ","int(cot(f*x+e)^2/(a+b*sec(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 +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{\left(a +b \right) b}}\right)}{2 f \left(a +b \right)^{2} a \sqrt{\left(a +b \right) b}}+\frac{b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{2} a^{2} \sqrt{\left(a +b \right) b}}-\frac{1}{f \left(a +b \right)^{2} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"1/2/f*b^2/(a+b)^2/a*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)+5/2/f*b^2/(a+b)^2/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f*b^3/(a+b)^2/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/(a+b)^2/tan(f*x+e)-1/f/a^2*arctan(tan(f*x+e))","A"
361,1,186,144,1.344000," ","int(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x)","-\frac{b^{3} \tan \left(f x +e \right)}{2 f a \left(a +b \right)^{3} \left(a +b +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{\left(a +b \right) b}}\right)}{2 f a \left(a +b \right)^{3} \sqrt{\left(a +b \right) b}}-\frac{b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{2} \left(a +b \right)^{3} \sqrt{\left(a +b \right) b}}-\frac{1}{3 f \left(a +b \right)^{2} \tan \left(f x +e \right)^{3}}+\frac{a}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}+\frac{3 b}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"-1/2/f*b^3/a/(a+b)^3*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)-7/2/f*b^3/a/(a+b)^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f*b^4/a^2/(a+b)^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/3/f/(a+b)^2/tan(f*x+e)^3+1/f/(a+b)^3/tan(f*x+e)*a+3/f/(a+b)^3/tan(f*x+e)*b+1/f/a^2*arctan(tan(f*x+e))","A"
362,1,248,189,1.351000," ","int(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x)","\frac{b^{4} \tan \left(f x +e \right)}{2 f \left(a +b \right)^{4} a \left(a +b +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{\left(a +b \right) b}}\right)}{2 f \left(a +b \right)^{4} a \sqrt{\left(a +b \right) b}}+\frac{b^{5} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{4} a^{2} \sqrt{\left(a +b \right) b}}-\frac{1}{5 f \left(a +b \right)^{2} \tan \left(f x +e \right)^{5}}+\frac{a}{3 f \left(a +b \right)^{3} \tan \left(f x +e \right)^{3}}+\frac{b}{f \left(a +b \right)^{3} \tan \left(f x +e \right)^{3}}-\frac{a^{2}}{f \left(a +b \right)^{4} \tan \left(f x +e \right)}-\frac{4 a b}{f \left(a +b \right)^{4} \tan \left(f x +e \right)}-\frac{6 b^{2}}{f \left(a +b \right)^{4} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{2}}"," ",0,"1/2/f*b^4/(a+b)^4/a*tan(f*x+e)/(a+b+b*tan(f*x+e)^2)+9/2/f*b^4/(a+b)^4/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f*b^5/(a+b)^4/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/5/f/(a+b)^2/tan(f*x+e)^5+1/3/f/(a+b)^3/tan(f*x+e)^3*a+1/f/(a+b)^3/tan(f*x+e)^3*b-1/f/(a+b)^4/tan(f*x+e)*a^2-4/f/(a+b)^4/tan(f*x+e)*a*b-6/f/(a+b)^4/tan(f*x+e)*b^2-1/f/a^2*arctan(tan(f*x+e))","A"
363,1,138,77,0.864000," ","int(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x)","\frac{1}{4 f a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b}{2 f \,a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{2}}{4 a^{3} f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{\ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 a^{3} f}-\frac{1}{f \,a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{b}{a^{3} f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}"," ",0,"1/4/f/a/(b+a*cos(f*x+e)^2)^2+1/2/f/a^2/(b+a*cos(f*x+e)^2)^2*b+1/4*b^2/a^3/f/(b+a*cos(f*x+e)^2)^2-1/2*ln(b+a*cos(f*x+e)^2)/a^3/f-1/f/a^2/(b+a*cos(f*x+e)^2)-b/a^3/f/(b+a*cos(f*x+e)^2)","A"
364,1,115,75,0.813000," ","int(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x)","-\frac{b}{4 f \,a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{2}}{4 a^{3} f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{\ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 a^{3} f}+\frac{1}{2 f \,a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{b}{a^{3} f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}"," ",0,"-1/4/f/a^2/(b+a*cos(f*x+e)^2)^2*b-1/4*b^2/a^3/f/(b+a*cos(f*x+e)^2)^2+1/2*ln(b+a*cos(f*x+e)^2)/a^3/f+1/2/f/a^2/(b+a*cos(f*x+e)^2)+b/a^3/f/(b+a*cos(f*x+e)^2)","A"
365,1,81,70,0.391000," ","int(tan(f*x+e)/(a+b*sec(f*x+e)^2)^3,x)","\frac{1}{4 f a \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{\ln \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)}{2 f \,a^{3}}+\frac{1}{2 f \,a^{2} \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)}+\frac{\ln \left(\sec \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"1/4/f/a/(a+b*sec(f*x+e)^2)^2-1/2/f/a^3*ln(a+b*sec(f*x+e)^2)+1/2/f/a^2/(a+b*sec(f*x+e)^2)+1/f/a^3*ln(sec(f*x+e))","A"
366,1,304,124,1.067000," ","int(cot(f*x+e)/(a+b*sec(f*x+e)^2)^3,x)","-\frac{b^{3}}{4 f \left(a +b \right)^{3} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{4}}{2 f \left(a +b \right)^{3} a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{5}}{4 a^{3} \left(a +b \right)^{3} f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 b \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{3} a}+\frac{3 b^{2} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{3} a^{2}}+\frac{b^{3} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{3} a^{3}}+\frac{3 b^{2}}{2 f \left(a +b \right)^{3} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{5 b^{3}}{2 f \left(a +b \right)^{3} a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{b^{4}}{f \left(a +b \right)^{3} a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{2 f \left(a +b \right)^{3}}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{2 f \left(a +b \right)^{3}}"," ",0,"-1/4/f*b^3/(a+b)^3/a/(b+a*cos(f*x+e)^2)^2-1/2/f*b^4/(a+b)^3/a^2/(b+a*cos(f*x+e)^2)^2-1/4*b^5/a^3/(a+b)^3/f/(b+a*cos(f*x+e)^2)^2+3/2/f*b/(a+b)^3/a*ln(b+a*cos(f*x+e)^2)+3/2/f*b^2/(a+b)^3/a^2*ln(b+a*cos(f*x+e)^2)+1/2/f*b^3/(a+b)^3/a^3*ln(b+a*cos(f*x+e)^2)+3/2/f*b^2/(a+b)^3/a/(b+a*cos(f*x+e)^2)+5/2/f*b^3/(a+b)^3/a^2/(b+a*cos(f*x+e)^2)+1/f*b^4/(a+b)^3/a^3/(b+a*cos(f*x+e)^2)+1/2/f/(a+b)^3*ln(-1+cos(f*x+e))+1/2/f/(a+b)^3*ln(1+cos(f*x+e))","B"
367,1,389,148,1.514000," ","int(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x)","\frac{b^{4}}{4 f \left(a +b \right)^{4} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{5}}{2 f \left(a +b \right)^{4} a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{6}}{4 f \left(a +b \right)^{4} a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{3 b^{2} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{f \left(a +b \right)^{4} a}-\frac{2 b^{3} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{f \left(a +b \right)^{4} a^{2}}-\frac{b^{4} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{4} a^{3}}-\frac{2 b^{3}}{f \left(a +b \right)^{4} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{3 b^{4}}{f \left(a +b \right)^{4} a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{b^{5}}{f \left(a +b \right)^{4} a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{1}{4 f \left(a +b \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a}{2 f \left(a +b \right)^{4}}-\frac{2 \ln \left(-1+\cos \left(f x +e \right)\right) b}{f \left(a +b \right)^{4}}-\frac{1}{4 f \left(a +b \right)^{3} \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) a}{2 f \left(a +b \right)^{4}}-\frac{2 \ln \left(1+\cos \left(f x +e \right)\right) b}{f \left(a +b \right)^{4}}"," ",0,"1/4/f*b^4/(a+b)^4/a/(b+a*cos(f*x+e)^2)^2+1/2/f*b^5/(a+b)^4/a^2/(b+a*cos(f*x+e)^2)^2+1/4/f*b^6/(a+b)^4/a^3/(b+a*cos(f*x+e)^2)^2-3/f*b^2/(a+b)^4/a*ln(b+a*cos(f*x+e)^2)-2/f*b^3/(a+b)^4/a^2*ln(b+a*cos(f*x+e)^2)-1/2/f*b^4/(a+b)^4/a^3*ln(b+a*cos(f*x+e)^2)-2/f*b^3/(a+b)^4/a/(b+a*cos(f*x+e)^2)-3/f*b^4/(a+b)^4/a^2/(b+a*cos(f*x+e)^2)-1/f*b^5/(a+b)^4/a^3/(b+a*cos(f*x+e)^2)+1/4/f/(a+b)^3/(-1+cos(f*x+e))-1/2/f/(a+b)^4*ln(-1+cos(f*x+e))*a-2/f/(a+b)^4*ln(-1+cos(f*x+e))*b-1/4/f/(a+b)^3/(1+cos(f*x+e))-1/2/f/(a+b)^4*ln(1+cos(f*x+e))*a-2/f/(a+b)^4*ln(1+cos(f*x+e))*b","B"
368,1,522,182,1.459000," ","int(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x)","\frac{5 b^{3} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{f \left(a +b \right)^{5} a}+\frac{5 b^{4} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{5} a^{2}}+\frac{b^{5} \ln \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}{2 f \left(a +b \right)^{5} a^{3}}-\frac{b^{5}}{4 f \left(a +b \right)^{5} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{6}}{2 f \left(a +b \right)^{5} a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{7}}{4 f \left(a +b \right)^{5} a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{5 b^{4}}{2 f \left(a +b \right)^{5} a \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{7 b^{5}}{2 f \left(a +b \right)^{5} a^{2} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}+\frac{b^{6}}{f \left(a +b \right)^{5} a^{3} \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)}-\frac{1}{16 f \left(a +b \right)^{3} \left(-1+\cos \left(f x +e \right)\right)^{2}}-\frac{7 a}{16 f \left(a +b \right)^{4} \left(-1+\cos \left(f x +e \right)\right)}-\frac{19 b}{16 f \left(a +b \right)^{4} \left(-1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a^{2}}{2 f \left(a +b \right)^{5}}+\frac{5 \ln \left(-1+\cos \left(f x +e \right)\right) a b}{2 f \left(a +b \right)^{5}}+\frac{5 \ln \left(-1+\cos \left(f x +e \right)\right) b^{2}}{f \left(a +b \right)^{5}}-\frac{1}{16 f \left(a +b \right)^{3} \left(1+\cos \left(f x +e \right)\right)^{2}}+\frac{7 a}{16 f \left(a +b \right)^{4} \left(1+\cos \left(f x +e \right)\right)}+\frac{19 b}{16 f \left(a +b \right)^{4} \left(1+\cos \left(f x +e \right)\right)}+\frac{\ln \left(1+\cos \left(f x +e \right)\right) a^{2}}{2 f \left(a +b \right)^{5}}+\frac{5 \ln \left(1+\cos \left(f x +e \right)\right) a b}{2 f \left(a +b \right)^{5}}+\frac{5 \ln \left(1+\cos \left(f x +e \right)\right) b^{2}}{f \left(a +b \right)^{5}}"," ",0,"5/f*b^3/(a+b)^5/a*ln(b+a*cos(f*x+e)^2)+5/2/f*b^4/(a+b)^5/a^2*ln(b+a*cos(f*x+e)^2)+1/2/f*b^5/(a+b)^5/a^3*ln(b+a*cos(f*x+e)^2)-1/4/f*b^5/(a+b)^5/a/(b+a*cos(f*x+e)^2)^2-1/2/f*b^6/(a+b)^5/a^2/(b+a*cos(f*x+e)^2)^2-1/4/f*b^7/(a+b)^5/a^3/(b+a*cos(f*x+e)^2)^2+5/2/f*b^4/(a+b)^5/a/(b+a*cos(f*x+e)^2)+7/2/f*b^5/(a+b)^5/a^2/(b+a*cos(f*x+e)^2)+1/f*b^6/(a+b)^5/a^3/(b+a*cos(f*x+e)^2)-1/16/f/(a+b)^3/(-1+cos(f*x+e))^2-7/16/f/(a+b)^4/(-1+cos(f*x+e))*a-19/16/f/(a+b)^4/(-1+cos(f*x+e))*b+1/2/f/(a+b)^5*ln(-1+cos(f*x+e))*a^2+5/2/f/(a+b)^5*ln(-1+cos(f*x+e))*a*b+5/f/(a+b)^5*ln(-1+cos(f*x+e))*b^2-1/16/f/(a+b)^3/(1+cos(f*x+e))^2+7/16/f/(a+b)^4/(1+cos(f*x+e))*a+19/16/f/(a+b)^4/(1+cos(f*x+e))*b+1/2/f/(a+b)^5*ln(1+cos(f*x+e))*a^2+5/2/f/(a+b)^5*ln(1+cos(f*x+e))*a*b+5/f/(a+b)^5*ln(1+cos(f*x+e))*b^2","B"
369,1,356,133,1.087000," ","int(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x)","-\frac{5 \left(\tan^{3}\left(f x +e \right)\right)}{8 f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b}-\frac{\tan^{3}\left(f x +e \right)}{8 f a \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{3 a \tan \left(f x +e \right)}{8 f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b^{2}}-\frac{\tan \left(f x +e \right)}{4 f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b}+\frac{5 \tan \left(f x +e \right)}{8 a f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f \,b^{2} \sqrt{\left(a +b \right) b}}-\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f a b \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,a^{2} \sqrt{\left(a +b \right) b}}+\frac{b \left(\tan^{3}\left(f x +e \right)\right)}{2 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b \tan \left(f x +e \right)}{2 a^{2} f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \sqrt{\left(a +b \right) b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"-5/8/f/(a+b+b*tan(f*x+e)^2)^2/b*tan(f*x+e)^3-1/8/f/a/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-3/8/f*a/(a+b+b*tan(f*x+e)^2)^2/b^2*tan(f*x+e)-1/4/f/(a+b+b*tan(f*x+e)^2)^2/b*tan(f*x+e)+5/8*tan(f*x+e)/a/f/(a+b+b*tan(f*x+e)^2)^2+3/8/f/b^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/8/f/a/b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/2/f/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/2/f/a^2*b/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+1/2*b*tan(f*x+e)/a^2/f/(a+b+b*tan(f*x+e)^2)^2+1/f/a^3*b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a^3*arctan(tan(f*x+e))","B"
370,1,264,123,0.863000," ","int(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x)","\frac{\tan^{3}\left(f x +e \right)}{8 f a \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b \left(\tan^{3}\left(f x +e \right)\right)}{2 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{\tan \left(f x +e \right)}{8 f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} b}-\frac{5 \tan \left(f x +e \right)}{8 a f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b \tan \left(f x +e \right)}{2 a^{2} f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f a b \sqrt{\left(a +b \right) b}}-\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,a^{2} \sqrt{\left(a +b \right) b}}-\frac{b \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"1/8/f/a/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-1/2/f/a^2*b/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-1/8/f/(a+b+b*tan(f*x+e)^2)^2/b*tan(f*x+e)-5/8*tan(f*x+e)/a/f/(a+b+b*tan(f*x+e)^2)^2-1/2*b*tan(f*x+e)/a^2/f/(a+b+b*tan(f*x+e)^2)^2+1/8/f/a/b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/2/f/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a^3*b/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a^3*arctan(tan(f*x+e))","B"
371,1,263,124,0.721000," ","int(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x)","\frac{3 b \left(\tan^{3}\left(f x +e \right)\right)}{8 f a \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}+\frac{b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{2 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}+\frac{5 \tan \left(f x +e \right)}{8 a f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b \tan \left(f x +e \right)}{2 a^{2} f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{3 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f a \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{3 \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right) b}{2 f \,a^{2} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right) b^{2}}{f \,a^{3} \left(a +b \right) \sqrt{\left(a +b \right) b}}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"3/8/f/a/(a+b+b*tan(f*x+e)^2)^2*b/(a+b)*tan(f*x+e)^3+1/2/f/a^2/(a+b+b*tan(f*x+e)^2)^2*b^2/(a+b)*tan(f*x+e)^3+5/8*tan(f*x+e)/a/f/(a+b+b*tan(f*x+e)^2)^2+1/2*b*tan(f*x+e)/a^2/f/(a+b+b*tan(f*x+e)^2)^2+3/8/f/a/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+3/2/f/a^2/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))*b+1/f/a^3/(a+b)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))*b^2-1/f/a^3*arctan(tan(f*x+e))","B"
372,1,321,130,0.844000," ","int(1/(a+b*sec(f*x+e)^2)^3,x)","-\frac{7 b^{2} \left(\tan^{3}\left(f x +e \right)\right)}{8 f a \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{3} \left(\tan^{3}\left(f x +e \right)\right)}{2 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{9 b \tan \left(f x +e \right)}{8 a \left(a +b \right) f \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{2} \tan \left(f x +e \right)}{2 f \,a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2} \left(a +b \right)}-\frac{15 b \arctan \left(\frac{\tan \left(f x +e \right) b}{\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{\tan \left(f x +e \right) b}{\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{\tan \left(f x +e \right) b}{\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{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"-7/8/f/a*b^2/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3-1/2/f/a^2*b^3/(a+b+b*tan(f*x+e)^2)^2/(a^2+2*a*b+b^2)*tan(f*x+e)^3-9/8*b*tan(f*x+e)/a/(a+b)/f/(a+b+b*tan(f*x+e)^2)^2-1/2/f/a^2*b^2/(a+b+b*tan(f*x+e)^2)^2/(a+b)*tan(f*x+e)-15/8/f/a*b/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-5/2/f/a^2*b^2/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/a^3*b^3/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f/a^3*arctan(tan(f*x+e))","B"
373,1,337,165,1.154000," ","int(cot(f*x+e)^2/(a+b*sec(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} a \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{2 f \left(a +b \right)^{3} a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{13 b^{2} \tan \left(f x +e \right)}{8 f \left(a +b \right)^{3} \left(a +b +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} a \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{4} \tan \left(f x +e \right)}{2 f \left(a +b \right)^{3} a^{2} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{35 b^{2} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{8 f \left(a +b \right)^{3} a \sqrt{\left(a +b \right) b}}+\frac{7 b^{3} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \left(a +b \right)^{3} a^{2} \sqrt{\left(a +b \right) b}}+\frac{b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \left(a +b \right)^{3} a^{3} \sqrt{\left(a +b \right) b}}-\frac{1}{f \left(a +b \right)^{3} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"11/8/f*b^3/(a+b)^3/a/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+1/2/f*b^4/(a+b)^3/a^2/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+13/8/f*b^2/(a+b)^3/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)+17/8/f*b^3/(a+b)^3/a/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)+1/2/f*b^4/(a+b)^3/a^2/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)+35/8/f*b^2/(a+b)^3/a/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+7/2/f*b^3/(a+b)^3/a^2/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f*b^4/(a+b)^3/a^3/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f/(a+b)^3/tan(f*x+e)-1/f/a^3*arctan(tan(f*x+e))","B"
374,1,374,212,1.480000," ","int(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x)","-\frac{15 b^{4} \left(\tan^{3}\left(f x +e \right)\right)}{8 f a \left(a +b \right)^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{5} \left(\tan^{3}\left(f x +e \right)\right)}{2 f \,a^{2} \left(a +b \right)^{4} \left(a +b +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)^{4} \left(a +b +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 \left(a +b \right)^{4} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}-\frac{b^{5} \tan \left(f x +e \right)}{2 f \,a^{2} \left(a +b \right)^{4} \left(a +b +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{\left(a +b \right) b}}\right)}{8 f a \left(a +b \right)^{4} \sqrt{\left(a +b \right) b}}-\frac{9 b^{4} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,a^{2} \left(a +b \right)^{4} \sqrt{\left(a +b \right) b}}-\frac{b^{5} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \left(a +b \right)^{4} \sqrt{\left(a +b \right) b}}-\frac{1}{3 f \left(a +b \right)^{3} \tan \left(f x +e \right)^{3}}+\frac{a}{f \left(a +b \right)^{4} \tan \left(f x +e \right)}+\frac{4 b}{f \left(a +b \right)^{4} \tan \left(f x +e \right)}+\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"-15/8/f*b^4/a/(a+b)^4/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-1/2/f*b^5/a^2/(a+b)^4/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3-17/8/f*b^3/(a+b)^4/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-21/8/f*b^4/a/(a+b)^4/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-1/2/f*b^5/a^2/(a+b)^4/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)-63/8/f*b^3/a/(a+b)^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-9/2/f*b^4/a^2/(a+b)^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/f*b^5/a^3/(a+b)^4/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/3/f/(a+b)^3/tan(f*x+e)^3+1/f/(a+b)^4/tan(f*x+e)*a+4/f/(a+b)^4/tan(f*x+e)*b+1/f/a^3*arctan(tan(f*x+e))","A"
375,1,437,265,1.634000," ","int(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x)","\frac{19 b^{5} \left(\tan^{3}\left(f x +e \right)\right)}{8 f a \left(a +b \right)^{5} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{6} \left(\tan^{3}\left(f x +e \right)\right)}{2 f \,a^{2} \left(a +b \right)^{5} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{21 b^{4} \tan \left(f x +e \right)}{8 f \left(a +b \right)^{5} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{25 b^{5} \tan \left(f x +e \right)}{8 f a \left(a +b \right)^{5} \left(a +b +b \left(\tan^{2}\left(f x +e \right)\right)\right)^{2}}+\frac{b^{6} \tan \left(f x +e \right)}{2 f \,a^{2} \left(a +b \right)^{5} \left(a +b +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{\left(a +b \right) b}}\right)}{8 f a \left(a +b \right)^{5} \sqrt{\left(a +b \right) b}}+\frac{11 b^{5} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 f \,a^{2} \left(a +b \right)^{5} \sqrt{\left(a +b \right) b}}+\frac{b^{6} \arctan \left(\frac{\tan \left(f x +e \right) b}{\sqrt{\left(a +b \right) b}}\right)}{f \,a^{3} \left(a +b \right)^{5} \sqrt{\left(a +b \right) b}}-\frac{1}{5 f \left(a +b \right)^{3} \tan \left(f x +e \right)^{5}}+\frac{a}{3 f \left(a +b \right)^{4} \tan \left(f x +e \right)^{3}}+\frac{4 b}{3 f \left(a +b \right)^{4} \tan \left(f x +e \right)^{3}}-\frac{a^{2}}{f \left(a +b \right)^{5} \tan \left(f x +e \right)}-\frac{5 a b}{f \left(a +b \right)^{5} \tan \left(f x +e \right)}-\frac{10 b^{2}}{f \left(a +b \right)^{5} \tan \left(f x +e \right)}-\frac{\arctan \left(\tan \left(f x +e \right)\right)}{f \,a^{3}}"," ",0,"19/8/f*b^5/a/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+1/2/f*b^6/a^2/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)^3+21/8/f*b^4/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)+25/8/f*b^5/a/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)+1/2/f*b^6/a^2/(a+b)^5/(a+b+b*tan(f*x+e)^2)^2*tan(f*x+e)+99/8/f*b^4/a/(a+b)^5/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+11/2/f*b^5/a^2/(a+b)^5/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))+1/f*b^6/a^3/(a+b)^5/((a+b)*b)^(1/2)*arctan(tan(f*x+e)*b/((a+b)*b)^(1/2))-1/5/f/(a+b)^3/tan(f*x+e)^5+1/3/f/(a+b)^4/tan(f*x+e)^3*a+4/3/f/(a+b)^4/tan(f*x+e)^3*b-1/f/(a+b)^5/tan(f*x+e)*a^2-5/f/(a+b)^5/tan(f*x+e)*a*b-10/f/(a+b)^5/tan(f*x+e)*b^2-1/f/a^3*arctan(tan(f*x+e))","A"
376,1,924,95,2.052000," ","int((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^5,x)","\frac{\sqrt{4}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \left(-1+\cos \left(f x +e \right)\right) \left(15 \sqrt{a +b}\, \left(\cos^{5}\left(f x +e \right)\right) \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) \sqrt{a}\, b^{2}+2 \sqrt{a +b}\, \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a^{2}+10 \sqrt{a +b}\, \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a b -15 \sqrt{a +b}\, \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{2}-15 \left(\cos^{5}\left(f x +e \right)\right) \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a \,b^{2}+15 \left(\cos^{5}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a \,b^{2}+2 \sqrt{a +b}\, \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a^{2}+10 \sqrt{a +b}\, \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a b -15 \sqrt{a +b}\, \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{2}-\sqrt{a +b}\, \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a b +10 \sqrt{a +b}\, \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{2}-\sqrt{a +b}\, \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a b +10 \sqrt{a +b}\, \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{2}-3 \sqrt{a +b}\, \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{2}-3 \sqrt{a +b}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b^{2}\right)}{30 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)^{4} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}\, b^{2}}"," ",0,"1/30/f*4^(1/2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*(-1+cos(f*x+e))*(15*(a+b)^(1/2)*cos(f*x+e)^5*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a^(1/2)*b^2+2*(a+b)^(1/2)*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2+10*(a+b)^(1/2)*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b-15*(a+b)^(1/2)*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^2-15*cos(f*x+e)^5*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b^2+15*cos(f*x+e)^5*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b^2+2*(a+b)^(1/2)*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2+10*(a+b)^(1/2)*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b-15*(a+b)^(1/2)*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^2-(a+b)^(1/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b+10*(a+b)^(1/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^2-(a+b)^(1/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b+10*(a+b)^(1/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^2-3*(a+b)^(1/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^2-3*(a+b)^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^2)/sin(f*x+e)^2/cos(f*x+e)^4/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)/(a+b)^(1/2)/b^2","B"
377,1,648,68,1.557000," ","int((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^3,x)","-\frac{\sqrt{4}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \left(-1+\cos \left(f x +e \right)\right) \left(3 \sqrt{a +b}\, \left(\cos^{3}\left(f x +e \right)\right) \sqrt{a}\, \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) b +\sqrt{a +b}\, \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a -3 \sqrt{a +b}\, \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b -3 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{4 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a b +3 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a b +\sqrt{a +b}\, \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a -3 \sqrt{a +b}\, \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b +\sqrt{a +b}\, \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b +\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b \sqrt{a +b}\right)}{6 f \sin \left(f x +e \right)^{2} \cos \left(f x +e \right)^{2} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}\, b}"," ",0,"-1/6/f*4^(1/2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*(-1+cos(f*x+e))*(3*(a+b)^(1/2)*cos(f*x+e)^3*a^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*b+(a+b)^(1/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a-3*(a+b)^(1/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b-3*cos(f*x+e)^3*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b+3*cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b+(a+b)^(1/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a-3*(a+b)^(1/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b+(a+b)^(1/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b*(a+b)^(1/2))/sin(f*x+e)^2/cos(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)/(a+b)^(1/2)/b","B"
378,1,61,46,0.251000," ","int((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e),x)","-\frac{\sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{\sec \left(f x +e \right)}\right)}{f}+\frac{\sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{f}"," ",0,"-1/f*a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sec(f*x+e)^2)^(1/2))/sec(f*x+e))+(a+b*sec(f*x+e)^2)^(1/2)/f","A"
379,1,570,58,1.851000," ","int(cot(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \sqrt{4}\, \cos \left(f x +e \right) \left(2 \sqrt{a}\, \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) \sqrt{a +b}+\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a +\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) b -\ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) a -\ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) b \right) \left(-1+\cos \left(f x +e \right)\right)}{4 f \sin \left(f x +e \right)^{2} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}}"," ",0,"-1/4/f*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*4^(1/2)*cos(f*x+e)*(2*a^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(1/2)+ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a+ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b-ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a-ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b)*(-1+cos(f*x+e))/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)/(a+b)^(1/2)","B"
380,1,2528,91,1.710000," ","int(cot(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/8/f*(-1+cos(f*x+e))*(-4*4^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^2*(a+b)^(3/2)*a^(1/2)*b+5*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*4^(1/2)*a^2*b+4*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*4^(1/2)*a*b^2+2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*4^(1/2)*cos(f*x+e)^2*a^3+ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*4^(1/2)*cos(f*x+e)^2*b^3-2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*4^(1/2)*cos(f*x+e)^2*a^3-4*4^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^2*(a+b)^(3/2)*a^(3/2)-ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*4^(1/2)*cos(f*x+e)^2*b^3+4*4^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(3/2)*a^(3/2)-4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*4^(1/2)*(a+b)^(3/2)*b-5*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*4^(1/2)*a^2*b-4*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*4^(1/2)*a*b^2-ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*4^(1/2)*b^3+2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*4^(1/2)*a^3+ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*4^(1/2)*b^3+8*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)^2*(a+b)^(3/2)+16*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*cos(f*x+e)*(a+b)^(3/2)-2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*4^(1/2)*a^3+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*4^(1/2)*cos(f*x+e)*(a+b)^(3/2)*a+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*4^(1/2)*cos(f*x+e)*(a+b)^(3/2)*b-2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*4^(1/2)*cos(f*x+e)^2*(a+b)^(3/2)*a+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*4^(1/2)*cos(f*x+e)^2*(a+b)^(3/2)*b+5*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*4^(1/2)*cos(f*x+e)^2*a^2*b+4*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*4^(1/2)*cos(f*x+e)^2*a*b^2-5*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*4^(1/2)*cos(f*x+e)^2*a^2*b-4*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*4^(1/2)*cos(f*x+e)^2*a*b^2+4*4^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(3/2)*a^(1/2)*b+8*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)*(a+b)^(3/2))*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)/sin(f*x+e)^4/(a+b)^(5/2)","B"
381,1,7346,139,1.811000," ","int(cot(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
382,1,2756,193,2.283000," ","int((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^6,x)","\text{Expression too large to display}"," ",0,"1/48/f*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*(90*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2+10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b-10*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2-15*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b+3*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-96*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2+30*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3+40*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-40*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-14*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+33*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+14*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-33*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-26*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+26*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+33*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-33*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-3*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3+6*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3-30*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3+15*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/cos(f*x+e)^5/b^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
383,1,2005,143,1.952000," ","int((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^4,x)","\frac{\sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \left(16 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b +\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-12 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}+\left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}-5 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -\left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}+5 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -5 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +5 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \cos \left(f x +e \right)^{3} b \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/8/f*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*(16*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b+sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2-2*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-3*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2-2*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2-12*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b+6*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2+cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2-5*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+5*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-5*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+5*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/cos(f*x+e)^3/b/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
384,1,1331,100,1.576000," ","int((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^2,x)","\frac{\sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \left(\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) a +\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) b +2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) a -2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) b -4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/2/f*sin(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*(2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*b+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*b-4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a+cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/cos(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
385,1,589,67,1.763000," ","int((a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\sqrt{2}\, \left(-\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a -\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b +2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b +2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \right) \cos \left(f x +e \right) \left(\sin^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}}{f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/f*2^(1/2)*(-EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a-EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b+2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b+2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a)*cos(f*x+e)*sin(f*x+e)^2*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
386,1,1004,61,1.701000," ","int(cot(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(a \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a +a \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right)}{f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \sin \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/f*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)*cos(f*x+e)*(a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)*sin(f*x+e)*a+a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)-2*a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)+cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/(b+a*cos(f*x+e)^2)/sin(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
387,1,3855,100,1.573000," ","int(cot(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/3/f*(3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a*b-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^2-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a*b+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2+3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a*b-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2-3*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)*sin(f*x+e)*a*b-3*a^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)-3*a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)+4*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+3*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+3*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(b+a*cos(f*x+e)^2)/sin(f*x+e)^3/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(a+b)","C"
388,1,8605,149,1.898000," ","int(cot(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
389,1,2606,115,1.692000," ","int((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^5,x)","\text{Expression too large to display}"," ",0,"1/420/f*4^(1/2)*(-1+cos(f*x+e))^3*(-30*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*b^4+84*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*b^4-30*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*b^4-30*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b^3-210*cos(f*x+e)^7*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^6*b^2-945*cos(f*x+e)^7*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^5*b^3-1575*cos(f*x+e)^7*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4*b^4-1155*cos(f*x+e)^7*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b^5-315*cos(f*x+e)^7*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^6+210*cos(f*x+e)^7*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^6*b^2+945*cos(f*x+e)^7*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^5*b^3+1575*cos(f*x+e)^7*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4*b^4+1155*cos(f*x+e)^7*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b^5+315*cos(f*x+e)^7*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^6+12*cos(f*x+e)^7*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^4+12*cos(f*x+e)^6*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^4-70*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*b^4-70*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*b^4+84*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*b^4+96*cos(f*x+e)^7*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^3*b+210*cos(f*x+e)^7*a^(5/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(7/2)*b^2+210*cos(f*x+e)^7*a^(3/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(7/2)*b^3-196*cos(f*x+e)^7*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^2*b^2-280*cos(f*x+e)^7*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b^3+96*cos(f*x+e)^6*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^3*b-196*cos(f*x+e)^6*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^2*b^2-280*cos(f*x+e)^6*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b^3-6*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^3*b+162*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^2*b^2+98*cos(f*x+e)^5*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b^3-6*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^3*b+162*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^2*b^2+98*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b^3-48*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^2*b^2+36*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b^3-48*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a^2*b^2+36*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b^3-30*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b^3)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/sin(f*x+e)^6/cos(f*x+e)^4/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)/b^2/(a+b)^(9/2)","B"
390,1,2150,88,1.587000," ","int((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^3,x)","\text{Expression too large to display}"," ",0,"-1/60/f*4^(1/2)*(-1+cos(f*x+e))^3*(6*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*b^3-135*cos(f*x+e)^5*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^5*b^2-225*cos(f*x+e)^5*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4*b^3-165*cos(f*x+e)^5*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b^4-45*cos(f*x+e)^5*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^5+30*cos(f*x+e)^5*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^6*b+135*cos(f*x+e)^5*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^5*b^2+225*cos(f*x+e)^5*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4*b^3+165*cos(f*x+e)^5*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b^4-10*cos(f*x+e)^3*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^3-10*cos(f*x+e)^2*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^3+6*cos(f*x+e)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^3+6*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b^2+6*cos(f*x+e)^5*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^3+6*cos(f*x+e)^4*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^3+45*cos(f*x+e)^5*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^5-30*cos(f*x+e)^5*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^6*b+30*cos(f*x+e)^5*(a+b)^(7/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a^(3/2)*b^2+30*cos(f*x+e)^5*(a+b)^(7/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a^(5/2)*b-34*cos(f*x+e)^5*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2*b-40*cos(f*x+e)^5*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b^2-34*cos(f*x+e)^4*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2*b-40*cos(f*x+e)^4*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b^2+12*cos(f*x+e)^3*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2*b+2*cos(f*x+e)^3*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b^2+12*cos(f*x+e)^2*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2*b+2*cos(f*x+e)^2*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b^2+6*cos(f*x+e)*(a+b)^(7/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b^2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/sin(f*x+e)^6/cos(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)/b/(a+b)^(9/2)","B"
391,1,81,66,0.304000," ","int((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e),x)","\frac{\left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{3 f}-\frac{a^{\frac{3}{2}} \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{\sec \left(f x +e \right)}\right)}{f}+\frac{a \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{f}"," ",0,"1/3*(a+b*sec(f*x+e)^2)^(3/2)/f-1/f*a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sec(f*x+e)^2)^(1/2))/sec(f*x+e))+a*(a+b*sec(f*x+e)^2)^(1/2)/f","A"
392,1,2424,77,1.839000," ","int(cot(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/4/f*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^2*(-1+cos(f*x+e))^3*(2*a^(5/2)*cos(f*x+e)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(7/2)+2*a^(3/2)*cos(f*x+e)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(7/2)*b+2*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*a*b+2*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(7/2)*b^2+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b*(a+b)^(7/2)+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^2*(a+b)^(7/2)+3*cos(f*x+e)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^5*b+9*cos(f*x+e)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4*b^2+9*cos(f*x+e)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b^3+3*cos(f*x+e)*ln(-4*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^4+cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^6+3*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^5*b+6*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4*b^2+11*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b^3+12*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^4+6*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b^5+cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^6-cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^6-6*cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^5*b-15*cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4*b^2-20*cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b^3-15*cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^4-6*cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a*b^5-cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^6)*4^(1/2)/sin(f*x+e)^6/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)/(a+b)^(9/2)","B"
393,1,1609,96,1.858000," ","int(cot(f*x+e)^3*(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\sqrt{4}\, \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(\cos^{3}\left(f x +e \right)\right) \left(4 \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) \cos \left(f x +e \right) \left(a +b \right)^{\frac{3}{2}} a^{\frac{3}{2}}-4 a^{\frac{3}{2}} \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) \left(a +b \right)^{\frac{3}{2}}-2 \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \left(a +b \right)^{\frac{3}{2}} a -2 \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \left(a +b \right)^{\frac{3}{2}} b -2 \ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) \cos \left(f x +e \right) a^{3}-3 \ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) \cos \left(f x +e \right) a^{2} b +\ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) \cos \left(f x +e \right) b^{3}+2 \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) \cos \left(f x +e \right) a^{3}+3 \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) \cos \left(f x +e \right) a^{2} b -\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) \cos \left(f x +e \right) b^{3}+2 a^{3} \ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right)+3 a^{2} \ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) b -b^{3} \ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right)-2 \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a^{3}-3 \ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) a^{2} b +\ln \left(-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) b^{3}\right)}{8 f \sin \left(f x +e \right)^{6} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right)^{\frac{3}{2}} \left(a +b \right)^{\frac{3}{2}}}"," ",0,"1/8/f*4^(1/2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*(-1+cos(f*x+e))^2*cos(f*x+e)^3*(4*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)*(a+b)^(3/2)*a^(3/2)-4*a^(3/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(3/2)-2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(3/2)*a-2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(3/2)*b-2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a^3-3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*a^2*b+ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*cos(f*x+e)*b^3+2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*a^3+3*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*a^2*b-ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*cos(f*x+e)*b^3+2*a^3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))+3*a^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b-b^3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))-2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3-3*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b+ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^3)/sin(f*x+e)^6/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)/(a+b)^(3/2)","B"
394,1,4955,137,1.658000," ","int(cot(f*x+e)^5*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"-1/32/f*4^(1/2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*(-1+cos(f*x+e))^2*cos(f*x+e)^3*(8*cos(f*x+e)^3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4-20*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b-15*a^2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^2-2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^3*a-8*cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4-8*cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4-16*a^(3/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(5/2)-cos(f*x+e)^3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^4+cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^4+8*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4-cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^4-8*cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^4+cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^4+8*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^4-cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^4+20*a^3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b+15*a^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^2+2*b^3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a+15*cos(f*x+e)^3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^2+2*cos(f*x+e)^3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a*b^3-20*cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b-15*cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^2-2*cos(f*x+e)^3*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b^3-20*cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b-15*cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^2-2*cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a*b^3+20*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b+15*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^2+2*cos(f*x+e)^2*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b^3-20*cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b-15*cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^2*b^2-2*cos(f*x+e)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a*b^3+20*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^3*b+15*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^2*b^2+2*cos(f*x+e)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a*b^3+12*(a+b)^(5/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+2*(a+b)^(5/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b-8*(a+b)^(5/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a+2*(a+b)^(5/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b-16*(a+b)^(5/2)*cos(f*x+e)^3*a^(3/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))+16*(a+b)^(5/2)*cos(f*x+e)^2*a^(3/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))+16*(a+b)^(5/2)*cos(f*x+e)*a^(3/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))+20*cos(f*x+e)^3*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^3*b+cos(f*x+e)^2*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^4-b^4*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))-8*a^4*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))+b^4*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))+8*a^4*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e))))/sin(f*x+e)^8/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(3/2)/(a+b)^(5/2)","B"
395,1,3583,260,2.436000," ","int((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^6,x)","\text{output too large to display}"," ",0,"-1/384/f*sin(f*x+e)*(60*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3*b-48*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^4+380*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3-380*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3-57*cos(f*x+e)^8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b+337*cos(f*x+e)^8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2-15*cos(f*x+e)^8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3+301*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2-455*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3+57*cos(f*x+e)^9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b-337*cos(f*x+e)^9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2+15*cos(f*x+e)^9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3-3*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3*b-301*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b^2+455*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^3+120*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^3+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3*b-78*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b^2+78*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b^2-120*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^3-15*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^4-18*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^4+30*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^4+9*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^4+9*cos(f*x+e)^9*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4-9*cos(f*x+e)^8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^4+15*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4-15*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4-118*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4+118*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4+136*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4-136*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4+48*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^4-114*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b^2-180*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^3-120*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3*b-540*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b^2+360*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^3+768*sin(f*x+e)*cos(f*x+e)^8*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b^2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/cos(f*x+e)^5/b^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
396,1,2757,188,1.913000," ","int((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^4,x)","\text{Expression too large to display}"," ",0,"1/48/f*sin(f*x+e)*(54*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2+22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2+17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*a^2*b-17*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*a^2*b-22*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2-21*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b-27*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2-54*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^6*a^3+96*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^6*a^2*b+52*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-52*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-38*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+3*cos(f*x+e)^7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+38*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-3*cos(f*x+e)^6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^7*a^3+8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-14*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+14*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+3*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3-3*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3+3*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^3-6*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3+6*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3-3*sin(f*x+e)*cos(f*x+e)^6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3-8*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/cos(f*x+e)^3/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/b","C"
397,1,2002,144,1.532000," ","int((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^2,x)","\frac{\sin \left(f x +e \right) \left(5 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-12 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -2 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}-16 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2}+5 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}-\left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -5 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}+\left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +7 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -\left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}-7 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{8 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \cos \left(f x +e \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/8/f*sin(f*x+e)*(5*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2+6*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2+6*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2-12*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b-2*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-16*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2+5*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2-cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-5*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-7*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/cos(f*x+e)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
398,1,1557,100,1.435000," ","int((a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\left(6 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) a b +2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) b^{2}-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b -\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) b^{2}+4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \cos \left(f x +e \right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/2/f*(6*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*a*b+2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*b^2-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2-3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*b^2+4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*sin(f*x+e)/(-1+cos(f*x+e))/(b+a*cos(f*x+e)^2)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
399,1,1952,97,2.032000," ","int(cot(f*x+e)^2*(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(f x +e \right)\right) \left(\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}-\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right) \cos \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}+a^{2} \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{f \sin \left(f x +e \right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/f*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)*cos(f*x+e)^3*(2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)*cos(f*x+e)+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)*cos(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2+a^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/sin(f*x+e)/(b+a*cos(f*x+e)^2)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
400,1,2014,98,1.873000," ","int(cot(f*x+e)^4*(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{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 \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{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 \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}+4 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) a^{2}-3 a^{2} \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right)-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}+5 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right) \left(\cos^{3}\left(f x +e \right)\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}}}{3 f \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right)^{2} \sin \left(f x +e \right)^{3} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/3/f*(-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^3*sin(f*x+e)*a^2-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2+4*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2-3*a^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(b+a*cos(f*x+e)^2)^2/sin(f*x+e)^3/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
401,1,5850,147,2.015000," ","int(cot(f*x+e)^6*(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
402,1,358,77,1.780000," ","int(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{\left(\sin^{2}\left(f x +e \right)\right) \left(2 \left(\cos^{4}\left(f x +e \right)\right) a^{\frac{5}{2}}+3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) b^{2}+6 \left(\cos^{4}\left(f x +e \right)\right) a^{\frac{3}{2}} b +3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) b^{2}+\left(\cos^{2}\left(f x +e \right)\right) a^{\frac{3}{2}} b +6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{a}\, b^{2}-\sqrt{a}\, b^{2}\right)}{3 f \cos \left(f x +e \right)^{4} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)-1\right) b^{2} \sqrt{a}}"," ",0,"1/3/f*sin(f*x+e)^2*(2*cos(f*x+e)^4*a^(5/2)+3*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*b^2+6*cos(f*x+e)^4*a^(3/2)*b+3*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*b^2+cos(f*x+e)^2*a^(3/2)*b+6*cos(f*x+e)^2*a^(1/2)*b^2-a^(1/2)*b^2)/cos(f*x+e)^4/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(cos(f*x+e)^2-1)/b^2/a^(1/2)","B"
403,1,303,48,1.503000," ","int(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\left(\sin^{2}\left(f x +e \right)\right) \left(a^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right)+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) b +\cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) b +\sqrt{a}\, b \right)}{f \cos \left(f x +e \right)^{2} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)-1\right) b \sqrt{a}}"," ",0,"-1/f*sin(f*x+e)^2*(a^(3/2)*cos(f*x+e)^2+cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*b+cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*b+a^(1/2)*b)/cos(f*x+e)^2/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(cos(f*x+e)^2-1)/b/a^(1/2)","B"
404,1,42,27,0.253000," ","int(tan(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{\sec \left(f x +e \right)}\right)}{f \sqrt{a}}"," ",0,"-1/f/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sec(f*x+e)^2)^(1/2))/sec(f*x+e))","A"
405,1,376,58,1.875000," ","int(cot(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\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{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}-a \cos \left(f x +e \right)+b \right)}{\sin \left(f x +e \right)^{2} \sqrt{a +b}}\right) \sqrt{a}+2 \ln \left(4 \cos \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a}+4 a \cos \left(f x +e \right)+4 \sqrt{a}\, \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\right) \sqrt{a +b}-\ln \left(-\frac{4 \left(\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sqrt{a +b}+a \cos \left(f x +e \right)+\sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \sqrt{a +b}+b \right)}{-1+\cos \left(f x +e \right)}\right) \sqrt{a}\right) \left(\sin^{2}\left(f x +e \right)\right)}{2 f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{a +b}\, \sqrt{a}}"," ",0,"-1/2/f*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*a^(1/2)+2*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*(a+b)^(1/2)-ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*a^(1/2))*sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/(a+b)^(1/2)/a^(1/2)","B"
406,1,4245,98,2.012000," ","int(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"-1/4/f*(2*(a+b)^(3/2)*a^(3/2)*cos(f*x+e)^3+2*a^(5/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))-2*a^(5/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))-2*a^(5/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))+2*a^(5/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))+2*(a+b)^(3/2)*a^(1/2)*cos(f*x+e)*b+4*(a+b)^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a+4*(a+b)^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*b+5*a^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b-5*a^(3/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b+3*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^2-3*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^2-2*a^(5/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))+2*a^(5/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))+2*a^(5/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))-2*a^(5/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))+3*a^(1/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^2-4*(a+b)^(3/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a-4*(a+b)^(3/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*b-5*a^(3/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b+5*a^(3/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b-3*a^(1/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^2+3*a^(1/2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^2+4*(a+b)^(3/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a+4*(a+b)^(3/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*b+5*a^(3/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b-5*a^(3/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b+3*a^(1/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^2-3*a^(1/2)*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b^2-4*(a+b)^(3/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a-4*(a+b)^(3/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*b-5*a^(3/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b+5*a^(3/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-4*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+a*cos(f*x+e)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)+b)/(-1+cos(f*x+e)))*b-3*a^(1/2)*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(-2*(-1+cos(f*x+e))*(((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*(a+b)^(1/2)+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*(a+b)^(1/2)-a*cos(f*x+e)+b)/sin(f*x+e)^2/(a+b)^(1/2))*b^2)*sin(f*x+e)^2/(-1+cos(f*x+e))^2/cos(f*x+e)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/(1+cos(f*x+e))^2/(a+b)^(5/2)/a^(1/2)","B"
407,1,10441,144,2.674000," ","int(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
408,1,1993,151,2.342000," ","int(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sin \left(f x +e \right) \left(3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+10 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +7 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-20 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -30 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}+16 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2}+3 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}+9 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}-9 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b +9 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -9 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}+2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{8 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{5} \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}}"," ",0,"-1/8/f*sin(f*x+e)*(3*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2+10*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b+7*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2-6*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2-20*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b-30*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2+16*sin(f*x+e)*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2+3*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+9*cos(f*x+e)^5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-3*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2-9*cos(f*x+e)^4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b+9*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b-9*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/b^2","C"
409,1,1322,102,1.731000," ","int(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sin \left(f x +e \right) \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) a +6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) b -4 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) b -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) a -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right)^{3} b \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/2/f*sin(f*x+e)*(2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*b-4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*b-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*b-cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)^3/b/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
410,1,404,68,1.515000," ","int(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x)","\frac{2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right)-\EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right)\right) \left(\sin^{2}\left(f x +e \right)\right)}{f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"2/f*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*(EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))-EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)))*sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
411,1,380,33,1.640000," ","int(1/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right)-2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right)\right) \left(\sin^{2}\left(f x +e \right)\right)}{f \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"-1/f*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*(EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))-2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)))*sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
412,1,1865,66,1.862000," ","int(cot(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x)","-\frac{a \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a -2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right) \cos \left(f x +e \right)+a \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b}{f \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}}\, \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(a +b \right)}"," ",0,"-1/f*(a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)*cos(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)*sin(f*x+e)*a-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)*cos(f*x+e)+a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-2*a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)+cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/cos(f*x+e)/sin(f*x+e)/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/(a+b)","C"
413,1,5619,105,1.923000," ","int(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
414,1,11267,154,2.269000," ","int(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
415,1,6593,78,1.979000," ","int(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
416,1,2368,58,1.697000," ","int(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/f*(-1+cos(f*x+e))^2*(1+cos(f*x+e))^2*(-3*cos(f*x+e)^5*a^(11/2)*b+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a^2*b^4+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a*b^5+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*a^3*b^3-3*cos(f*x+e)*a^(7/2)*b^3-3*cos(f*x+e)*a^(5/2)*b^4-cos(f*x+e)*a^(3/2)*b^5-3*cos(f*x+e)^5*a^(9/2)*b^2-cos(f*x+e)^5*a^(7/2)*b^3-2*cos(f*x+e)^3*a^(11/2)*b-6*cos(f*x+e)^3*a^(9/2)*b^2-6*cos(f*x+e)^3*a^(7/2)*b^3-2*cos(f*x+e)^3*a^(5/2)*b^4-cos(f*x+e)*a^(9/2)*b^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)*a*b^5+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^5*a^5*b+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^5*a^4*b^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^5*a^3*b^3+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^4*a^5*b+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^4*a^4*b^2+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^4*a^3*b^3+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^3*a^4*b^2+4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^3*a^3*b^3+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^3*a^2*b^4+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^2*a^4*b^2+4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^2*a^3*b^3+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)^2*a^2*b^4+((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)*a^3*b^3+2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*ln(4*cos(f*x+e)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^(1/2)+4*a*cos(f*x+e)+4*a^(1/2)*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2))*cos(f*x+e)*a^2*b^4-cos(f*x+e)^5*a^(13/2))*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/(a+b)/(b+a*cos(f*x+e)^2)^4/sin(f*x+e)^4/a^(3/2)/((-a*b)^(1/2)-a)/((-a*b)^(1/2)+a)/b","B"
417,1,64,49,0.210000," ","int(tan(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{1}{a f \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{\sec \left(f x +e \right)}\right)}{f \,a^{\frac{3}{2}}}"," ",0,"1/a/f/(a+b*sec(f*x+e)^2)^(1/2)-1/f/a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sec(f*x+e)^2)^(1/2))/sec(f*x+e))","A"
418,1,9693,86,2.056000," ","int(cot(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
419,1,19968,131,2.253000," ","int(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
420,1,32565,187,2.939000," ","int(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
421,1,3860,152,1.789000," ","int(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"1/4/f*(4*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(5/2)*a+10*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(3/2)*a^2-20*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(3/2)*a^2-8*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)^4*2^(1/2)*b^(5/2)*sin(f*x+e)*a+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^5*b^(5/2)*a-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^4*b^(5/2)*a+8*cos(f*x+e)^5*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+6*cos(f*x+e)^5*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3-8*cos(f*x+e)^4*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+8*cos(f*x+e)^3*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-6*cos(f*x+e)^4*b^(1/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^3+8*cos(f*x+e)^3*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2-8*cos(f*x+e)^2*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-8*cos(f*x+e)^2*b^(3/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2+2*cos(f*x+e)*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a-2*b^(5/2)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+4*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(7/2)-4*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(7/2)+6*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(1/2)*a^3-12*cos(f*x+e)^4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(1/2)*a^3+10*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(5/2)*a-20*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(5/2)*a+6*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(3/2)*a^2-12*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*b^(3/2)*a^2+7*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-7*cos(f*x+e)^2*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+7*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-7*cos(f*x+e)^4*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b+4*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*b^(7/2)-8*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*2^(1/2)*b^(7/2)*sin(f*x+e)*cos(f*x+e)^2)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/b^(5/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a","C"
422,1,2662,102,1.722000," ","int(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/2/f*(4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*b^(3/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a-2*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a+4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*b^(5/2)*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))-2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^(5/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)+4*cos(f*x+e)^2*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2-2*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^(1/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2+4*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a-2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^(3/2)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a+cos(f*x+e)^2*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2-cos(f*x+e)^2*sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(3/2)*cos(f*x+e)^3*a-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(5/2)*cos(f*x+e)+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(3/2)*cos(f*x+e)^2*a-2*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(1/2)*a^2+sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/8*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2)*4^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b-sin(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*arctanh(1/4*(-1+cos(f*x+e))*(cos(f*x+e)*4^(1/2)-2*cos(f*x+e)-4^(1/2)-2)/sin(f*x+e)^2/((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*b^(1/2))*((b+a*cos(f*x+e)^2)/(1+cos(f*x+e))^2)^(1/2)*a*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(5/2)-2*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(3/2)*a+2*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(1/2)*a^2+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^(3/2)*a)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/b^(3/2)/a/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
423,1,569,63,1.643000," ","int(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x)","\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right)+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right)-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\right) \sin \left(f x +e \right)}{f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{3} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a}"," ",0,"1/f*(b+a*cos(f*x+e)^2)*(2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^3/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a","C"
424,1,1007,69,1.986000," ","int(1/(a+b*sec(f*x+e)^2)^(3/2),x)","-\frac{\left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right) \sin \left(f x +e \right)}{f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{3} \left(a +b \right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a}"," ",0,"-1/f*(b+a*cos(f*x+e)^2)*(a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)+2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-2*a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)-2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)+cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)*sin(f*x+e)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/cos(f*x+e)^3/(a+b)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a","C"
425,1,2841,109,1.964000," ","int(cot(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"1/f/(b+a*cos(f*x+e)^2)^2*(2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2+4*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b+2*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2-2*cos(f*x+e)*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)*cos(f*x+e)+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2+4*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)+2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)-a^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)-2*a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)*cos(f*x+e)^3*((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(3/2)/sin(f*x+e)/(a+b)^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a","C"
426,1,7541,158,2.115000," ","int(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
427,1,14137,221,2.262000," ","int(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
428,1,10947,85,3.577000," ","int(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
429,1,10839,81,3.203000," ","int(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
430,1,86,71,0.230000," ","int(tan(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x)","\frac{1}{3 a f \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{1}{a^{2} f \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sec^{2}\left(f x +e \right)\right)}}{\sec \left(f x +e \right)}\right)}{f \,a^{\frac{5}{2}}}"," ",0,"1/3/a/f/(a+b*sec(f*x+e)^2)^(3/2)+1/a^2/f/(a+b*sec(f*x+e)^2)^(1/2)-1/f/a^(5/2)*ln((2*a+2*a^(1/2)*(a+b*sec(f*x+e)^2)^(1/2))/sec(f*x+e))","A"
431,1,68989,119,5.236000," ","int(cot(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
432,1,105237,174,7.392000," ","int(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
433,1,145925,238,18.803000," ","int(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
434,1,2256,139,1.937000," ","int(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x)","-\frac{\sin \left(f x +e \right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) a^{3}-3 \left(\cos^{2}\left(f x +e \right)\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}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, a \,b^{2}+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-6 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{3}+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a^{2} b \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{3} \sin \left(f x +e \right)+6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{3} \sin \left(f x +e \right)-6 \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a^{2} b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{3}-\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2} b -4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a \,b^{2}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{3}+\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b +4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}+4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a^{2} b +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a \,b^{2}-3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{3}-4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2} b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a \,b^{2}+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{3}\right)}{3 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{5} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} a^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}}"," ",0,"-1/3/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3-3*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b^2+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a*b^2-6*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^3+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)-6*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^3-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^3+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a^2*b+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a^2*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/a^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/b^2","C"
435,1,1142,106,1.651000," ","int(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x)","\frac{\sin \left(f x +e \right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) a -3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \sin \left(f x +e \right) a +6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b \sin \left(f x +e \right)-3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)-4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a +4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a +\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b -\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b \right)}{3 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{5} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a^{2}}"," ",0,"1/3/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b*sin(f*x+e)-3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)-4*cos(f*x+e)^3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+4*cos(f*x+e)^2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a-3*cos(f*x+e)*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b-((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b)/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/a^2","C"
436,1,2112,105,1.523000," ","int(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x)","\frac{\sin \left(f x +e \right) \left(b +a \left(\cos^{2}\left(f x +e \right)\right)\right) \left(3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) a b -6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-6 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b +3 a \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b \sin \left(f x +e \right)+3 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{-\frac{4 i a^{\frac{3}{2}} \sqrt{b}-4 i \sqrt{a}\, b^{\frac{3}{2}}-a^{2}+6 a b -b^{2}}{\left(a +b \right)^{2}}}\right) b^{2} \sin \left(f x +e \right)-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) a b \sin \left(f x +e \right)-6 \sqrt{2}\, \sqrt{\frac{i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}+a \cos \left(f x +e \right)+b}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{-\frac{2 \left(i \sqrt{a}\, \sqrt{b}\, \cos \left(f x +e \right)-i \sqrt{a}\, \sqrt{b}-a \cos \left(f x +e \right)-b \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{2 i \sqrt{a}\, \sqrt{b}+a -b}, \frac{\sqrt{-\frac{2 i \sqrt{a}\, \sqrt{b}-a +b}{a +b}}}{\sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}\right) b^{2} \sin \left(f x +e \right)+3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2}+4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2}-4 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \left(\cos^{2}\left(f x +e \right)\right) a b +2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) a b +3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, \cos \left(f x +e \right) b^{2}-2 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, a b -3 \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}\, b^{2}\right)}{3 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{5} \left(\frac{b +a \left(\cos^{2}\left(f x +e \right)\right)}{\cos \left(f x +e \right)^{2}}\right)^{\frac{5}{2}} \left(a +b \right) a^{2} \sqrt{\frac{2 i \sqrt{a}\, \sqrt{b}+a -b}{a +b}}}"," ",0,"1/3/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2+3*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*cos(f*x+e)^2*sin(f*x+e)*a^2-6*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b+3*a*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b*sin(f*x+e)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^2*sin(f*x+e)+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b+2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2-2*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^2)/(-1+cos(f*x+e))/cos(f*x+e)^5/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/(a+b)/a^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
437,1,3024,111,2.196000," ","int(1/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"-1/3/f*sin(f*x+e)*(b+a*cos(f*x+e)^2)*(3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3+6*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*b+3*cos(f*x+e)^2*sin(f*x+e)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*a*b^2-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^3-12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a^2*b-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)^2*a*b^2+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a^2*b*sin(f*x+e)+6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*a*b^2*sin(f*x+e)+3*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),(-(4*I*a^(3/2)*b^(1/2)-4*I*a^(1/2)*b^(3/2)-a^2+6*a*b-b^2)/(a+b)^2)^(1/2))*b^3*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a^2*b*sin(f*x+e)-12*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*a*b^2*sin(f*x+e)-6*2^(1/2)*((I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)+a*cos(f*x+e)+b)/(1+cos(f*x+e))/(a+b))^(1/2)*(-2*(I*a^(1/2)*b^(1/2)*cos(f*x+e)-I*a^(1/2)*b^(1/2)-a*cos(f*x+e)-b)/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)/sin(f*x+e),-1/(2*I*a^(1/2)*b^(1/2)+a-b)*(a+b),(-(2*I*a^(1/2)*b^(1/2)-a+b)/(a+b))^(1/2)/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2))*b^3*sin(f*x+e)+6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a^2*b+4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^3*a*b^2-6*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*b-4*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b^2+5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b^2+3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*cos(f*x+e)*b^3-5*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*a*b^2-3*((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)*b^3)/(-1+cos(f*x+e))/((b+a*cos(f*x+e)^2)/cos(f*x+e)^2)^(5/2)/cos(f*x+e)^5/(a^2+2*a*b+b^2)/a^2/((2*I*a^(1/2)*b^(1/2)+a-b)/(a+b))^(1/2)","C"
438,1,7586,156,2.271000," ","int(cot(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
439,1,15128,216,2.489000," ","int(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
440,1,22712,289,2.516000," ","int(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
441,0,0,101,2.892000," ","int((a+b*sec(f*x+e)^2)^p*(d*tan(f*x+e))^m,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(d \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*(d*tan(f*x+e))^m,x)","F"
442,0,0,118,1.482000," ","int((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^5,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(\tan^{5}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^5,x)","F"
443,0,0,84,1.153000," ","int((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^3,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(\tan^{3}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^3,x)","F"
444,0,0,54,1.312000," ","int((a+b*sec(f*x+e)^2)^p*tan(f*x+e),x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \tan \left(f x +e \right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*tan(f*x+e),x)","F"
445,0,0,114,2.031000," ","int(cot(f*x+e)*(a+b*sec(f*x+e)^2)^p,x)","\int \cot \left(f x +e \right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)*(a+b*sec(f*x+e)^2)^p,x)","F"
446,0,0,155,1.463000," ","int(cot(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\cot^{3}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x)","F"
447,0,0,82,1.602000," ","int((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^4,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^4,x)","F"
448,0,0,82,1.159000," ","int((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^2,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^2,x)","F"
449,0,0,79,0.046000," ","int((a+b*sec(f*x+e)^2)^p,x)","\int \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*sec(f*x+e)^2)^p,x)","F"
450,0,0,80,1.273000," ","int(cot(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x)","F"
451,0,0,82,1.542000," ","int(cot(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x)","\int \left(\cot^{4}\left(f x +e \right)\right) \left(a +b \left(\sec^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x)","F"
452,1,183,84,1.095000," ","int((a+b*sec(f*x+e)^3)*tan(f*x+e)^5,x)","\frac{\left(\tan^{4}\left(f x +e \right)\right) a}{4 f}-\frac{a \left(\tan^{2}\left(f x +e \right)\right)}{2 f}-\frac{a \ln \left(\cos \left(f x +e \right)\right)}{f}+\frac{b \left(\sin^{6}\left(f x +e \right)\right)}{7 f \cos \left(f x +e \right)^{7}}+\frac{b \left(\sin^{6}\left(f x +e \right)\right)}{35 f \cos \left(f x +e \right)^{5}}-\frac{b \left(\sin^{6}\left(f x +e \right)\right)}{105 f \cos \left(f x +e \right)^{3}}+\frac{b \left(\sin^{6}\left(f x +e \right)\right)}{35 f \cos \left(f x +e \right)}+\frac{8 b \cos \left(f x +e \right)}{105 f}+\frac{b \cos \left(f x +e \right) \left(\sin^{4}\left(f x +e \right)\right)}{35 f}+\frac{4 b \cos \left(f x +e \right) \left(\sin^{2}\left(f x +e \right)\right)}{105 f}"," ",0,"1/4/f*tan(f*x+e)^4*a-1/2/f*a*tan(f*x+e)^2-a*ln(cos(f*x+e))/f+1/7/f*b*sin(f*x+e)^6/cos(f*x+e)^7+1/35/f*b*sin(f*x+e)^6/cos(f*x+e)^5-1/105/f*b*sin(f*x+e)^6/cos(f*x+e)^3+1/35/f*b*sin(f*x+e)^6/cos(f*x+e)+8/105/f*b*cos(f*x+e)+1/35/f*b*cos(f*x+e)*sin(f*x+e)^4+4/105/f*b*cos(f*x+e)*sin(f*x+e)^2","B"
453,1,126,55,0.979000," ","int((a+b*sec(f*x+e)^3)*tan(f*x+e)^3,x)","\frac{a \left(\tan^{2}\left(f x +e \right)\right)}{2 f}+\frac{a \ln \left(\cos \left(f x +e \right)\right)}{f}+\frac{b \left(\sin^{4}\left(f x +e \right)\right)}{5 f \cos \left(f x +e \right)^{5}}+\frac{b \left(\sin^{4}\left(f x +e \right)\right)}{15 f \cos \left(f x +e \right)^{3}}-\frac{b \left(\sin^{4}\left(f x +e \right)\right)}{15 f \cos \left(f x +e \right)}-\frac{b \cos \left(f x +e \right) \left(\sin^{2}\left(f x +e \right)\right)}{15 f}-\frac{2 b \cos \left(f x +e \right)}{15 f}"," ",0,"1/2/f*a*tan(f*x+e)^2+a*ln(cos(f*x+e))/f+1/5/f*b*sin(f*x+e)^4/cos(f*x+e)^5+1/15/f*b*sin(f*x+e)^4/cos(f*x+e)^3-1/15/f*b*sin(f*x+e)^4/cos(f*x+e)-1/15/f*b*cos(f*x+e)*sin(f*x+e)^2-2/15/f*b*cos(f*x+e)","B"
454,1,28,28,0.363000," ","int((a+b*sec(f*x+e)^3)*tan(f*x+e),x)","\frac{b \left(\sec^{3}\left(f x +e \right)\right)}{3 f}+\frac{a \ln \left(\sec \left(f x +e \right)\right)}{f}"," ",0,"1/3*b*sec(f*x+e)^3/f+1/f*a*ln(sec(f*x+e))","A"
455,1,48,50,0.688000," ","int(cot(f*x+e)*(a+b*sec(f*x+e)^3),x)","\frac{a \ln \left(\sin \left(f x +e \right)\right)}{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,"a*ln(sin(f*x+e))/f+1/f*b/cos(f*x+e)+1/f*b*ln(csc(f*x+e)-cot(f*x+e))","A"
456,1,69,66,1.104000," ","int(cot(f*x+e)^3*(a+b*sec(f*x+e)^3),x)","-\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}-\frac{b \csc \left(f x +e \right) \cot \left(f x +e \right)}{2 f}+\frac{b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}"," ",0,"-1/2*a*cot(f*x+e)^2/f-a*ln(sin(f*x+e))/f-1/2/f*b*csc(f*x+e)*cot(f*x+e)+1/2/f*b*ln(csc(f*x+e)-cot(f*x+e))","A"
457,1,274,168,0.661000," ","int(tan(f*x+e)^5/(a+b*sec(f*x+e)^3),x)","\frac{2 \ln \left(\cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{3 f a \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{\ln \left(\cos^{2}\left(f x +e \right)-\left(\frac{b}{a}\right)^{\frac{1}{3}} \cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{3 f a \left(\frac{b}{a}\right)^{\frac{2}{3}}}+\frac{2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \cos \left(f x +e \right)}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 f a \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{\ln \left(\cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{3 f b \left(\frac{b}{a}\right)^{\frac{1}{3}}}+\frac{\ln \left(\cos^{2}\left(f x +e \right)-\left(\frac{b}{a}\right)^{\frac{1}{3}} \cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 f b \left(\frac{b}{a}\right)^{\frac{1}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \cos \left(f x +e \right)}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 f b \left(\frac{b}{a}\right)^{\frac{1}{3}}}-\frac{\ln \left(b +a \left(\cos^{3}\left(f x +e \right)\right)\right)}{3 a f}+\frac{1}{f b \cos \left(f x +e \right)}"," ",0,"2/3/f/a/(1/a*b)^(2/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))-1/3/f/a/(1/a*b)^(2/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b)^(2/3))+2/3/f/a/(1/a*b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))-1/3/f/b/(1/a*b)^(1/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))+1/6/f/b/(1/a*b)^(1/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b)^(2/3))+1/3/f/b*3^(1/2)/(1/a*b)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))-1/3*ln(b+a*cos(f*x+e)^3)/a/f+1/f/b/cos(f*x+e)","A"
458,1,141,128,0.774000," ","int(tan(f*x+e)^3/(a+b*sec(f*x+e)^3),x)","-\frac{\ln \left(\cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{3 f a \left(\frac{b}{a}\right)^{\frac{2}{3}}}+\frac{\ln \left(\cos^{2}\left(f x +e \right)-\left(\frac{b}{a}\right)^{\frac{1}{3}} \cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 f a \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \cos \left(f x +e \right)}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 f a \left(\frac{b}{a}\right)^{\frac{2}{3}}}+\frac{\ln \left(b +a \left(\cos^{3}\left(f x +e \right)\right)\right)}{3 a f}"," ",0,"-1/3/f/a/(1/a*b)^(2/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))+1/6/f/a/(1/a*b)^(2/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b)^(2/3))-1/3/f/a/(1/a*b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))+1/3*ln(b+a*cos(f*x+e)^3)/a/f","A"
459,1,37,21,0.166000," ","int(tan(f*x+e)/(a+b*sec(f*x+e)^3),x)","-\frac{\ln \left(a +b \left(\sec^{3}\left(f x +e \right)\right)\right)}{3 f a}+\frac{\ln \left(\sec \left(f x +e \right)\right)}{f a}"," ",0,"-1/3/f/a*ln(a+b*sec(f*x+e)^3)+1/f/a*ln(sec(f*x+e))","A"
460,1,393,236,1.041000," ","int(cot(f*x+e)/(a+b*sec(f*x+e)^3),x)","-\frac{b^{2} \ln \left(\cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{3 f \left(a -b \right) \left(a +b \right) a \left(\frac{b}{a}\right)^{\frac{2}{3}}}+\frac{b^{2} \ln \left(\cos^{2}\left(f x +e \right)-\left(\frac{b}{a}\right)^{\frac{1}{3}} \cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 f \left(a -b \right) \left(a +b \right) a \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{b^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \cos \left(f x +e \right)}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 f \left(a -b \right) \left(a +b \right) a \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{b \ln \left(\cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{3 f \left(a -b \right) \left(a +b \right) \left(\frac{b}{a}\right)^{\frac{1}{3}}}+\frac{b \ln \left(\cos^{2}\left(f x +e \right)-\left(\frac{b}{a}\right)^{\frac{1}{3}} \cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 f \left(a -b \right) \left(a +b \right) \left(\frac{b}{a}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \cos \left(f x +e \right)}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 f \left(a -b \right) \left(a +b \right) \left(\frac{b}{a}\right)^{\frac{1}{3}}}-\frac{b^{2} \ln \left(b +a \left(\cos^{3}\left(f x +e \right)\right)\right)}{3 f \left(a -b \right) \left(a +b \right) a}+\frac{\ln \left(-1+\cos \left(f x +e \right)\right)}{f \left(2 a +2 b \right)}+\frac{\ln \left(1+\cos \left(f x +e \right)\right)}{f \left(2 a -2 b \right)}"," ",0,"-1/3/f*b^2/(a-b)/(a+b)/a/(1/a*b)^(2/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))+1/6/f*b^2/(a-b)/(a+b)/a/(1/a*b)^(2/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b)^(2/3))-1/3/f*b^2/(a-b)/(a+b)/a/(1/a*b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))-1/3/f*b/(a-b)/(a+b)/(1/a*b)^(1/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))+1/6/f*b/(a-b)/(a+b)/(1/a*b)^(1/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b)^(2/3))+1/3/f*b/(a-b)/(a+b)*3^(1/2)/(1/a*b)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))-1/3/f*b^2/(a-b)/(a+b)/a*ln(b+a*cos(f*x+e)^3)+1/f/(2*a+2*b)*ln(-1+cos(f*x+e))+1/f/(2*a-2*b)*ln(1+cos(f*x+e))","A"
461,1,676,335,1.334000," ","int(cot(f*x+e)^3/(a+b*sec(f*x+e)^3),x)","-\frac{b^{2} a \ln \left(\cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{3 f \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{2 b^{4} \ln \left(\cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{3 f \left(a -b \right)^{2} \left(a +b \right)^{2} a \left(\frac{b}{a}\right)^{\frac{2}{3}}}+\frac{b^{2} a \ln \left(\cos^{2}\left(f x +e \right)-\left(\frac{b}{a}\right)^{\frac{1}{3}} \cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 f \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}}}+\frac{b^{4} \ln \left(\cos^{2}\left(f x +e \right)-\left(\frac{b}{a}\right)^{\frac{1}{3}} \cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{3 f \left(a -b \right)^{2} \left(a +b \right)^{2} a \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{b^{2} a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \cos \left(f x +e \right)}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 f \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{2 b^{4} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \cos \left(f x +e \right)}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 f \left(a -b \right)^{2} \left(a +b \right)^{2} a \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{b^{3} \ln \left(\cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{f \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{b}{a}\right)^{\frac{1}{3}}}+\frac{b^{3} \ln \left(\cos^{2}\left(f x +e \right)-\left(\frac{b}{a}\right)^{\frac{1}{3}} \cos \left(f x +e \right)+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{2 f \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{b}{a}\right)^{\frac{1}{3}}}+\frac{b^{3} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \cos \left(f x +e \right)}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{f \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{b}{a}\right)^{\frac{1}{3}}}-\frac{2 b^{2} a \ln \left(b +a \left(\cos^{3}\left(f x +e \right)\right)\right)}{3 f \left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{b^{4} \ln \left(b +a \left(\cos^{3}\left(f x +e \right)\right)\right)}{3 f \left(a -b \right)^{2} \left(a +b \right)^{2} a}+\frac{1}{f \left(4 a +4 b \right) \left(-1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(-1+\cos \left(f x +e \right)\right) a}{2 f \left(a +b \right)^{2}}-\frac{5 \ln \left(-1+\cos \left(f x +e \right)\right) b}{4 f \left(a +b \right)^{2}}-\frac{1}{f \left(4 a -4 b \right) \left(1+\cos \left(f x +e \right)\right)}-\frac{\ln \left(1+\cos \left(f x +e \right)\right) a}{2 f \left(a -b \right)^{2}}+\frac{5 \ln \left(1+\cos \left(f x +e \right)\right) b}{4 f \left(a -b \right)^{2}}"," ",0,"-1/3/f*b^2/(a-b)^2/(a+b)^2*a/(1/a*b)^(2/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))-2/3/f*b^4/(a-b)^2/(a+b)^2/a/(1/a*b)^(2/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))+1/6/f*b^2/(a-b)^2/(a+b)^2*a/(1/a*b)^(2/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b)^(2/3))+1/3/f*b^4/(a-b)^2/(a+b)^2/a/(1/a*b)^(2/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b)^(2/3))-1/3/f*b^2/(a-b)^2/(a+b)^2*a/(1/a*b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))-2/3/f*b^4/(a-b)^2/(a+b)^2/a/(1/a*b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))-1/f*b^3/(a-b)^2/(a+b)^2/(1/a*b)^(1/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))+1/2/f*b^3/(a-b)^2/(a+b)^2/(1/a*b)^(1/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b)^(2/3))+1/f*b^3/(a-b)^2/(a+b)^2*3^(1/2)/(1/a*b)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))-2/3/f*b^2/(a-b)^2/(a+b)^2*a*ln(b+a*cos(f*x+e)^3)-1/3/f*b^4/(a-b)^2/(a+b)^2/a*ln(b+a*cos(f*x+e)^3)+1/f/(4*a+4*b)/(-1+cos(f*x+e))-1/2/f/(a+b)^2*ln(-1+cos(f*x+e))*a-5/4/f/(a+b)^2*ln(-1+cos(f*x+e))*b-1/f/(4*a-4*b)/(1+cos(f*x+e))-1/2/f/(a-b)^2*ln(1+cos(f*x+e))*a+5/4/f/(a-b)^2*ln(1+cos(f*x+e))*b","B"
462,0,0,29,6.115000," ","int((a+b*(c*sec(f*x+e))^n)^p*(d*tan(f*x+e))^m,x)","\int \left(a +b \left(c \sec \left(f x +e \right)\right)^{n}\right)^{p} \left(d \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*(c*sec(f*x+e))^n)^p*(d*tan(f*x+e))^m,x)","F"
463,0,0,230,1.925000," ","int((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e)^5,x)","\int \left(a +b \left(c \sec \left(f x +e \right)\right)^{n}\right)^{p} \left(\tan^{5}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e)^5,x)","F"
464,0,0,145,1.636000," ","int((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e)^3,x)","\int \left(a +b \left(c \sec \left(f x +e \right)\right)^{n}\right)^{p} \left(\tan^{3}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e)^3,x)","F"
465,0,0,61,1.272000," ","int((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e),x)","\int \left(a +b \left(c \sec \left(f x +e \right)\right)^{n}\right)^{p} \tan \left(f x +e \right)\, dx"," ",0,"int((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e),x)","F"
466,0,0,25,1.822000," ","int(cot(f*x+e)*(a+b*(c*sec(f*x+e))^n)^p,x)","\int \cot \left(f x +e \right) \left(a +b \left(c \sec \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cot(f*x+e)*(a+b*(c*sec(f*x+e))^n)^p,x)","F"
467,0,0,27,2.128000," ","int(cot(f*x+e)^3*(a+b*(c*sec(f*x+e))^n)^p,x)","\int \left(\cot^{3}\left(f x +e \right)\right) \left(a +b \left(c \sec \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^3*(a+b*(c*sec(f*x+e))^n)^p,x)","F"
468,0,0,27,1.645000," ","int((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e)^2,x)","\int \left(a +b \left(c \sec \left(f x +e \right)\right)^{n}\right)^{p} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e)^2,x)","F"
469,0,0,18,1.699000," ","int((a+b*(c*sec(f*x+e))^n)^p,x)","\int \left(a +b \left(c \sec \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int((a+b*(c*sec(f*x+e))^n)^p,x)","F"
470,0,0,27,1.755000," ","int(cot(f*x+e)^2*(a+b*(c*sec(f*x+e))^n)^p,x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(a +b \left(c \sec \left(f x +e \right)\right)^{n}\right)^{p}\, dx"," ",0,"int(cot(f*x+e)^2*(a+b*(c*sec(f*x+e))^n)^p,x)","F"