1,1,69,83,0.471000," ","int(sec(d*x+c)^10*(a+I*a*tan(d*x+c)),x)","\frac{\frac{i a}{10 \cos \left(d x +c \right)^{10}}-a \left(-\frac{128}{315}-\frac{\left(\sec^{8}\left(d x +c \right)\right)}{9}-\frac{8 \left(\sec^{6}\left(d x +c \right)\right)}{63}-\frac{16 \left(\sec^{4}\left(d x +c \right)\right)}{105}-\frac{64 \left(\sec^{2}\left(d x +c \right)\right)}{315}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(1/10*I*a/cos(d*x+c)^10-a*(-128/315-1/9*sec(d*x+c)^8-8/63*sec(d*x+c)^6-16/105*sec(d*x+c)^4-64/315*sec(d*x+c)^2)*tan(d*x+c))","A"
2,1,59,68,0.443000," ","int(sec(d*x+c)^8*(a+I*a*tan(d*x+c)),x)","\frac{\frac{i a}{8 \cos \left(d x +c \right)^{8}}-a \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*(1/8*I*a/cos(d*x+c)^8-a*(-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"
3,1,49,55,0.439000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c)),x)","\frac{\frac{i a}{6 \cos \left(d x +c \right)^{6}}-a \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(1/6*I*a/cos(d*x+c)^6-a*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","A"
4,1,39,41,0.421000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c)),x)","\frac{\frac{i a}{4 \cos \left(d x +c \right)^{4}}-a \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(1/4*I*a/cos(d*x+c)^4-a*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","A"
5,1,26,23,0.388000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c)),x)","\frac{\frac{i a}{2 \cos \left(d x +c \right)^{2}}+a \tan \left(d x +c \right)}{d}"," ",0,"1/d*(1/2*I*a/cos(d*x+c)^2+a*tan(d*x+c))","A"
6,1,23,18,0.012000," ","int(a+I*a*tan(d*x+c),x)","a x +\frac{i a \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"a*x+1/2*I*a/d*ln(1+tan(d*x+c)^2)","A"
7,1,42,38,0.319000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c)),x)","\frac{-\frac{i a \left(\cos^{2}\left(d x +c \right)\right)}{2}+a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(-1/2*I*a*cos(d*x+c)^2+a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
8,1,53,58,0.436000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c)),x)","\frac{-\frac{i a \left(\cos^{4}\left(d x +c \right)\right)}{4}+a \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(-1/4*I*a*cos(d*x+c)^4+a*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
9,1,63,78,0.438000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c)),x)","\frac{-\frac{i a \left(\cos^{6}\left(d x +c \right)\right)}{6}+a \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(-1/6*I*a*cos(d*x+c)^6+a*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
10,1,73,98,0.443000," ","int(cos(d*x+c)^8*(a+I*a*tan(d*x+c)),x)","\frac{-\frac{i a \left(\cos^{8}\left(d x +c \right)\right)}{8}+a \left(\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)}{d}"," ",0,"1/d*(-1/8*I*a*cos(d*x+c)^8+a*(1/8*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/128*d*x+35/128*c))","A"
11,1,95,87,0.451000," ","int(sec(d*x+c)^7*(a+I*a*tan(d*x+c)),x)","\frac{i a}{7 d \cos \left(d x +c \right)^{7}}+\frac{a \left(\sec^{5}\left(d x +c \right)\right) \tan \left(d x +c \right)}{6 d}+\frac{5 a \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{24 d}+\frac{5 a \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{5 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}"," ",0,"1/7*I/d*a/cos(d*x+c)^7+1/6*a*sec(d*x+c)^5*tan(d*x+c)/d+5/24*a*sec(d*x+c)^3*tan(d*x+c)/d+5/16*a*sec(d*x+c)*tan(d*x+c)/d+5/16/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
12,1,75,67,0.436000," ","int(sec(d*x+c)^5*(a+I*a*tan(d*x+c)),x)","\frac{i a}{5 d \cos \left(d x +c \right)^{5}}+\frac{a \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/5*I/d*a/cos(d*x+c)^5+1/4*a*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
13,1,55,47,0.422000," ","int(sec(d*x+c)^3*(a+I*a*tan(d*x+c)),x)","\frac{i a}{3 d \cos \left(d x +c \right)^{3}}+\frac{a \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/3*I/d*a/cos(d*x+c)^3+1/2*a*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
14,1,36,26,0.098000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c)),x)","\frac{i a}{d \cos \left(d x +c \right)}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"I/d*a/cos(d*x+c)+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
15,1,24,25,0.276000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c)),x)","\frac{-i a \cos \left(d x +c \right)+a \sin \left(d x +c \right)}{d}"," ",0,"1/d*(-I*a*cos(d*x+c)+a*sin(d*x+c))","A"
16,1,37,41,0.407000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c)),x)","\frac{-\frac{i a \left(\cos^{3}\left(d x +c \right)\right)}{3}+\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/3*I*a*cos(d*x+c)^3+1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
17,1,47,55,0.420000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c)),x)","\frac{-\frac{i a \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(-1/5*I*a*cos(d*x+c)^5+1/5*a*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
18,1,57,69,0.422000," ","int(cos(d*x+c)^7*(a+I*a*tan(d*x+c)),x)","\frac{-\frac{i a \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(-1/7*I*a*cos(d*x+c)^7+1/7*a*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
19,1,141,93,0.444000," ","int(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+\frac{i a^{2}}{4 \cos \left(d x +c \right)^{8}}-a^{2} \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^2*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+1/4*I*a^2/cos(d*x+c)^8-a^2*(-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"
20,1,113,70,0.441000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+\frac{i a^{2}}{3 \cos \left(d x +c \right)^{6}}-a^{2} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(-a^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+1/3*I*a^2/cos(d*x+c)^6-a^2*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","A"
21,1,85,47,0.422000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+\frac{i a^{2}}{2 \cos \left(d x +c \right)^{4}}-a^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(-a^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+1/2*I*a^2/cos(d*x+c)^4-a^2*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","A"
22,1,51,23,0.428000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x)","\frac{-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+\frac{i a^{2}}{\cos \left(d x +c \right)^{2}}+a^{2} \tan \left(d x +c \right)}{d}"," ",0,"1/d*(-1/3*a^2*sin(d*x+c)^3/cos(d*x+c)^3+I*a^2/cos(d*x+c)^2+a^2*tan(d*x+c))","B"
23,1,51,37,0.016000," ","int((a+I*a*tan(d*x+c))^2,x)","\frac{i a^{2} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}-\frac{a^{2} \tan \left(d x +c \right)}{d}+\frac{2 a^{2} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"I/d*a^2*ln(1+tan(d*x+c)^2)-a^2*tan(d*x+c)/d+2/d*a^2*arctan(tan(d*x+c))","A"
24,1,73,23,0.307000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-i a^{2} \left(\cos^{2}\left(d x +c \right)\right)+a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(-a^2*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-I*a^2*cos(d*x+c)^2+a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","B"
25,1,100,53,0.476000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{i a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{2}+a^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(-a^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-1/2*I*a^2*cos(d*x+c)^4+a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
26,1,121,99,0.521000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{i a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{3}+a^{2} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(-a^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-1/3*I*a^2*cos(d*x+c)^6+a^2*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
27,1,141,145,0.545000," ","int(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{i a^{2} \left(\cos^{8}\left(d x +c \right)\right)}{4}+a^{2} \left(\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)}{d}"," ",0,"1/d*(-a^2*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-1/4*I*a^2*cos(d*x+c)^8+a^2*(1/8*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/128*d*x+35/128*c))","A"
28,1,169,105,0.443000," ","int(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x)","-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}-\frac{a^{2} \sin \left(d x +c \right)}{16 d}+\frac{7 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{2 i a^{2}}{5 d \cos \left(d x +c \right)^{5}}+\frac{a^{2} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}"," ",0,"-1/6/d*a^2*sin(d*x+c)^3/cos(d*x+c)^6-1/8/d*a^2*sin(d*x+c)^3/cos(d*x+c)^4-1/16/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2-1/16*a^2*sin(d*x+c)/d+7/16/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/5*I/d*a^2/cos(d*x+c)^5+1/4*a^2*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^2*sec(d*x+c)*tan(d*x+c)/d","A"
29,1,123,83,0.437000," ","int(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x)","-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a^{2} \sin \left(d x +c \right)}{8 d}+\frac{5 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 i a^{2}}{3 d \cos \left(d x +c \right)^{3}}+\frac{a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"-1/4/d*a^2*sin(d*x+c)^3/cos(d*x+c)^4-1/8/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2-1/8*a^2*sin(d*x+c)/d+5/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/3*I/d*a^2/cos(d*x+c)^3+1/2*a^2*sec(d*x+c)*tan(d*x+c)/d","A"
30,1,79,59,0.145000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c))^2,x)","-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{a^{2} \sin \left(d x +c \right)}{2 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 i a^{2}}{d \cos \left(d x +c \right)}"," ",0,"-1/2/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2-1/2*a^2*sin(d*x+c)/d+3/2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2*I/d*a^2/cos(d*x+c)","A"
31,1,53,44,0.298000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^2,x)","-\frac{2 i a^{2} \cos \left(d x +c \right)}{d}+\frac{2 a^{2} \sin \left(d x +c \right)}{d}-\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-2*I/d*a^2*cos(d*x+c)+2*a^2*sin(d*x+c)/d-1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))","A"
32,1,54,45,0.440000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x)","\frac{-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3}-\frac{2 i a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3}+\frac{a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/3*a^2*sin(d*x+c)^3-2/3*I*a^2*cos(d*x+c)^3+1/3*a^2*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
33,1,91,61,0.524000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{2 i a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a^{2} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(-a^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-2/5*I*a^2*cos(d*x+c)^5+1/5*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
34,1,111,77,0.529000," ","int(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{2 i a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{2} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(-a^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-2/7*I*a^2*cos(d*x+c)^7+1/7*a^2*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
35,1,131,93,0.523000," ","int(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{2 i a^{2} \left(\cos^{9}\left(d x +c \right)\right)}{9}+\frac{a^{2} \left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{9}}{d}"," ",0,"1/d*(-a^2*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-2/9*I*a^2*cos(d*x+c)^9+1/9*a^2*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))","A"
36,1,220,93,0.460000," ","int(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^3,x)","\frac{-i a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{40 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{40 \cos \left(d x +c \right)^{4}}\right)-3 a^{3} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+\frac{3 i a^{3}}{8 \cos \left(d x +c \right)^{8}}-a^{3} \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*(-I*a^3*(1/10*sin(d*x+c)^4/cos(d*x+c)^10+3/40*sin(d*x+c)^4/cos(d*x+c)^8+1/20*sin(d*x+c)^4/cos(d*x+c)^6+1/40*sin(d*x+c)^4/cos(d*x+c)^4)-3*a^3*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+3/8*I*a^3/cos(d*x+c)^8-a^3*(-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))","B"
37,1,174,70,0.445000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x)","\frac{-i a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{4}}\right)-3 a^{3} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+\frac{i a^{3}}{2 \cos \left(d x +c \right)^{6}}-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)}{d}"," ",0,"1/d*(-I*a^3*(1/8*sin(d*x+c)^4/cos(d*x+c)^8+1/12*sin(d*x+c)^4/cos(d*x+c)^6+1/24*sin(d*x+c)^4/cos(d*x+c)^4)-3*a^3*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+1/2*I*a^3/cos(d*x+c)^6-a^3*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","B"
38,1,128,47,0.437000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x)","\frac{-i a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{6 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{4}}\right)-3 a^{3} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+\frac{3 i a^{3}}{4 \cos \left(d x +c \right)^{4}}-a^{3} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(-I*a^3*(1/6*sin(d*x+c)^4/cos(d*x+c)^6+1/12*sin(d*x+c)^4/cos(d*x+c)^4)-3*a^3*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+3/4*I*a^3/cos(d*x+c)^4-a^3*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","B"
39,1,73,23,0.446000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x)","\frac{-\frac{i a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 \cos \left(d x +c \right)^{4}}-\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{3}}+\frac{3 i a^{3}}{2 \cos \left(d x +c \right)^{2}}+a^{3} \tan \left(d x +c \right)}{d}"," ",0,"1/d*(-1/4*I*a^3*sin(d*x+c)^4/cos(d*x+c)^4-a^3*sin(d*x+c)^3/cos(d*x+c)^3+3/2*I*a^3/cos(d*x+c)^2+a^3*tan(d*x+c))","B"
40,1,68,58,0.016000," ","int((a+I*a*tan(d*x+c))^3,x)","-\frac{3 a^{3} \tan \left(d x +c \right)}{d}-\frac{i a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 i a^{3} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 a^{3} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-3*a^3*tan(d*x+c)/d-1/2*I/d*a^3*tan(d*x+c)^2+2*I/d*a^3*ln(1+tan(d*x+c)^2)+4/d*a^3*arctan(tan(d*x+c))","A"
41,1,87,46,0.321000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x)","\frac{i a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}+\frac{i a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}-a^{3} x -\frac{a^{3} c}{d}-\frac{3 i a^{3} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/2*I/d*a^3*sin(d*x+c)^2+I*a^3*ln(cos(d*x+c))/d+2*a^3*cos(d*x+c)*sin(d*x+c)/d-a^3*x-1/d*a^3*c-3/2*I/d*a^3*cos(d*x+c)^2","A"
42,1,114,23,0.494000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x)","\frac{-\frac{i a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4}-3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{3 i a^{3} \left(\cos^{4}\left(d x +c \right)\right)}{4}+a^{3} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(-1/4*I*a^3*sin(d*x+c)^4-3*a^3*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-3/4*I*a^3*cos(d*x+c)^4+a^3*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","B"
43,1,156,76,0.515000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x)","\frac{-i a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)-3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{i a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{2}+a^{3} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(-I*a^3*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)-3*a^3*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-1/2*I*a^3*cos(d*x+c)^6+a^3*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","B"
44,1,176,122,0.515000," ","int(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^3,x)","\frac{-i a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)-3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{3 i a^{3} \left(\cos^{8}\left(d x +c \right)\right)}{8}+a^{3} \left(\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)}{d}"," ",0,"1/d*(-I*a^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)-3*a^3*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-3/8*I*a^3*cos(d*x+c)^8+a^3*(1/8*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/128*d*x+35/128*c))","A"
45,1,236,112,0.533000," ","int(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x)","-\frac{i a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}-\frac{i a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}+\frac{i a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)}+\frac{i a^{3} \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{15 d}+\frac{2 i a^{3} \cos \left(d x +c \right)}{15 d}-\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{3} \sin \left(d x +c \right)}{8 d}+\frac{7 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{i a^{3}}{d \cos \left(d x +c \right)^{3}}+\frac{a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"-1/5*I/d*a^3*sin(d*x+c)^4/cos(d*x+c)^5-1/15*I/d*a^3*sin(d*x+c)^4/cos(d*x+c)^3+1/15*I/d*a^3*sin(d*x+c)^4/cos(d*x+c)+1/15*I/d*a^3*sin(d*x+c)^2*cos(d*x+c)+2/15*I/d*a^3*cos(d*x+c)-3/4/d*a^3*sin(d*x+c)^3/cos(d*x+c)^4-3/8/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2-3/8*a^3*sin(d*x+c)/d+7/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+I/d*a^3/cos(d*x+c)^3+1/2*a^3*sec(d*x+c)*tan(d*x+c)/d","B"
46,1,167,86,0.271000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c))^3,x)","-\frac{i a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}+\frac{i a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}+\frac{i a^{3} \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3 d}+\frac{2 i a^{3} \cos \left(d x +c \right)}{3 d}-\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{3} \sin \left(d x +c \right)}{2 d}+\frac{5 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 i a^{3}}{d \cos \left(d x +c \right)}"," ",0,"-1/3*I/d*a^3*sin(d*x+c)^4/cos(d*x+c)^3+1/3*I/d*a^3*sin(d*x+c)^4/cos(d*x+c)+1/3*I/d*a^3*cos(d*x+c)*sin(d*x+c)^2+2/3*I/d*a^3*cos(d*x+c)-3/2/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2-3/2*a^3*sin(d*x+c)/d+5/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3*I/d*a^3/cos(d*x+c)","A"
47,1,101,58,0.373000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^3,x)","-\frac{i a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{i a^{3} \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{d}-\frac{5 i a^{3} \cos \left(d x +c \right)}{d}+\frac{4 a^{3} \sin \left(d x +c \right)}{d}-\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-I/d*a^3*sin(d*x+c)^4/cos(d*x+c)-I/d*a^3*sin(d*x+c)^2*cos(d*x+c)-5*I/d*a^3*cos(d*x+c)+4*a^3*sin(d*x+c)/d-3/d*a^3*ln(sec(d*x+c)+tan(d*x+c))","A"
48,1,76,28,0.460000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x)","\frac{\frac{i a^{3} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}-a^{3} \left(\sin^{3}\left(d x +c \right)\right)-i a^{3} \left(\cos^{3}\left(d x +c \right)\right)+\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/3*I*a^3*(2+sin(d*x+c)^2)*cos(d*x+c)-a^3*sin(d*x+c)^3-I*a^3*cos(d*x+c)^3+1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c))","B"
49,1,126,77,0.512000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^3,x)","\frac{-i a^{3} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)-3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{3 i a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a^{3} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(-I*a^3*(-1/5*cos(d*x+c)^3*sin(d*x+c)^2-2/15*cos(d*x+c)^3)-3*a^3*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-3/5*I*a^3*cos(d*x+c)^5+1/5*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
50,1,146,93,0.510000," ","int(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^3,x)","\frac{-i a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)-3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{3 i a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{3} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(-I*a^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)-3*a^3*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-3/7*I*a^3*cos(d*x+c)^7+1/7*a^3*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
51,1,166,109,0.536000," ","int(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^3,x)","\frac{-i a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)-3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{i a^{3} \left(\cos^{9}\left(d x +c \right)\right)}{3}+\frac{a^{3} \left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{9}}{d}"," ",0,"1/d*(-I*a^3*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)-3*a^3*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-1/3*I*a^3*cos(d*x+c)^9+1/9*a^3*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))","A"
52,1,324,144,0.518000," ","int(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x)","\frac{a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}-\frac{a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{2}}-\frac{a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{48 d}-\frac{13 a^{4} \sin \left(d x +c \right)}{16 d}+\frac{21 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{4 i a^{4}}{3 d \cos \left(d x +c \right)^{3}}+\frac{8 i a^{4} \cos \left(d x +c \right)}{15 d}-\frac{4 i a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}+\frac{4 i a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)}+\frac{4 i a^{4} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{3 a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{4 i a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}+\frac{a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"1/6/d*a^4*sin(d*x+c)^5/cos(d*x+c)^6+1/24/d*a^4*sin(d*x+c)^5/cos(d*x+c)^4-1/48/d*a^4*sin(d*x+c)^5/cos(d*x+c)^2-1/48*a^4*sin(d*x+c)^3/d-13/16*a^4*sin(d*x+c)/d+21/16/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+4/3*I/d*a^4/cos(d*x+c)^3+8/15*I/d*a^4*cos(d*x+c)-4/15*I/d*a^4*sin(d*x+c)^4/cos(d*x+c)^3+4/15*I/d*a^4*sin(d*x+c)^4/cos(d*x+c)+4/15*I/d*a^4*cos(d*x+c)*sin(d*x+c)^2-3/2/d*a^4*sin(d*x+c)^3/cos(d*x+c)^4-3/4/d*a^4*sin(d*x+c)^3/cos(d*x+c)^2-4/5*I/d*a^4*sin(d*x+c)^4/cos(d*x+c)^5+1/2*a^4*sec(d*x+c)*tan(d*x+c)/d","B"
53,1,231,116,0.268000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c))^4,x)","\frac{a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{27 a^{4} \sin \left(d x +c \right)}{8 d}+\frac{35 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}-\frac{4 i a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}+\frac{4 i a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}+\frac{4 i a^{4} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}+\frac{8 i a^{4} \cos \left(d x +c \right)}{3 d}-\frac{3 a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{4 i a^{4}}{d \cos \left(d x +c \right)}"," ",0,"1/4/d*a^4*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a^4*sin(d*x+c)^5/cos(d*x+c)^2-1/8*a^4*sin(d*x+c)^3/d-27/8*a^4*sin(d*x+c)/d+35/8/d*a^4*ln(sec(d*x+c)+tan(d*x+c))-4/3*I/d*a^4*sin(d*x+c)^4/cos(d*x+c)^3+4/3*I/d*a^4*sin(d*x+c)^4/cos(d*x+c)+4/3*I/d*a^4*cos(d*x+c)*sin(d*x+c)^2+8/3*I/d*a^4*cos(d*x+c)-3/d*a^4*sin(d*x+c)^3/cos(d*x+c)^2+4*I/d*a^4/cos(d*x+c)","A"
54,1,141,86,0.401000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^4,x)","\frac{a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{17 a^{4} \sin \left(d x +c \right)}{2 d}-\frac{15 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{4 i a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{4 i a^{4} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{12 i a^{4} \cos \left(d x +c \right)}{d}"," ",0,"1/2/d*a^4*sin(d*x+c)^5/cos(d*x+c)^2+1/2*a^4*sin(d*x+c)^3/d+17/2*a^4*sin(d*x+c)/d-15/2/d*a^4*ln(sec(d*x+c)+tan(d*x+c))-4*I/d*a^4*sin(d*x+c)^4/cos(d*x+c)-4*I/d*a^4*sin(d*x+c)^2*cos(d*x+c)-12*I/d*a^4*cos(d*x+c)","A"
55,1,130,72,0.454000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x)","-\frac{7 a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{4} \sin \left(d x +c \right)}{3 d}+\frac{a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 i a^{4} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}+\frac{8 i a^{4} \cos \left(d x +c \right)}{3 d}-\frac{4 i a^{4} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}"," ",0,"-7/3*a^4*sin(d*x+c)^3/d-1/3*a^4*sin(d*x+c)/d+1/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+4/3*I/d*a^4*cos(d*x+c)*sin(d*x+c)^2+8/3*I/d*a^4*cos(d*x+c)-4/3*I/d*a^4*cos(d*x+c)^3+1/3/d*sin(d*x+c)*cos(d*x+c)^2*a^4","A"
56,1,139,58,0.510000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^4,x)","\frac{\frac{a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{5}-4 i a^{4} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)-6 a^{4} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{4 i a^{4} \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a^{4} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(1/5*a^4*sin(d*x+c)^5-4*I*a^4*(-1/5*cos(d*x+c)^3*sin(d*x+c)^2-2/15*cos(d*x+c)^3)-6*a^4*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-4/5*I*a^4*cos(d*x+c)^5+1/5*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","B"
57,1,203,90,0.588000," ","int(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^4,x)","\frac{a^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)-4 i a^{4} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)-6 a^{4} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{4 i a^{4} \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{4} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(a^4*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*sin(d*x+c)*cos(d*x+c)^4+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))-4*I*a^4*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)-6*a^4*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-4/7*I*a^4*cos(d*x+c)^7+1/7*a^4*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","B"
58,1,233,106,0.621000," ","int(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^4,x)","\frac{a^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)-4 i a^{4} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)-6 a^{4} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{4 i a^{4} \left(\cos^{9}\left(d x +c \right)\right)}{9}+\frac{a^{4} \left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{9}}{d}"," ",0,"1/d*(a^4*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-4*I*a^4*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)-6*a^4*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-4/9*I*a^4*cos(d*x+c)^9+1/9*a^4*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))","B"
59,1,377,93,0.502000," ","int(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{12}}+\frac{\sin^{6}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{10}}+\frac{\sin^{6}\left(d x +c \right)}{40 \cos \left(d x +c \right)^{8}}+\frac{\sin^{6}\left(d x +c \right)}{120 \cos \left(d x +c \right)^{6}}\right)+5 a^{5} \left(\frac{\sin^{5}\left(d x +c \right)}{11 \cos \left(d x +c \right)^{11}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{33 \cos \left(d x +c \right)^{9}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{231 \cos \left(d x +c \right)^{7}}+\frac{16 \left(\sin^{5}\left(d x +c \right)\right)}{1155 \cos \left(d x +c \right)^{5}}\right)-10 i a^{5} \left(\frac{\sin^{4}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{40 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{40 \cos \left(d x +c \right)^{4}}\right)-10 a^{5} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+\frac{5 i a^{5}}{8 \cos \left(d x +c \right)^{8}}-a^{5} \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*(I*a^5*(1/12*sin(d*x+c)^6/cos(d*x+c)^12+1/20*sin(d*x+c)^6/cos(d*x+c)^10+1/40*sin(d*x+c)^6/cos(d*x+c)^8+1/120*sin(d*x+c)^6/cos(d*x+c)^6)+5*a^5*(1/11*sin(d*x+c)^5/cos(d*x+c)^11+2/33*sin(d*x+c)^5/cos(d*x+c)^9+8/231*sin(d*x+c)^5/cos(d*x+c)^7+16/1155*sin(d*x+c)^5/cos(d*x+c)^5)-10*I*a^5*(1/10*sin(d*x+c)^4/cos(d*x+c)^10+3/40*sin(d*x+c)^4/cos(d*x+c)^8+1/20*sin(d*x+c)^4/cos(d*x+c)^6+1/40*sin(d*x+c)^4/cos(d*x+c)^4)-10*a^5*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+5/8*I*a^5/cos(d*x+c)^8-a^5*(-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))","B"
60,1,295,70,0.523000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{\sin^{6}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{8}}+\frac{\sin^{6}\left(d x +c \right)}{60 \cos \left(d x +c \right)^{6}}\right)+5 a^{5} \left(\frac{\sin^{5}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{4 \left(\sin^{5}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{5}}\right)-10 i a^{5} \left(\frac{\sin^{4}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{4}}\right)-10 a^{5} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+\frac{5 i a^{5}}{6 \cos \left(d x +c \right)^{6}}-a^{5} \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*(I*a^5*(1/10*sin(d*x+c)^6/cos(d*x+c)^10+1/20*sin(d*x+c)^6/cos(d*x+c)^8+1/60*sin(d*x+c)^6/cos(d*x+c)^6)+5*a^5*(1/9*sin(d*x+c)^5/cos(d*x+c)^9+4/63*sin(d*x+c)^5/cos(d*x+c)^7+8/315*sin(d*x+c)^5/cos(d*x+c)^5)-10*I*a^5*(1/8*sin(d*x+c)^4/cos(d*x+c)^8+1/12*sin(d*x+c)^4/cos(d*x+c)^6+1/24*sin(d*x+c)^4/cos(d*x+c)^4)-10*a^5*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+5/6*I*a^5/cos(d*x+c)^6-a^5*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","B"
61,1,213,47,0.447000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{6}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{6}}\right)+5 a^{5} \left(\frac{\sin^{5}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}\right)-10 i a^{5} \left(\frac{\sin^{4}\left(d x +c \right)}{6 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{4}}\right)-10 a^{5} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+\frac{5 i a^{5}}{4 \cos \left(d x +c \right)^{4}}-a^{5} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(I*a^5*(1/8*sin(d*x+c)^6/cos(d*x+c)^8+1/24*sin(d*x+c)^6/cos(d*x+c)^6)+5*a^5*(1/7*sin(d*x+c)^5/cos(d*x+c)^7+2/35*sin(d*x+c)^5/cos(d*x+c)^5)-10*I*a^5*(1/6*sin(d*x+c)^4/cos(d*x+c)^6+1/12*sin(d*x+c)^4/cos(d*x+c)^4)-10*a^5*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+5/4*I*a^5/cos(d*x+c)^4-a^5*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","B"
62,1,115,23,0.442000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^5,x)","\frac{\frac{i a^{5} \left(\sin^{6}\left(d x +c \right)\right)}{6 \cos \left(d x +c \right)^{6}}+\frac{a^{5} \left(\sin^{5}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{5}}-\frac{5 i a^{5} \left(\sin^{4}\left(d x +c \right)\right)}{2 \cos \left(d x +c \right)^{4}}-\frac{10 a^{5} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+\frac{5 i a^{5}}{2 \cos \left(d x +c \right)^{2}}+a^{5} \tan \left(d x +c \right)}{d}"," ",0,"1/d*(1/6*I*a^5*sin(d*x+c)^6/cos(d*x+c)^6+a^5*sin(d*x+c)^5/cos(d*x+c)^5-5/2*I*a^5*sin(d*x+c)^4/cos(d*x+c)^4-10/3*a^5*sin(d*x+c)^3/cos(d*x+c)^3+5/2*I*a^5/cos(d*x+c)^2+a^5*tan(d*x+c))","B"
63,1,101,106,0.016000," ","int((a+I*a*tan(d*x+c))^5,x)","-\frac{15 a^{5} \tan \left(d x +c \right)}{d}+\frac{i a^{5} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{5 a^{5} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{11 i a^{5} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{8 i a^{5} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{16 a^{5} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-15*a^5*tan(d*x+c)/d+1/4*I/d*a^5*tan(d*x+c)^4+5/3/d*a^5*tan(d*x+c)^3-11/2*I/d*a^5*tan(d*x+c)^2+8*I/d*a^5*ln(1+tan(d*x+c)^2)+16/d*a^5*arctan(tan(d*x+c))","A"
64,1,175,77,0.421000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}-\frac{5 i a^{5} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{i a^{5} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{6 i a^{5} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{5 a^{5} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{5 a^{5} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{13 a^{5} \sin \left(d x +c \right) \cos \left(d x +c \right)}{d}-12 a^{5} x -\frac{12 a^{5} c}{d}+\frac{12 i a^{5} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/2*I/d*a^5*sin(d*x+c)^4-5/2*I/d*a^5*cos(d*x+c)^2+1/2*I/d*a^5*sin(d*x+c)^6/cos(d*x+c)^2+6*I/d*a^5*sin(d*x+c)^2+5/d*a^5*sin(d*x+c)^5/cos(d*x+c)+5/d*a^5*cos(d*x+c)*sin(d*x+c)^3+13/d*a^5*sin(d*x+c)*cos(d*x+c)-12*a^5*x-12/d*a^5*c+12*I*a^5*ln(cos(d*x+c))/d","B"
65,1,146,68,0.473000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^5,x)","-\frac{11 i a^{5} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{i a^{5} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{i a^{5} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{5 a^{5} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{11 a^{5} \sin \left(d x +c \right) \cos \left(d x +c \right)}{4 d}+a^{5} x +\frac{a^{5} c}{d}-\frac{5 i a^{5} \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{11 a^{5} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4 d}"," ",0,"-11/4*I/d*a^5*sin(d*x+c)^4-I*a^5*ln(cos(d*x+c))/d-1/2*I/d*a^5*sin(d*x+c)^2-5/4/d*a^5*cos(d*x+c)*sin(d*x+c)^3-11/4/d*a^5*sin(d*x+c)*cos(d*x+c)+a^5*x+1/d*a^5*c-5/4*I/d*a^5*cos(d*x+c)^4+11/4/d*a^5*sin(d*x+c)*cos(d*x+c)^3","B"
66,1,231,47,0.523000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^5,x)","\frac{\frac{i a^{5} \left(\sin^{6}\left(d x +c \right)\right)}{6}+5 a^{5} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)-10 i a^{5} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)-10 a^{5} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{5 i a^{5} \left(\cos^{6}\left(d x +c \right)\right)}{6}+a^{5} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(1/6*I*a^5*sin(d*x+c)^6+5*a^5*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*sin(d*x+c)*cos(d*x+c)^3+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)-10*I*a^5*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)-10*a^5*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-5/6*I*a^5*cos(d*x+c)^6+a^5*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","B"
67,1,301,23,0.602000," ","int(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{8}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{12}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{24}\right)+5 a^{5} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)-10 i a^{5} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)-10 a^{5} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{5 i a^{5} \left(\cos^{8}\left(d x +c \right)\right)}{8}+a^{5} \left(\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)}{d}"," ",0,"1/d*(I*a^5*(-1/8*sin(d*x+c)^4*cos(d*x+c)^4-1/12*sin(d*x+c)^2*cos(d*x+c)^4-1/24*cos(d*x+c)^4)+5*a^5*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)-10*I*a^5*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)-10*a^5*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-5/8*I*a^5*cos(d*x+c)^8+a^5*(1/8*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/128*d*x+35/128*c))","B"
68,1,331,122,0.625000," ","int(cos(d*x+c)^10*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)+5 a^{5} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)-10 i a^{5} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{10}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{40}\right)-10 a^{5} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)}{10}+\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{80}+\frac{7 d x}{256}+\frac{7 c}{256}\right)-\frac{i a^{5} \left(\cos^{10}\left(d x +c \right)\right)}{2}+a^{5} \left(\frac{\left(\cos^{9}\left(d x +c \right)+\frac{9 \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{21 \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{105 \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{315 \cos \left(d x +c \right)}{128}\right) \sin \left(d x +c \right)}{10}+\frac{63 d x}{256}+\frac{63 c}{256}\right)}{d}"," ",0,"1/d*(I*a^5*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6)+5*a^5*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*sin(d*x+c)*cos(d*x+c)^7+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)-10*I*a^5*(-1/10*sin(d*x+c)^2*cos(d*x+c)^8-1/40*cos(d*x+c)^8)-10*a^5*(-1/10*sin(d*x+c)*cos(d*x+c)^9+1/80*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+7/256*d*x+7/256*c)-1/2*I*a^5*cos(d*x+c)^10+a^5*(1/10*(cos(d*x+c)^9+9/8*cos(d*x+c)^7+21/16*cos(d*x+c)^5+105/64*cos(d*x+c)^3+315/128*cos(d*x+c))*sin(d*x+c)+63/256*d*x+63/256*c))","B"
69,1,361,168,0.627000," ","int(cos(d*x+c)^12*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{30}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{120}\right)+5 a^{5} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{12}-\frac{\sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)}{40}+\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{320}+\frac{7 d x}{1024}+\frac{7 c}{1024}\right)-10 i a^{5} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{12}-\frac{\left(\cos^{10}\left(d x +c \right)\right)}{60}\right)-10 a^{5} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)}{12}+\frac{\left(\cos^{9}\left(d x +c \right)+\frac{9 \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{21 \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{105 \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{315 \cos \left(d x +c \right)}{128}\right) \sin \left(d x +c \right)}{120}+\frac{21 d x}{1024}+\frac{21 c}{1024}\right)-\frac{5 i a^{5} \left(\cos^{12}\left(d x +c \right)\right)}{12}+a^{5} \left(\frac{\left(\cos^{11}\left(d x +c \right)+\frac{11 \left(\cos^{9}\left(d x +c \right)\right)}{10}+\frac{99 \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{231 \left(\cos^{5}\left(d x +c \right)\right)}{160}+\frac{231 \left(\cos^{3}\left(d x +c \right)\right)}{128}+\frac{693 \cos \left(d x +c \right)}{256}\right) \sin \left(d x +c \right)}{12}+\frac{231 d x}{1024}+\frac{231 c}{1024}\right)}{d}"," ",0,"1/d*(I*a^5*(-1/12*sin(d*x+c)^4*cos(d*x+c)^8-1/30*sin(d*x+c)^2*cos(d*x+c)^8-1/120*cos(d*x+c)^8)+5*a^5*(-1/12*sin(d*x+c)^3*cos(d*x+c)^9-1/40*sin(d*x+c)*cos(d*x+c)^9+1/320*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+7/1024*d*x+7/1024*c)-10*I*a^5*(-1/12*sin(d*x+c)^2*cos(d*x+c)^10-1/60*cos(d*x+c)^10)-10*a^5*(-1/12*sin(d*x+c)*cos(d*x+c)^11+1/120*(cos(d*x+c)^9+9/8*cos(d*x+c)^7+21/16*cos(d*x+c)^5+105/64*cos(d*x+c)^3+315/128*cos(d*x+c))*sin(d*x+c)+21/1024*d*x+21/1024*c)-5/12*I*a^5*cos(d*x+c)^12+a^5*(1/12*(cos(d*x+c)^11+11/10*cos(d*x+c)^9+99/80*cos(d*x+c)^7+231/160*cos(d*x+c)^5+231/128*cos(d*x+c)^3+693/256*cos(d*x+c))*sin(d*x+c)+231/1024*d*x+231/1024*c))","B"
70,1,329,146,0.338000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c))^5,x)","-\frac{i a^{5} \left(\sin^{6}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}-\frac{10 i a^{5} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}+\frac{18 i a^{5} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{5 d}+\frac{i a^{5} \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}+\frac{5 i a^{5}}{d \cos \left(d x +c \right)}+\frac{i a^{5} \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)}+\frac{5 a^{5} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{5 a^{5} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{5 a^{5} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{55 a^{5} \sin \left(d x +c \right)}{8 d}+\frac{63 a^{5} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{36 i a^{5} \cos \left(d x +c \right)}{5 d}+\frac{10 i a^{5} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}+\frac{i a^{5} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}-\frac{5 a^{5} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}"," ",0,"-1/15*I/d*a^5*sin(d*x+c)^6/cos(d*x+c)^3-10/3*I/d*a^5*sin(d*x+c)^4/cos(d*x+c)^3+18/5*I/d*a^5*cos(d*x+c)*sin(d*x+c)^2+1/5*I/d*a^5*sin(d*x+c)^6/cos(d*x+c)^5+5*I/d*a^5/cos(d*x+c)+1/5*I/d*a^5*sin(d*x+c)^6/cos(d*x+c)+5/4/d*a^5*sin(d*x+c)^5/cos(d*x+c)^4-5/8/d*a^5*sin(d*x+c)^5/cos(d*x+c)^2-5/8*a^5*sin(d*x+c)^3/d-55/8*a^5*sin(d*x+c)/d+63/8/d*a^5*ln(sec(d*x+c)+tan(d*x+c))+36/5*I/d*a^5*cos(d*x+c)+10/3*I/d*a^5*sin(d*x+c)^4/cos(d*x+c)+1/5*I/d*a^5*cos(d*x+c)*sin(d*x+c)^4-5/d*a^5*sin(d*x+c)^3/cos(d*x+c)^2","B"
71,1,214,115,0.475000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(\sin^{6}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{34 i a^{5} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{i a^{5} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{i a^{5} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{83 i a^{5} \cos \left(d x +c \right)}{3 d}+\frac{5 a^{5} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{5 a^{5} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{37 a^{5} \sin \left(d x +c \right)}{2 d}-\frac{35 a^{5} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{10 i a^{5} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}"," ",0,"1/3*I/d*a^5*sin(d*x+c)^6/cos(d*x+c)^3-34/3*I/d*a^5*cos(d*x+c)*sin(d*x+c)^2-I/d*a^5*sin(d*x+c)^6/cos(d*x+c)-I/d*a^5*cos(d*x+c)*sin(d*x+c)^4-83/3*I/d*a^5*cos(d*x+c)+5/2/d*a^5*sin(d*x+c)^5/cos(d*x+c)^2+5/2*a^5*sin(d*x+c)^3/d+37/2*a^5*sin(d*x+c)/d-35/2/d*a^5*ln(sec(d*x+c)+tan(d*x+c))-10*I/d*a^5*sin(d*x+c)^4/cos(d*x+c)","A"
72,1,179,89,0.530000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{28 i a^{5} \cos \left(d x +c \right)}{3 d}+\frac{i a^{5} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{14 i a^{5} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{5 a^{5} \left(\sin^{3}\left(d x +c \right)\right)}{d}-\frac{13 a^{5} \sin \left(d x +c \right)}{3 d}+\frac{5 a^{5} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{5 i a^{5} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{5}}{3 d}"," ",0,"I/d*a^5*sin(d*x+c)^6/cos(d*x+c)+28/3*I/d*a^5*cos(d*x+c)+I/d*a^5*cos(d*x+c)*sin(d*x+c)^4+14/3*I/d*a^5*cos(d*x+c)*sin(d*x+c)^2-5*a^5*sin(d*x+c)^3/d-13/3*a^5*sin(d*x+c)/d+5/d*a^5*ln(sec(d*x+c)+tan(d*x+c))-5/3*I/d*a^5*cos(d*x+c)^3+1/3/d*sin(d*x+c)*cos(d*x+c)^2*a^5","A"
73,1,170,28,0.540000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^5,x)","\frac{-\frac{i a^{5} \left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}+a^{5} \left(\sin^{5}\left(d x +c \right)\right)-10 i a^{5} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)-10 a^{5} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-i a^{5} \left(\cos^{5}\left(d x +c \right)\right)+\frac{a^{5} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(-1/5*I*a^5*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)+a^5*sin(d*x+c)^5-10*I*a^5*(-1/5*cos(d*x+c)^3*sin(d*x+c)^2-2/15*cos(d*x+c)^3)-10*a^5*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-I*a^5*cos(d*x+c)^5+1/5*a^5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","B"
74,1,257,89,0.596000," ","int(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{7}-\frac{4 \left(\cos^{3}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right)}{105}\right)+5 a^{5} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)-10 i a^{5} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)-10 a^{5} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{5 i a^{5} \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{5} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(I*a^5*(-1/7*sin(d*x+c)^4*cos(d*x+c)^3-4/35*cos(d*x+c)^3*sin(d*x+c)^2-8/105*cos(d*x+c)^3)+5*a^5*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*sin(d*x+c)*cos(d*x+c)^4+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))-10*I*a^5*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)-10*a^5*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-5/7*I*a^5*cos(d*x+c)^7+1/7*a^5*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","B"
75,1,287,124,0.540000," ","int(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+5 a^{5} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)-10 i a^{5} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)-10 a^{5} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{5 i a^{5} \left(\cos^{9}\left(d x +c \right)\right)}{9}+\frac{a^{5} \left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{9}}{d}"," ",0,"1/d*(I*a^5*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+5*a^5*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-10*I*a^5*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)-10*a^5*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-5/9*I*a^5*cos(d*x+c)^9+1/9*a^5*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))","B"
76,1,317,140,0.605000," ","int(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^5,x)","\frac{i a^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+5 a^{5} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{11}-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{33}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{231}\right)-10 i a^{5} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{11}-\frac{2 \left(\cos^{9}\left(d x +c \right)\right)}{99}\right)-10 a^{5} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)}{11}+\frac{\left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{99}\right)-\frac{5 i a^{5} \left(\cos^{11}\left(d x +c \right)\right)}{11}+\frac{a^{5} \left(\frac{256}{63}+\cos^{10}\left(d x +c \right)+\frac{10 \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{80 \left(\cos^{6}\left(d x +c \right)\right)}{63}+\frac{32 \left(\cos^{4}\left(d x +c \right)\right)}{21}+\frac{128 \left(\cos^{2}\left(d x +c \right)\right)}{63}\right) \sin \left(d x +c \right)}{11}}{d}"," ",0,"1/d*(I*a^5*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+5*a^5*(-1/11*sin(d*x+c)^3*cos(d*x+c)^8-1/33*sin(d*x+c)*cos(d*x+c)^8+1/231*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-10*I*a^5*(-1/11*sin(d*x+c)^2*cos(d*x+c)^9-2/99*cos(d*x+c)^9)-10*a^5*(-1/11*sin(d*x+c)*cos(d*x+c)^10+1/99*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))-5/11*I*a^5*cos(d*x+c)^11+1/11*a^5*(256/63+cos(d*x+c)^10+10/9*cos(d*x+c)^8+80/63*cos(d*x+c)^6+32/21*cos(d*x+c)^4+128/63*cos(d*x+c)^2)*sin(d*x+c))","B"
77,1,611,93,0.551000," ","int(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(\frac{\sin^{9}\left(d x +c \right)}{15 \cos \left(d x +c \right)^{15}}+\frac{2 \left(\sin^{9}\left(d x +c \right)\right)}{65 \cos \left(d x +c \right)^{13}}+\frac{8 \left(\sin^{9}\left(d x +c \right)\right)}{715 \cos \left(d x +c \right)^{11}}+\frac{16 \left(\sin^{9}\left(d x +c \right)\right)}{6435 \cos \left(d x +c \right)^{9}}\right)+\frac{i a^{8}}{\cos \left(d x +c \right)^{8}}-28 a^{8} \left(\frac{\sin^{7}\left(d x +c \right)}{13 \cos \left(d x +c \right)^{13}}+\frac{6 \left(\sin^{7}\left(d x +c \right)\right)}{143 \cos \left(d x +c \right)^{11}}+\frac{8 \left(\sin^{7}\left(d x +c \right)\right)}{429 \cos \left(d x +c \right)^{9}}+\frac{16 \left(\sin^{7}\left(d x +c \right)\right)}{3003 \cos \left(d x +c \right)^{7}}\right)-8 i a^{8} \left(\frac{\sin^{8}\left(d x +c \right)}{14 \cos \left(d x +c \right)^{14}}+\frac{\sin^{8}\left(d x +c \right)}{28 \cos \left(d x +c \right)^{12}}+\frac{\sin^{8}\left(d x +c \right)}{70 \cos \left(d x +c \right)^{10}}+\frac{\sin^{8}\left(d x +c \right)}{280 \cos \left(d x +c \right)^{8}}\right)+70 a^{8} \left(\frac{\sin^{5}\left(d x +c \right)}{11 \cos \left(d x +c \right)^{11}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{33 \cos \left(d x +c \right)^{9}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{231 \cos \left(d x +c \right)^{7}}+\frac{16 \left(\sin^{5}\left(d x +c \right)\right)}{1155 \cos \left(d x +c \right)^{5}}\right)+56 i a^{8} \left(\frac{\sin^{6}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{12}}+\frac{\sin^{6}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{10}}+\frac{\sin^{6}\left(d x +c \right)}{40 \cos \left(d x +c \right)^{8}}+\frac{\sin^{6}\left(d x +c \right)}{120 \cos \left(d x +c \right)^{6}}\right)-28 a^{8} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)-56 i a^{8} \left(\frac{\sin^{4}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{40 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{40 \cos \left(d x +c \right)^{4}}\right)-a^{8} \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^8*(1/15*sin(d*x+c)^9/cos(d*x+c)^15+2/65*sin(d*x+c)^9/cos(d*x+c)^13+8/715*sin(d*x+c)^9/cos(d*x+c)^11+16/6435*sin(d*x+c)^9/cos(d*x+c)^9)+I*a^8/cos(d*x+c)^8-28*a^8*(1/13*sin(d*x+c)^7/cos(d*x+c)^13+6/143*sin(d*x+c)^7/cos(d*x+c)^11+8/429*sin(d*x+c)^7/cos(d*x+c)^9+16/3003*sin(d*x+c)^7/cos(d*x+c)^7)-8*I*a^8*(1/14*sin(d*x+c)^8/cos(d*x+c)^14+1/28*sin(d*x+c)^8/cos(d*x+c)^12+1/70*sin(d*x+c)^8/cos(d*x+c)^10+1/280*sin(d*x+c)^8/cos(d*x+c)^8)+70*a^8*(1/11*sin(d*x+c)^5/cos(d*x+c)^11+2/33*sin(d*x+c)^5/cos(d*x+c)^9+8/231*sin(d*x+c)^5/cos(d*x+c)^7+16/1155*sin(d*x+c)^5/cos(d*x+c)^5)+56*I*a^8*(1/12*sin(d*x+c)^6/cos(d*x+c)^12+1/20*sin(d*x+c)^6/cos(d*x+c)^10+1/40*sin(d*x+c)^6/cos(d*x+c)^8+1/120*sin(d*x+c)^6/cos(d*x+c)^6)-28*a^8*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)-56*I*a^8*(1/10*sin(d*x+c)^4/cos(d*x+c)^10+3/40*sin(d*x+c)^4/cos(d*x+c)^8+1/20*sin(d*x+c)^4/cos(d*x+c)^6+1/40*sin(d*x+c)^4/cos(d*x+c)^4)-a^8*(-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))","B"
78,1,475,70,0.530000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(\frac{\sin^{9}\left(d x +c \right)}{13 \cos \left(d x +c \right)^{13}}+\frac{4 \left(\sin^{9}\left(d x +c \right)\right)}{143 \cos \left(d x +c \right)^{11}}+\frac{8 \left(\sin^{9}\left(d x +c \right)\right)}{1287 \cos \left(d x +c \right)^{9}}\right)+\frac{4 i a^{8}}{3 \cos \left(d x +c \right)^{6}}-28 a^{8} \left(\frac{\sin^{7}\left(d x +c \right)}{11 \cos \left(d x +c \right)^{11}}+\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{99 \cos \left(d x +c \right)^{9}}+\frac{8 \left(\sin^{7}\left(d x +c \right)\right)}{693 \cos \left(d x +c \right)^{7}}\right)-56 i a^{8} \left(\frac{\sin^{4}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{4}}\right)+70 a^{8} \left(\frac{\sin^{5}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{4 \left(\sin^{5}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{5}}\right)+56 i a^{8} \left(\frac{\sin^{6}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{\sin^{6}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{8}}+\frac{\sin^{6}\left(d x +c \right)}{60 \cos \left(d x +c \right)^{6}}\right)-28 a^{8} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)-8 i a^{8} \left(\frac{\sin^{8}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{12}}+\frac{\sin^{8}\left(d x +c \right)}{30 \cos \left(d x +c \right)^{10}}+\frac{\sin^{8}\left(d x +c \right)}{120 \cos \left(d x +c \right)^{8}}\right)-a^{8} \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^8*(1/13*sin(d*x+c)^9/cos(d*x+c)^13+4/143*sin(d*x+c)^9/cos(d*x+c)^11+8/1287*sin(d*x+c)^9/cos(d*x+c)^9)+4/3*I*a^8/cos(d*x+c)^6-28*a^8*(1/11*sin(d*x+c)^7/cos(d*x+c)^11+4/99*sin(d*x+c)^7/cos(d*x+c)^9+8/693*sin(d*x+c)^7/cos(d*x+c)^7)-56*I*a^8*(1/8*sin(d*x+c)^4/cos(d*x+c)^8+1/12*sin(d*x+c)^4/cos(d*x+c)^6+1/24*sin(d*x+c)^4/cos(d*x+c)^4)+70*a^8*(1/9*sin(d*x+c)^5/cos(d*x+c)^9+4/63*sin(d*x+c)^5/cos(d*x+c)^7+8/315*sin(d*x+c)^5/cos(d*x+c)^5)+56*I*a^8*(1/10*sin(d*x+c)^6/cos(d*x+c)^10+1/20*sin(d*x+c)^6/cos(d*x+c)^8+1/60*sin(d*x+c)^6/cos(d*x+c)^6)-28*a^8*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)-8*I*a^8*(1/12*sin(d*x+c)^8/cos(d*x+c)^12+1/30*sin(d*x+c)^8/cos(d*x+c)^10+1/120*sin(d*x+c)^8/cos(d*x+c)^8)-a^8*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","B"
79,1,339,47,0.509000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(\frac{\sin^{9}\left(d x +c \right)}{11 \cos \left(d x +c \right)^{11}}+\frac{2 \left(\sin^{9}\left(d x +c \right)\right)}{99 \cos \left(d x +c \right)^{9}}\right)-56 i a^{8} \left(\frac{\sin^{4}\left(d x +c \right)}{6 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{4}}\right)-28 a^{8} \left(\frac{\sin^{7}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{7}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}\right)+\frac{2 i a^{8}}{\cos \left(d x +c \right)^{4}}+70 a^{8} \left(\frac{\sin^{5}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}\right)+56 i a^{8} \left(\frac{\sin^{6}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{6}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{6}}\right)-28 a^{8} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)-8 i a^{8} \left(\frac{\sin^{8}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{\sin^{8}\left(d x +c \right)}{40 \cos \left(d x +c \right)^{8}}\right)-a^{8} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^8*(1/11*sin(d*x+c)^9/cos(d*x+c)^11+2/99*sin(d*x+c)^9/cos(d*x+c)^9)-56*I*a^8*(1/6*sin(d*x+c)^4/cos(d*x+c)^6+1/12*sin(d*x+c)^4/cos(d*x+c)^4)-28*a^8*(1/9*sin(d*x+c)^7/cos(d*x+c)^9+2/63*sin(d*x+c)^7/cos(d*x+c)^7)+2*I*a^8/cos(d*x+c)^4+70*a^8*(1/7*sin(d*x+c)^5/cos(d*x+c)^7+2/35*sin(d*x+c)^5/cos(d*x+c)^5)+56*I*a^8*(1/8*sin(d*x+c)^6/cos(d*x+c)^8+1/24*sin(d*x+c)^6/cos(d*x+c)^6)-28*a^8*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)-8*I*a^8*(1/10*sin(d*x+c)^8/cos(d*x+c)^10+1/40*sin(d*x+c)^8/cos(d*x+c)^8)-a^8*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","B"
80,1,180,23,0.483000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^8,x)","\frac{\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{9 \cos \left(d x +c \right)^{9}}-\frac{14 i a^{8} \left(\sin^{4}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{4}}-\frac{4 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{7}}+\frac{28 i a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{6}}+\frac{14 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{5}}-\frac{i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{8}}-\frac{28 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+\frac{4 i a^{8}}{\cos \left(d x +c \right)^{2}}+a^{8} \tan \left(d x +c \right)}{d}"," ",0,"1/d*(1/9*a^8*sin(d*x+c)^9/cos(d*x+c)^9-14*I*a^8*sin(d*x+c)^4/cos(d*x+c)^4-4*a^8*sin(d*x+c)^7/cos(d*x+c)^7+28/3*I*a^8*sin(d*x+c)^6/cos(d*x+c)^6+14*a^8*sin(d*x+c)^5/cos(d*x+c)^5-I*a^8*sin(d*x+c)^8/cos(d*x+c)^8-28/3*a^8*sin(d*x+c)^3/cos(d*x+c)^3+4*I*a^8/cos(d*x+c)^2+a^8*tan(d*x+c))","B"
81,1,150,179,0.017000," ","int((a+I*a*tan(d*x+c))^8,x)","-\frac{127 a^{8} \tan \left(d x +c \right)}{d}+\frac{a^{8} \left(\tan^{7}\left(d x +c \right)\right)}{7 d}-\frac{4 i a^{8} \left(\tan^{6}\left(d x +c \right)\right)}{3 d}-\frac{29 a^{8} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{16 i a^{8} \left(\tan^{4}\left(d x +c \right)\right)}{d}+\frac{33 a^{8} \left(\tan^{3}\left(d x +c \right)\right)}{d}-\frac{60 i a^{8} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{64 i a^{8} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d}+\frac{128 a^{8} \arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-127*a^8*tan(d*x+c)/d+1/7/d*a^8*tan(d*x+c)^7-4/3*I/d*a^8*tan(d*x+c)^6-29/5*a^8*tan(d*x+c)^5/d+16*I/d*a^8*tan(d*x+c)^4+33*a^8*tan(d*x+c)^3/d-60*I/d*a^8*tan(d*x+c)^2+64*I/d*a^8*ln(1+tan(d*x+c)^2)+128/d*a^8*arctan(tan(d*x+c))","A"
82,1,406,126,0.594000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^8,x)","\frac{4 i a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{d}+\frac{8 a^{8} \cos \left(d x +c \right) \left(\sin^{7}\left(d x +c \right)\right)}{5 d}-\frac{192 a^{8} c}{d}+\frac{34 i a^{8} \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{28 i a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}-\frac{2 i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}+\frac{4 i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{70 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{192 i a^{8} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{4 i a^{8} \left(\cos^{2}\left(d x +c \right)\right)}{d}+\frac{96 i a^{8} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{193 a^{8} \sin \left(d x +c \right) \cos \left(d x +c \right)}{d}-\frac{28 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}+\frac{112 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-192 a^{8} x +\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}-\frac{4 a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}+\frac{8 a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)}+\frac{196 a^{8} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{5 d}+\frac{119 a^{8} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{d}"," ",0,"4*I/d*a^8*sin(d*x+c)^6+8/5/d*a^8*cos(d*x+c)*sin(d*x+c)^7-192/d*a^8*c+34*I/d*a^8*sin(d*x+c)^4+28*I/d*a^8*sin(d*x+c)^6/cos(d*x+c)^2-2*I/d*a^8*sin(d*x+c)^8/cos(d*x+c)^4+4*I/d*a^8*sin(d*x+c)^8/cos(d*x+c)^2+70/d*a^8*sin(d*x+c)^5/cos(d*x+c)+192*I*a^8*ln(cos(d*x+c))/d-4*I/d*a^8*cos(d*x+c)^2+96*I/d*a^8*sin(d*x+c)^2+193/d*a^8*sin(d*x+c)*cos(d*x+c)-28/3/d*a^8*sin(d*x+c)^7/cos(d*x+c)^3+112/3/d*a^8*sin(d*x+c)^7/cos(d*x+c)-192*a^8*x+1/5/d*a^8*sin(d*x+c)^9/cos(d*x+c)^5-4/15/d*a^8*sin(d*x+c)^9/cos(d*x+c)^3+8/5/d*a^8*sin(d*x+c)^9/cos(d*x+c)+196/5/d*a^8*cos(d*x+c)*sin(d*x+c)^5+119/d*a^8*cos(d*x+c)*sin(d*x+c)^3","B"
83,1,306,116,0.647000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^8,x)","-\frac{2 a^{8} \cos \left(d x +c \right) \left(\sin^{7}\left(d x +c \right)\right)}{d}+\frac{80 a^{8} c}{d}-\frac{4 i a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{d}-\frac{4 i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}-\frac{34 i a^{8} \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{80 i a^{8} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{29 a^{8} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{28 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{2 a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{91 a^{8} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{3 d}-\frac{665 a^{8} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{12 d}-\frac{345 a^{8} \sin \left(d x +c \right) \cos \left(d x +c \right)}{4 d}-\frac{2 i a^{8} \left(\cos^{4}\left(d x +c \right)\right)}{d}+80 a^{8} x -\frac{40 i a^{8} \left(\sin^{2}\left(d x +c \right)\right)}{d}"," ",0,"-2/d*a^8*cos(d*x+c)*sin(d*x+c)^7+80/d*a^8*c-4*I/d*a^8*sin(d*x+c)^6-4*I/d*a^8*sin(d*x+c)^8/cos(d*x+c)^2-34*I/d*a^8*sin(d*x+c)^4-80*I*a^8*ln(cos(d*x+c))/d+29/4/d*a^8*cos(d*x+c)^3*sin(d*x+c)-28/d*a^8*sin(d*x+c)^7/cos(d*x+c)+1/3/d*a^8*sin(d*x+c)^9/cos(d*x+c)^3-2/d*a^8*sin(d*x+c)^9/cos(d*x+c)-91/3/d*a^8*cos(d*x+c)*sin(d*x+c)^5-665/12/d*a^8*cos(d*x+c)*sin(d*x+c)^3-345/4/d*a^8*sin(d*x+c)*cos(d*x+c)-2*I/d*a^8*cos(d*x+c)^4+80*a^8*x-40*I/d*a^8*sin(d*x+c)^2","B"
84,1,319,105,0.622000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \cos \left(d x +c \right) \left(\sin^{7}\left(d x +c \right)\right)}{d}-\frac{8 a^{8} c}{d}+\frac{4 i a^{8} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{29 a^{8} \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6 d}-\frac{233 a^{8} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{24 d}+\frac{111 a^{8} \sin \left(d x +c \right) \cos \left(d x +c \right)}{8 d}+\frac{32 i a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{3 d}+\frac{2 i a^{8} \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{28 i a^{8} \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{3 d}-\frac{35 a^{8} \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{35 a^{8} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{6 d}+\frac{175 a^{8} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{24 d}+\frac{14 i a^{8} \left(\cos^{4}\left(d x +c \right)\right)}{3 d}+\frac{8 i a^{8} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{4 i a^{8} \left(\cos^{6}\left(d x +c \right)\right)}{3 d}-8 a^{8} x"," ",0,"1/d*a^8*cos(d*x+c)*sin(d*x+c)^7-8/d*a^8*c+4*I/d*a^8*sin(d*x+c)^2+29/6/d*a^8*sin(d*x+c)*cos(d*x+c)^5-233/24/d*a^8*cos(d*x+c)^3*sin(d*x+c)+111/8/d*a^8*sin(d*x+c)*cos(d*x+c)+32/3*I/d*a^8*sin(d*x+c)^6+2*I/d*a^8*sin(d*x+c)^4+28/3*I/d*a^8*sin(d*x+c)^2*cos(d*x+c)^4-35/3/d*a^8*sin(d*x+c)^3*cos(d*x+c)^3+1/d*a^8*sin(d*x+c)^9/cos(d*x+c)+35/6/d*a^8*cos(d*x+c)*sin(d*x+c)^5+175/24/d*a^8*cos(d*x+c)*sin(d*x+c)^3+14/3*I/d*a^8*cos(d*x+c)^4+8*I*a^8*ln(cos(d*x+c))/d-4/3*I/d*a^8*cos(d*x+c)^6-8*a^8*x","B"
85,1,451,38,0.623000," ","int(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)-i a^{8} \left(\sin^{8}\left(d x +c \right)\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{8}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{48}-\frac{5 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{5 \cos \left(d x +c \right) \sin \left(d x +c \right)}{128}+\frac{5 d x}{128}+\frac{5 c}{128}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{8}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{12}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{24}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)-28 a^{8} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-i a^{8} \left(\cos^{8}\left(d x +c \right)\right)+a^{8} \left(\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)}{d}"," ",0,"1/d*(a^8*(-1/8*(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)+35/128*d*x+35/128*c)-I*a^8*sin(d*x+c)^8-28*a^8*(-1/8*sin(d*x+c)^5*cos(d*x+c)^3-5/48*sin(d*x+c)^3*cos(d*x+c)^3-5/64*sin(d*x+c)*cos(d*x+c)^3+5/128*cos(d*x+c)*sin(d*x+c)+5/128*d*x+5/128*c)+56*I*a^8*(-1/8*sin(d*x+c)^4*cos(d*x+c)^4-1/12*sin(d*x+c)^2*cos(d*x+c)^4-1/24*cos(d*x+c)^4)+70*a^8*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)-56*I*a^8*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)-28*a^8*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-I*a^8*cos(d*x+c)^8+a^8*(1/8*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/128*d*x+35/128*c))","B"
86,1,588,70,0.692000," ","int(cos(d*x+c)^10*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{10}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{80}-\frac{7 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{96}-\frac{7 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{128}+\frac{7 \cos \left(d x +c \right) \sin \left(d x +c \right)}{256}+\frac{7 d x}{256}+\frac{7 c}{256}\right)-8 i a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{10}-\frac{3 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{40}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{40}\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{16}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{32}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{128}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{10}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{40}\right)-28 a^{8} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)}{10}+\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{80}+\frac{7 d x}{256}+\frac{7 c}{256}\right)-\frac{4 i a^{8} \left(\cos^{10}\left(d x +c \right)\right)}{5}+a^{8} \left(\frac{\left(\cos^{9}\left(d x +c \right)+\frac{9 \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{21 \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{105 \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{315 \cos \left(d x +c \right)}{128}\right) \sin \left(d x +c \right)}{10}+\frac{63 d x}{256}+\frac{63 c}{256}\right)}{d}"," ",0,"1/d*(a^8*(-1/10*sin(d*x+c)^7*cos(d*x+c)^3-7/80*sin(d*x+c)^5*cos(d*x+c)^3-7/96*sin(d*x+c)^3*cos(d*x+c)^3-7/128*sin(d*x+c)*cos(d*x+c)^3+7/256*cos(d*x+c)*sin(d*x+c)+7/256*d*x+7/256*c)-8*I*a^8*(-1/10*sin(d*x+c)^6*cos(d*x+c)^4-3/40*sin(d*x+c)^4*cos(d*x+c)^4-1/20*sin(d*x+c)^2*cos(d*x+c)^4-1/40*cos(d*x+c)^4)-28*a^8*(-1/10*sin(d*x+c)^5*cos(d*x+c)^5-1/16*sin(d*x+c)^3*cos(d*x+c)^5-1/32*sin(d*x+c)*cos(d*x+c)^5+1/128*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+56*I*a^8*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6)+70*a^8*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*sin(d*x+c)*cos(d*x+c)^7+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)-56*I*a^8*(-1/10*sin(d*x+c)^2*cos(d*x+c)^8-1/40*cos(d*x+c)^8)-28*a^8*(-1/10*sin(d*x+c)*cos(d*x+c)^9+1/80*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+7/256*d*x+7/256*c)-4/5*I*a^8*cos(d*x+c)^10+a^8*(1/10*(cos(d*x+c)^9+9/8*cos(d*x+c)^7+21/16*cos(d*x+c)^5+105/64*cos(d*x+c)^3+315/128*cos(d*x+c))*sin(d*x+c)+63/256*d*x+63/256*c))","B"
87,1,639,47,0.758000," ","int(cos(d*x+c)^12*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{12}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{120}-\frac{7 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{192}-\frac{7 \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{384}+\frac{7 \left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{1536}+\frac{7 d x}{1024}+\frac{7 c}{1024}\right)-8 i a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{40}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{120}\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{24}-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{64}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{384}+\frac{5 d x}{1024}+\frac{5 c}{1024}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{30}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{120}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{12}-\frac{\sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)}{40}+\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{320}+\frac{7 d x}{1024}+\frac{7 c}{1024}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{12}-\frac{\left(\cos^{10}\left(d x +c \right)\right)}{60}\right)-28 a^{8} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)}{12}+\frac{\left(\cos^{9}\left(d x +c \right)+\frac{9 \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{21 \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{105 \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{315 \cos \left(d x +c \right)}{128}\right) \sin \left(d x +c \right)}{120}+\frac{21 d x}{1024}+\frac{21 c}{1024}\right)-\frac{2 i a^{8} \left(\cos^{12}\left(d x +c \right)\right)}{3}+a^{8} \left(\frac{\left(\cos^{11}\left(d x +c \right)+\frac{11 \left(\cos^{9}\left(d x +c \right)\right)}{10}+\frac{99 \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{231 \left(\cos^{5}\left(d x +c \right)\right)}{160}+\frac{231 \left(\cos^{3}\left(d x +c \right)\right)}{128}+\frac{693 \cos \left(d x +c \right)}{256}\right) \sin \left(d x +c \right)}{12}+\frac{231 d x}{1024}+\frac{231 c}{1024}\right)}{d}"," ",0,"1/d*(a^8*(-1/12*sin(d*x+c)^7*cos(d*x+c)^5-7/120*sin(d*x+c)^5*cos(d*x+c)^5-7/192*sin(d*x+c)^3*cos(d*x+c)^5-7/384*sin(d*x+c)*cos(d*x+c)^5+7/1536*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+7/1024*d*x+7/1024*c)-8*I*a^8*(-1/12*sin(d*x+c)^6*cos(d*x+c)^6-1/20*sin(d*x+c)^4*cos(d*x+c)^6-1/40*sin(d*x+c)^2*cos(d*x+c)^6-1/120*cos(d*x+c)^6)-28*a^8*(-1/12*sin(d*x+c)^5*cos(d*x+c)^7-1/24*sin(d*x+c)^3*cos(d*x+c)^7-1/64*sin(d*x+c)*cos(d*x+c)^7+1/384*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/1024*d*x+5/1024*c)+56*I*a^8*(-1/12*sin(d*x+c)^4*cos(d*x+c)^8-1/30*sin(d*x+c)^2*cos(d*x+c)^8-1/120*cos(d*x+c)^8)+70*a^8*(-1/12*sin(d*x+c)^3*cos(d*x+c)^9-1/40*sin(d*x+c)*cos(d*x+c)^9+1/320*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+7/1024*d*x+7/1024*c)-56*I*a^8*(-1/12*sin(d*x+c)^2*cos(d*x+c)^10-1/60*cos(d*x+c)^10)-28*a^8*(-1/12*sin(d*x+c)*cos(d*x+c)^11+1/120*(cos(d*x+c)^9+9/8*cos(d*x+c)^7+21/16*cos(d*x+c)^5+105/64*cos(d*x+c)^3+315/128*cos(d*x+c))*sin(d*x+c)+21/1024*d*x+21/1024*c)-2/3*I*a^8*cos(d*x+c)^12+a^8*(1/12*(cos(d*x+c)^11+11/10*cos(d*x+c)^9+99/80*cos(d*x+c)^7+231/160*cos(d*x+c)^5+231/128*cos(d*x+c)^3+693/256*cos(d*x+c))*sin(d*x+c)+231/1024*d*x+231/1024*c))","B"
88,1,689,23,0.773000," ","int(cos(d*x+c)^14*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{14}-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{24}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{48}-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{128}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{768}+\frac{5 d x}{2048}+\frac{5 c}{2048}\right)-8 i a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{14}-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{28}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{70}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{280}\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{14}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{168}-\frac{\sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)}{112}+\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{896}+\frac{5 d x}{2048}+\frac{5 c}{2048}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{14}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{42}-\frac{\left(\cos^{10}\left(d x +c \right)\right)}{210}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{11}\left(d x +c \right)\right)}{14}-\frac{\sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)}{56}+\frac{\left(\cos^{9}\left(d x +c \right)+\frac{9 \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{21 \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{105 \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{315 \cos \left(d x +c \right)}{128}\right) \sin \left(d x +c \right)}{560}+\frac{9 d x}{2048}+\frac{9 c}{2048}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{12}\left(d x +c \right)\right)}{14}-\frac{\left(\cos^{12}\left(d x +c \right)\right)}{84}\right)-28 a^{8} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{13}\left(d x +c \right)\right)}{14}+\frac{\left(\cos^{11}\left(d x +c \right)+\frac{11 \left(\cos^{9}\left(d x +c \right)\right)}{10}+\frac{99 \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{231 \left(\cos^{5}\left(d x +c \right)\right)}{160}+\frac{231 \left(\cos^{3}\left(d x +c \right)\right)}{128}+\frac{693 \cos \left(d x +c \right)}{256}\right) \sin \left(d x +c \right)}{168}+\frac{33 d x}{2048}+\frac{33 c}{2048}\right)-\frac{4 i a^{8} \left(\cos^{14}\left(d x +c \right)\right)}{7}+a^{8} \left(\frac{\left(\cos^{13}\left(d x +c \right)+\frac{13 \left(\cos^{11}\left(d x +c \right)\right)}{12}+\frac{143 \left(\cos^{9}\left(d x +c \right)\right)}{120}+\frac{429 \left(\cos^{7}\left(d x +c \right)\right)}{320}+\frac{1001 \left(\cos^{5}\left(d x +c \right)\right)}{640}+\frac{1001 \left(\cos^{3}\left(d x +c \right)\right)}{512}+\frac{3003 \cos \left(d x +c \right)}{1024}\right) \sin \left(d x +c \right)}{14}+\frac{429 d x}{2048}+\frac{429 c}{2048}\right)}{d}"," ",0,"1/d*(a^8*(-1/14*sin(d*x+c)^7*cos(d*x+c)^7-1/24*sin(d*x+c)^5*cos(d*x+c)^7-1/48*sin(d*x+c)^3*cos(d*x+c)^7-1/128*sin(d*x+c)*cos(d*x+c)^7+1/768*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/2048*d*x+5/2048*c)-8*I*a^8*(-1/14*sin(d*x+c)^6*cos(d*x+c)^8-1/28*sin(d*x+c)^4*cos(d*x+c)^8-1/70*sin(d*x+c)^2*cos(d*x+c)^8-1/280*cos(d*x+c)^8)-28*a^8*(-1/14*sin(d*x+c)^5*cos(d*x+c)^9-5/168*sin(d*x+c)^3*cos(d*x+c)^9-1/112*sin(d*x+c)*cos(d*x+c)^9+1/896*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+5/2048*d*x+5/2048*c)+56*I*a^8*(-1/14*sin(d*x+c)^4*cos(d*x+c)^10-1/42*sin(d*x+c)^2*cos(d*x+c)^10-1/210*cos(d*x+c)^10)+70*a^8*(-1/14*sin(d*x+c)^3*cos(d*x+c)^11-1/56*sin(d*x+c)*cos(d*x+c)^11+1/560*(cos(d*x+c)^9+9/8*cos(d*x+c)^7+21/16*cos(d*x+c)^5+105/64*cos(d*x+c)^3+315/128*cos(d*x+c))*sin(d*x+c)+9/2048*d*x+9/2048*c)-56*I*a^8*(-1/14*sin(d*x+c)^2*cos(d*x+c)^12-1/84*cos(d*x+c)^12)-28*a^8*(-1/14*sin(d*x+c)*cos(d*x+c)^13+1/168*(cos(d*x+c)^11+11/10*cos(d*x+c)^9+99/80*cos(d*x+c)^7+231/160*cos(d*x+c)^5+231/128*cos(d*x+c)^3+693/256*cos(d*x+c))*sin(d*x+c)+33/2048*d*x+33/2048*c)-4/7*I*a^8*cos(d*x+c)^14+a^8*(1/14*(cos(d*x+c)^13+13/12*cos(d*x+c)^11+143/120*cos(d*x+c)^9+429/320*cos(d*x+c)^7+1001/640*cos(d*x+c)^5+1001/512*cos(d*x+c)^3+3003/1024*cos(d*x+c))*sin(d*x+c)+429/2048*d*x+429/2048*c))","B"
89,1,739,191,0.773000," ","int(cos(d*x+c)^16*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{16}-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{32}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{384}-\frac{\sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)}{256}+\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{2048}+\frac{35 d x}{32768}+\frac{35 c}{32768}\right)-8 i a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{16}-\frac{3 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{112}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{112}-\frac{\left(\cos^{10}\left(d x +c \right)\right)}{560}\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{11}\left(d x +c \right)\right)}{16}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{11}\left(d x +c \right)\right)}{224}-\frac{5 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)}{896}+\frac{\left(\cos^{9}\left(d x +c \right)+\frac{9 \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{21 \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{105 \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{315 \cos \left(d x +c \right)}{128}\right) \sin \left(d x +c \right)}{1792}+\frac{45 d x}{32768}+\frac{45 c}{32768}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{12}\left(d x +c \right)\right)}{16}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{12}\left(d x +c \right)\right)}{56}-\frac{\left(\cos^{12}\left(d x +c \right)\right)}{336}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{13}\left(d x +c \right)\right)}{16}-\frac{3 \sin \left(d x +c \right) \left(\cos^{13}\left(d x +c \right)\right)}{224}+\frac{\left(\cos^{11}\left(d x +c \right)+\frac{11 \left(\cos^{9}\left(d x +c \right)\right)}{10}+\frac{99 \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{231 \left(\cos^{5}\left(d x +c \right)\right)}{160}+\frac{231 \left(\cos^{3}\left(d x +c \right)\right)}{128}+\frac{693 \cos \left(d x +c \right)}{256}\right) \sin \left(d x +c \right)}{896}+\frac{99 d x}{32768}+\frac{99 c}{32768}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{14}\left(d x +c \right)\right)}{16}-\frac{\left(\cos^{14}\left(d x +c \right)\right)}{112}\right)-28 a^{8} \left(-\frac{\left(\cos^{15}\left(d x +c \right)\right) \sin \left(d x +c \right)}{16}+\frac{\left(\cos^{13}\left(d x +c \right)+\frac{13 \left(\cos^{11}\left(d x +c \right)\right)}{12}+\frac{143 \left(\cos^{9}\left(d x +c \right)\right)}{120}+\frac{429 \left(\cos^{7}\left(d x +c \right)\right)}{320}+\frac{1001 \left(\cos^{5}\left(d x +c \right)\right)}{640}+\frac{1001 \left(\cos^{3}\left(d x +c \right)\right)}{512}+\frac{3003 \cos \left(d x +c \right)}{1024}\right) \sin \left(d x +c \right)}{224}+\frac{429 d x}{32768}+\frac{429 c}{32768}\right)-\frac{i a^{8} \left(\cos^{16}\left(d x +c \right)\right)}{2}+a^{8} \left(\frac{\left(\cos^{15}\left(d x +c \right)+\frac{15 \left(\cos^{13}\left(d x +c \right)\right)}{14}+\frac{65 \left(\cos^{11}\left(d x +c \right)\right)}{56}+\frac{143 \left(\cos^{9}\left(d x +c \right)\right)}{112}+\frac{1287 \left(\cos^{7}\left(d x +c \right)\right)}{896}+\frac{429 \left(\cos^{5}\left(d x +c \right)\right)}{256}+\frac{2145 \left(\cos^{3}\left(d x +c \right)\right)}{1024}+\frac{6435 \cos \left(d x +c \right)}{2048}\right) \sin \left(d x +c \right)}{16}+\frac{6435 d x}{32768}+\frac{6435 c}{32768}\right)}{d}"," ",0,"1/d*(a^8*(-1/16*sin(d*x+c)^7*cos(d*x+c)^9-1/32*sin(d*x+c)^5*cos(d*x+c)^9-5/384*sin(d*x+c)^3*cos(d*x+c)^9-1/256*sin(d*x+c)*cos(d*x+c)^9+1/2048*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/32768*d*x+35/32768*c)-8*I*a^8*(-1/16*sin(d*x+c)^6*cos(d*x+c)^10-3/112*sin(d*x+c)^4*cos(d*x+c)^10-1/112*sin(d*x+c)^2*cos(d*x+c)^10-1/560*cos(d*x+c)^10)-28*a^8*(-1/16*sin(d*x+c)^5*cos(d*x+c)^11-5/224*sin(d*x+c)^3*cos(d*x+c)^11-5/896*sin(d*x+c)*cos(d*x+c)^11+1/1792*(cos(d*x+c)^9+9/8*cos(d*x+c)^7+21/16*cos(d*x+c)^5+105/64*cos(d*x+c)^3+315/128*cos(d*x+c))*sin(d*x+c)+45/32768*d*x+45/32768*c)+56*I*a^8*(-1/16*sin(d*x+c)^4*cos(d*x+c)^12-1/56*sin(d*x+c)^2*cos(d*x+c)^12-1/336*cos(d*x+c)^12)+70*a^8*(-1/16*sin(d*x+c)^3*cos(d*x+c)^13-3/224*sin(d*x+c)*cos(d*x+c)^13+1/896*(cos(d*x+c)^11+11/10*cos(d*x+c)^9+99/80*cos(d*x+c)^7+231/160*cos(d*x+c)^5+231/128*cos(d*x+c)^3+693/256*cos(d*x+c))*sin(d*x+c)+99/32768*d*x+99/32768*c)-56*I*a^8*(-1/16*sin(d*x+c)^2*cos(d*x+c)^14-1/112*cos(d*x+c)^14)-28*a^8*(-1/16*cos(d*x+c)^15*sin(d*x+c)+1/224*(cos(d*x+c)^13+13/12*cos(d*x+c)^11+143/120*cos(d*x+c)^9+429/320*cos(d*x+c)^7+1001/640*cos(d*x+c)^5+1001/512*cos(d*x+c)^3+3003/1024*cos(d*x+c))*sin(d*x+c)+429/32768*d*x+429/32768*c)-1/2*I*a^8*cos(d*x+c)^16+a^8*(1/16*(cos(d*x+c)^15+15/14*cos(d*x+c)^13+65/56*cos(d*x+c)^11+143/112*cos(d*x+c)^9+1287/896*cos(d*x+c)^7+429/256*cos(d*x+c)^5+2145/1024*cos(d*x+c)^3+6435/2048*cos(d*x+c))*sin(d*x+c)+6435/32768*d*x+6435/32768*c))","B"
90,1,789,237,0.778000," ","int(cos(d*x+c)^18*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{11}\left(d x +c \right)\right)}{18}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{11}\left(d x +c \right)\right)}{288}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{11}\left(d x +c \right)\right)}{576}-\frac{5 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)}{2304}+\frac{\left(\cos^{9}\left(d x +c \right)+\frac{9 \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{21 \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{105 \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{315 \cos \left(d x +c \right)}{128}\right) \sin \left(d x +c \right)}{4608}+\frac{35 d x}{65536}+\frac{35 c}{65536}\right)-8 i a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{12}\left(d x +c \right)\right)}{18}-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{12}\left(d x +c \right)\right)}{48}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{12}\left(d x +c \right)\right)}{168}-\frac{\left(\cos^{12}\left(d x +c \right)\right)}{1008}\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{13}\left(d x +c \right)\right)}{18}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{13}\left(d x +c \right)\right)}{288}-\frac{5 \sin \left(d x +c \right) \left(\cos^{13}\left(d x +c \right)\right)}{1344}+\frac{5 \left(\cos^{11}\left(d x +c \right)+\frac{11 \left(\cos^{9}\left(d x +c \right)\right)}{10}+\frac{99 \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{231 \left(\cos^{5}\left(d x +c \right)\right)}{160}+\frac{231 \left(\cos^{3}\left(d x +c \right)\right)}{128}+\frac{693 \cos \left(d x +c \right)}{256}\right) \sin \left(d x +c \right)}{16128}+\frac{55 d x}{65536}+\frac{55 c}{65536}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{14}\left(d x +c \right)\right)}{18}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{14}\left(d x +c \right)\right)}{72}-\frac{\left(\cos^{14}\left(d x +c \right)\right)}{504}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{15}\left(d x +c \right)\right)}{18}-\frac{\left(\cos^{15}\left(d x +c \right)\right) \sin \left(d x +c \right)}{96}+\frac{\left(\cos^{13}\left(d x +c \right)+\frac{13 \left(\cos^{11}\left(d x +c \right)\right)}{12}+\frac{143 \left(\cos^{9}\left(d x +c \right)\right)}{120}+\frac{429 \left(\cos^{7}\left(d x +c \right)\right)}{320}+\frac{1001 \left(\cos^{5}\left(d x +c \right)\right)}{640}+\frac{1001 \left(\cos^{3}\left(d x +c \right)\right)}{512}+\frac{3003 \cos \left(d x +c \right)}{1024}\right) \sin \left(d x +c \right)}{1344}+\frac{143 d x}{65536}+\frac{143 c}{65536}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{16}\left(d x +c \right)\right)}{18}-\frac{\left(\cos^{16}\left(d x +c \right)\right)}{144}\right)-28 a^{8} \left(-\frac{\left(\cos^{17}\left(d x +c \right)\right) \sin \left(d x +c \right)}{18}+\frac{\left(\cos^{15}\left(d x +c \right)+\frac{15 \left(\cos^{13}\left(d x +c \right)\right)}{14}+\frac{65 \left(\cos^{11}\left(d x +c \right)\right)}{56}+\frac{143 \left(\cos^{9}\left(d x +c \right)\right)}{112}+\frac{1287 \left(\cos^{7}\left(d x +c \right)\right)}{896}+\frac{429 \left(\cos^{5}\left(d x +c \right)\right)}{256}+\frac{2145 \left(\cos^{3}\left(d x +c \right)\right)}{1024}+\frac{6435 \cos \left(d x +c \right)}{2048}\right) \sin \left(d x +c \right)}{288}+\frac{715 d x}{65536}+\frac{715 c}{65536}\right)-\frac{4 i a^{8} \left(\cos^{18}\left(d x +c \right)\right)}{9}+a^{8} \left(\frac{\left(\cos^{17}\left(d x +c \right)+\frac{17 \left(\cos^{15}\left(d x +c \right)\right)}{16}+\frac{255 \left(\cos^{13}\left(d x +c \right)\right)}{224}+\frac{1105 \left(\cos^{11}\left(d x +c \right)\right)}{896}+\frac{2431 \left(\cos^{9}\left(d x +c \right)\right)}{1792}+\frac{21879 \left(\cos^{7}\left(d x +c \right)\right)}{14336}+\frac{7293 \left(\cos^{5}\left(d x +c \right)\right)}{4096}+\frac{36465 \left(\cos^{3}\left(d x +c \right)\right)}{16384}+\frac{109395 \cos \left(d x +c \right)}{32768}\right) \sin \left(d x +c \right)}{18}+\frac{12155 d x}{65536}+\frac{12155 c}{65536}\right)}{d}"," ",0,"1/d*(a^8*(-1/18*sin(d*x+c)^7*cos(d*x+c)^11-7/288*sin(d*x+c)^5*cos(d*x+c)^11-5/576*sin(d*x+c)^3*cos(d*x+c)^11-5/2304*sin(d*x+c)*cos(d*x+c)^11+1/4608*(cos(d*x+c)^9+9/8*cos(d*x+c)^7+21/16*cos(d*x+c)^5+105/64*cos(d*x+c)^3+315/128*cos(d*x+c))*sin(d*x+c)+35/65536*d*x+35/65536*c)-8*I*a^8*(-1/18*sin(d*x+c)^6*cos(d*x+c)^12-1/48*sin(d*x+c)^4*cos(d*x+c)^12-1/168*sin(d*x+c)^2*cos(d*x+c)^12-1/1008*cos(d*x+c)^12)-28*a^8*(-1/18*sin(d*x+c)^5*cos(d*x+c)^13-5/288*sin(d*x+c)^3*cos(d*x+c)^13-5/1344*sin(d*x+c)*cos(d*x+c)^13+5/16128*(cos(d*x+c)^11+11/10*cos(d*x+c)^9+99/80*cos(d*x+c)^7+231/160*cos(d*x+c)^5+231/128*cos(d*x+c)^3+693/256*cos(d*x+c))*sin(d*x+c)+55/65536*d*x+55/65536*c)+56*I*a^8*(-1/18*sin(d*x+c)^4*cos(d*x+c)^14-1/72*sin(d*x+c)^2*cos(d*x+c)^14-1/504*cos(d*x+c)^14)+70*a^8*(-1/18*sin(d*x+c)^3*cos(d*x+c)^15-1/96*cos(d*x+c)^15*sin(d*x+c)+1/1344*(cos(d*x+c)^13+13/12*cos(d*x+c)^11+143/120*cos(d*x+c)^9+429/320*cos(d*x+c)^7+1001/640*cos(d*x+c)^5+1001/512*cos(d*x+c)^3+3003/1024*cos(d*x+c))*sin(d*x+c)+143/65536*d*x+143/65536*c)-56*I*a^8*(-1/18*sin(d*x+c)^2*cos(d*x+c)^16-1/144*cos(d*x+c)^16)-28*a^8*(-1/18*cos(d*x+c)^17*sin(d*x+c)+1/288*(cos(d*x+c)^15+15/14*cos(d*x+c)^13+65/56*cos(d*x+c)^11+143/112*cos(d*x+c)^9+1287/896*cos(d*x+c)^7+429/256*cos(d*x+c)^5+2145/1024*cos(d*x+c)^3+6435/2048*cos(d*x+c))*sin(d*x+c)+715/65536*d*x+715/65536*c)-4/9*I*a^8*cos(d*x+c)^18+a^8*(1/18*(cos(d*x+c)^17+17/16*cos(d*x+c)^15+255/224*cos(d*x+c)^13+1105/896*cos(d*x+c)^11+2431/1792*cos(d*x+c)^9+21879/14336*cos(d*x+c)^7+7293/4096*cos(d*x+c)^5+36465/16384*cos(d*x+c)^3+109395/32768*cos(d*x+c))*sin(d*x+c)+12155/65536*d*x+12155/65536*c))","B"
91,1,464,208,0.541000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^8,x)","-\frac{7 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}+\frac{21 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}-\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{5 a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}-\frac{8 i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{328 i a^{8} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}-\frac{8 i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}-\frac{56 i a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{2152 i a^{8} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}+\frac{8 i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{3}}+\frac{56 i a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{56 i a^{8} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{8 i a^{8} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{d}-\frac{4424 i a^{8} \cos \left(d x +c \right)}{15 d}+\frac{5 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{16 d}+\frac{175 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{16 d}+\frac{2555 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{48 d}-\frac{3003 a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{35 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{3019 a^{8} \sin \left(d x +c \right)}{16 d}"," ",0,"-7/d*a^8*sin(d*x+c)^7/cos(d*x+c)^4+21/2/d*a^8*sin(d*x+c)^7/cos(d*x+c)^2+1/6/d*a^8*sin(d*x+c)^9/cos(d*x+c)^6-1/8/d*a^8*sin(d*x+c)^9/cos(d*x+c)^4+5/16/d*a^8*sin(d*x+c)^9/cos(d*x+c)^2-8*I/d*a^8*sin(d*x+c)^8/cos(d*x+c)-328/5*I/d*a^8*cos(d*x+c)*sin(d*x+c)^4-8/5*I/d*a^8*sin(d*x+c)^8/cos(d*x+c)^5-56*I/d*a^8*sin(d*x+c)^6/cos(d*x+c)-2152/15*I/d*a^8*cos(d*x+c)*sin(d*x+c)^2+8/5*I/d*a^8*sin(d*x+c)^8/cos(d*x+c)^3+56/3*I/d*a^8*sin(d*x+c)^6/cos(d*x+c)^3-56*I/d*a^8*sin(d*x+c)^4/cos(d*x+c)-8*I/d*a^8*cos(d*x+c)*sin(d*x+c)^6-4424/15*I/d*a^8*cos(d*x+c)+5/16*a^8*sin(d*x+c)^7/d+175/16*a^8*sin(d*x+c)^5/d+2555/48*a^8*sin(d*x+c)^3/d-3003/16/d*a^8*ln(sec(d*x+c)+tan(d*x+c))+35/d*a^8*sin(d*x+c)^5/cos(d*x+c)^2+3019/16*a^8*sin(d*x+c)/d","B"
92,1,356,180,0.598000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^8,x)","\frac{40 i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}+\frac{72 i a^{8} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{8 i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}+\frac{40 i a^{8} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{3 d}+\frac{344 i a^{8} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}+\frac{688 i a^{8} \cos \left(d x +c \right)}{3 d}-\frac{8 i a^{8} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{56 i a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{8}}{3 d}-\frac{3449 a^{8} \sin \left(d x +c \right)}{24 d}+\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{5 a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{14 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}-\frac{5 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{8 d}-\frac{119 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}+\frac{1155 a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}-\frac{1379 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{24 d}"," ",0,"40/3*I/d*a^8*sin(d*x+c)^8/cos(d*x+c)+72*I/d*a^8*cos(d*x+c)*sin(d*x+c)^4-8/3*I/d*a^8*sin(d*x+c)^8/cos(d*x+c)^3+40/3*I/d*a^8*cos(d*x+c)*sin(d*x+c)^6+344/3*I/d*a^8*cos(d*x+c)*sin(d*x+c)^2+688/3*I/d*a^8*cos(d*x+c)-8/3*I/d*a^8*cos(d*x+c)^3+56*I/d*a^8*sin(d*x+c)^6/cos(d*x+c)+1/3/d*cos(d*x+c)^2*sin(d*x+c)*a^8-3449/24*a^8*sin(d*x+c)/d+1/4/d*a^8*sin(d*x+c)^9/cos(d*x+c)^4-5/8/d*a^8*sin(d*x+c)^9/cos(d*x+c)^2-14/d*a^8*sin(d*x+c)^7/cos(d*x+c)^2-5/8*a^8*sin(d*x+c)^7/d-119/8*a^8*sin(d*x+c)^5/d+1155/8/d*a^8*ln(sec(d*x+c)+tan(d*x+c))-1379/24*a^8*sin(d*x+c)^3/d","A"
93,1,322,152,0.617000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{2 d}+\frac{203 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{10 d}+\frac{21 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{283 a^{8} \sin \left(d x +c \right)}{10 d}-\frac{63 a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{8 i a^{8} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}-\frac{416 i a^{8} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{832 i a^{8} \cos \left(d x +c \right)}{15 d}+\frac{56 i a^{8} \left(\cos^{3}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right)}{5 d}+\frac{112 i a^{8} \left(\cos^{3}\left(d x +c \right)\right)}{15 d}-\frac{104 i a^{8} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}-\frac{8 i a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{8 i a^{8} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{d}+\frac{29 a^{8} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5 d}-\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{8}}{5 d}"," ",0,"1/2/d*a^8*sin(d*x+c)^9/cos(d*x+c)^2+1/2*a^8*sin(d*x+c)^7/d+203/10*a^8*sin(d*x+c)^5/d+21/2*a^8*sin(d*x+c)^3/d+283/10*a^8*sin(d*x+c)/d-63/2/d*a^8*ln(sec(d*x+c)+tan(d*x+c))-8/5*I/d*a^8*cos(d*x+c)^5-416/15*I/d*a^8*cos(d*x+c)*sin(d*x+c)^2-832/15*I/d*a^8*cos(d*x+c)+56/5*I/d*a^8*cos(d*x+c)^3*sin(d*x+c)^2+112/15*I/d*a^8*cos(d*x+c)^3-104/5*I/d*a^8*cos(d*x+c)*sin(d*x+c)^4-8*I/d*a^8*sin(d*x+c)^8/cos(d*x+c)-8*I/d*a^8*cos(d*x+c)*sin(d*x+c)^6+29/5/d*a^8*cos(d*x+c)^4*sin(d*x+c)-8/5/d*cos(d*x+c)^2*sin(d*x+c)*a^8","B"
94,1,385,138,0.610000," ","int(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^8,x)","-\frac{29 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{7 d}-\frac{a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}+\frac{139 a^{8} \sin \left(d x +c \right)}{105 d}+\frac{a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{128 i a^{8} \cos \left(d x +c \right)}{35 d}-\frac{32 i a^{8} \left(\cos^{3}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right)}{5 d}-\frac{10 a^{8} \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{d}-\frac{232 a^{8} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35 d}+\frac{122 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{8}}{105 d}+\frac{64 i a^{8} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{35 d}-\frac{8 i a^{8} \left(\cos^{7}\left(d x +c \right)\right)}{7 d}+\frac{48 i a^{8} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{35 d}+\frac{29 a^{8} \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)}{7 d}+\frac{16 i a^{8} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}-\frac{8 i a^{8} \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{d}+\frac{8 i a^{8} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{7 d}-\frac{64 i a^{8} \left(\cos^{3}\left(d x +c \right)\right)}{15 d}+\frac{8 i a^{8} \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{d}"," ",0,"-29/7*a^8*sin(d*x+c)^7/d-1/5*a^8*sin(d*x+c)^5/d-1/3*a^8*sin(d*x+c)^3/d+139/105*a^8*sin(d*x+c)/d+1/d*a^8*ln(sec(d*x+c)+tan(d*x+c))+128/35*I/d*a^8*cos(d*x+c)-32/5*I/d*a^8*cos(d*x+c)^3*sin(d*x+c)^2-10/d*a^8*sin(d*x+c)^3*cos(d*x+c)^4-232/35/d*a^8*cos(d*x+c)^4*sin(d*x+c)+122/105/d*cos(d*x+c)^2*sin(d*x+c)*a^8+64/35*I/d*a^8*cos(d*x+c)*sin(d*x+c)^2-8/7*I/d*a^8*cos(d*x+c)^7+48/35*I/d*a^8*cos(d*x+c)*sin(d*x+c)^4+29/7/d*a^8*cos(d*x+c)^6*sin(d*x+c)+16/5*I/d*a^8*cos(d*x+c)^5-8*I/d*a^8*sin(d*x+c)^4*cos(d*x+c)^3+8/7*I/d*a^8*cos(d*x+c)*sin(d*x+c)^6-64/15*I/d*a^8*cos(d*x+c)^3+8*I/d*a^8*sin(d*x+c)^2*cos(d*x+c)^5","B"
95,1,447,58,0.691000," ","int(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^8,x)","\frac{\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{9}-8 i a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{9}-\frac{2 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{21}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right)}{105}-\frac{16 \left(\cos^{3}\left(d x +c \right)\right)}{315}\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{9}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{63}-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{21}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{63}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)-28 a^{8} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{8 i a^{8} \left(\cos^{9}\left(d x +c \right)\right)}{9}+\frac{a^{8} \left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{9}}{d}"," ",0,"1/d*(1/9*a^8*sin(d*x+c)^9-8*I*a^8*(-1/9*sin(d*x+c)^6*cos(d*x+c)^3-2/21*sin(d*x+c)^4*cos(d*x+c)^3-8/105*cos(d*x+c)^3*sin(d*x+c)^2-16/315*cos(d*x+c)^3)-28*a^8*(-1/9*sin(d*x+c)^5*cos(d*x+c)^4-5/63*sin(d*x+c)^3*cos(d*x+c)^4-1/21*sin(d*x+c)*cos(d*x+c)^4+1/63*(2+cos(d*x+c)^2)*sin(d*x+c))+56*I*a^8*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+70*a^8*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-56*I*a^8*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)-28*a^8*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-8/9*I*a^8*cos(d*x+c)^9+1/9*a^8*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))","B"
96,1,567,120,0.735000," ","int(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{11}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{99}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{99}-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{33}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{99}\right)-8 i a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{11}-\frac{2 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{33}-\frac{8 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{231}-\frac{16 \left(\cos^{5}\left(d x +c \right)\right)}{1155}\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{11}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{99}-\frac{5 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{231}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{231}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{11}-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{33}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{231}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{11}-\frac{2 \left(\cos^{9}\left(d x +c \right)\right)}{99}\right)-28 a^{8} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)}{11}+\frac{\left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{99}\right)-\frac{8 i a^{8} \left(\cos^{11}\left(d x +c \right)\right)}{11}+\frac{a^{8} \left(\frac{256}{63}+\cos^{10}\left(d x +c \right)+\frac{10 \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{80 \left(\cos^{6}\left(d x +c \right)\right)}{63}+\frac{32 \left(\cos^{4}\left(d x +c \right)\right)}{21}+\frac{128 \left(\cos^{2}\left(d x +c \right)\right)}{63}\right) \sin \left(d x +c \right)}{11}}{d}"," ",0,"1/d*(a^8*(-1/11*sin(d*x+c)^7*cos(d*x+c)^4-7/99*sin(d*x+c)^5*cos(d*x+c)^4-5/99*sin(d*x+c)^3*cos(d*x+c)^4-1/33*sin(d*x+c)*cos(d*x+c)^4+1/99*(2+cos(d*x+c)^2)*sin(d*x+c))-8*I*a^8*(-1/11*sin(d*x+c)^6*cos(d*x+c)^5-2/33*sin(d*x+c)^4*cos(d*x+c)^5-8/231*sin(d*x+c)^2*cos(d*x+c)^5-16/1155*cos(d*x+c)^5)-28*a^8*(-1/11*sin(d*x+c)^5*cos(d*x+c)^6-5/99*sin(d*x+c)^3*cos(d*x+c)^6-5/231*sin(d*x+c)*cos(d*x+c)^6+1/231*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+56*I*a^8*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+70*a^8*(-1/11*sin(d*x+c)^3*cos(d*x+c)^8-1/33*sin(d*x+c)*cos(d*x+c)^8+1/231*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-56*I*a^8*(-1/11*sin(d*x+c)^2*cos(d*x+c)^9-2/99*cos(d*x+c)^9)-28*a^8*(-1/11*sin(d*x+c)*cos(d*x+c)^10+1/99*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))-8/11*I*a^8*cos(d*x+c)^11+1/11*a^8*(256/63+cos(d*x+c)^10+10/9*cos(d*x+c)^8+80/63*cos(d*x+c)^6+32/21*cos(d*x+c)^4+128/63*cos(d*x+c)^2)*sin(d*x+c))","B"
97,1,617,187,0.727000," ","int(cos(d*x+c)^13*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{13}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{143}-\frac{35 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{1287}-\frac{5 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{429}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{429}\right)-8 i a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{13}-\frac{6 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{143}-\frac{8 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{429}-\frac{16 \left(\cos^{7}\left(d x +c \right)\right)}{3003}\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{13}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{143}-\frac{5 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{429}+\frac{5 \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{3003}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{13}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{143}-\frac{8 \left(\cos^{9}\left(d x +c \right)\right)}{1287}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{13}-\frac{3 \sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)}{143}+\frac{\left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{429}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{11}\left(d x +c \right)\right)}{13}-\frac{2 \left(\cos^{11}\left(d x +c \right)\right)}{143}\right)-28 a^{8} \left(-\frac{\left(\cos^{12}\left(d x +c \right)\right) \sin \left(d x +c \right)}{13}+\frac{\left(\frac{256}{63}+\cos^{10}\left(d x +c \right)+\frac{10 \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{80 \left(\cos^{6}\left(d x +c \right)\right)}{63}+\frac{32 \left(\cos^{4}\left(d x +c \right)\right)}{21}+\frac{128 \left(\cos^{2}\left(d x +c \right)\right)}{63}\right) \sin \left(d x +c \right)}{143}\right)-\frac{8 i a^{8} \left(\cos^{13}\left(d x +c \right)\right)}{13}+\frac{a^{8} \left(\frac{1024}{231}+\cos^{12}\left(d x +c \right)+\frac{12 \left(\cos^{10}\left(d x +c \right)\right)}{11}+\frac{40 \left(\cos^{8}\left(d x +c \right)\right)}{33}+\frac{320 \left(\cos^{6}\left(d x +c \right)\right)}{231}+\frac{128 \left(\cos^{4}\left(d x +c \right)\right)}{77}+\frac{512 \left(\cos^{2}\left(d x +c \right)\right)}{231}\right) \sin \left(d x +c \right)}{13}}{d}"," ",0,"1/d*(a^8*(-1/13*sin(d*x+c)^7*cos(d*x+c)^6-7/143*sin(d*x+c)^5*cos(d*x+c)^6-35/1287*sin(d*x+c)^3*cos(d*x+c)^6-5/429*sin(d*x+c)*cos(d*x+c)^6+1/429*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-8*I*a^8*(-1/13*sin(d*x+c)^6*cos(d*x+c)^7-6/143*sin(d*x+c)^4*cos(d*x+c)^7-8/429*sin(d*x+c)^2*cos(d*x+c)^7-16/3003*cos(d*x+c)^7)-28*a^8*(-1/13*sin(d*x+c)^5*cos(d*x+c)^8-5/143*sin(d*x+c)^3*cos(d*x+c)^8-5/429*sin(d*x+c)*cos(d*x+c)^8+5/3003*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+56*I*a^8*(-1/13*sin(d*x+c)^4*cos(d*x+c)^9-4/143*sin(d*x+c)^2*cos(d*x+c)^9-8/1287*cos(d*x+c)^9)+70*a^8*(-1/13*sin(d*x+c)^3*cos(d*x+c)^10-3/143*sin(d*x+c)*cos(d*x+c)^10+1/429*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))-56*I*a^8*(-1/13*sin(d*x+c)^2*cos(d*x+c)^11-2/143*cos(d*x+c)^11)-28*a^8*(-1/13*cos(d*x+c)^12*sin(d*x+c)+1/143*(256/63+cos(d*x+c)^10+10/9*cos(d*x+c)^8+80/63*cos(d*x+c)^6+32/21*cos(d*x+c)^4+128/63*cos(d*x+c)^2)*sin(d*x+c))-8/13*I*a^8*cos(d*x+c)^13+1/13*a^8*(1024/231+cos(d*x+c)^12+12/11*cos(d*x+c)^10+40/33*cos(d*x+c)^8+320/231*cos(d*x+c)^6+128/77*cos(d*x+c)^4+512/231*cos(d*x+c)^2)*sin(d*x+c))","B"
98,1,667,188,0.747000," ","int(cos(d*x+c)^15*(a+I*a*tan(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{15}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{195}-\frac{7 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{429}-\frac{7 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{1287}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{1287}\right)-8 i a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{15}-\frac{2 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{65}-\frac{8 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{9}\left(d x +c \right)\right)}{715}-\frac{16 \left(\cos^{9}\left(d x +c \right)\right)}{6435}\right)-28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{15}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{10}\left(d x +c \right)\right)}{39}-\frac{\sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)}{143}+\frac{\left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{1287}\right)+56 i a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{11}\left(d x +c \right)\right)}{15}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{11}\left(d x +c \right)\right)}{195}-\frac{8 \left(\cos^{11}\left(d x +c \right)\right)}{2145}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{12}\left(d x +c \right)\right)}{15}-\frac{\left(\cos^{12}\left(d x +c \right)\right) \sin \left(d x +c \right)}{65}+\frac{\left(\frac{256}{63}+\cos^{10}\left(d x +c \right)+\frac{10 \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{80 \left(\cos^{6}\left(d x +c \right)\right)}{63}+\frac{32 \left(\cos^{4}\left(d x +c \right)\right)}{21}+\frac{128 \left(\cos^{2}\left(d x +c \right)\right)}{63}\right) \sin \left(d x +c \right)}{715}\right)-56 i a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{13}\left(d x +c \right)\right)}{15}-\frac{2 \left(\cos^{13}\left(d x +c \right)\right)}{195}\right)-28 a^{8} \left(-\frac{\left(\cos^{14}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}+\frac{\left(\frac{1024}{231}+\cos^{12}\left(d x +c \right)+\frac{12 \left(\cos^{10}\left(d x +c \right)\right)}{11}+\frac{40 \left(\cos^{8}\left(d x +c \right)\right)}{33}+\frac{320 \left(\cos^{6}\left(d x +c \right)\right)}{231}+\frac{128 \left(\cos^{4}\left(d x +c \right)\right)}{77}+\frac{512 \left(\cos^{2}\left(d x +c \right)\right)}{231}\right) \sin \left(d x +c \right)}{195}\right)-\frac{8 i a^{8} \left(\cos^{15}\left(d x +c \right)\right)}{15}+\frac{a^{8} \left(\frac{2048}{429}+\cos^{14}\left(d x +c \right)+\frac{14 \left(\cos^{12}\left(d x +c \right)\right)}{13}+\frac{168 \left(\cos^{10}\left(d x +c \right)\right)}{143}+\frac{560 \left(\cos^{8}\left(d x +c \right)\right)}{429}+\frac{640 \left(\cos^{6}\left(d x +c \right)\right)}{429}+\frac{256 \left(\cos^{4}\left(d x +c \right)\right)}{143}+\frac{1024 \left(\cos^{2}\left(d x +c \right)\right)}{429}\right) \sin \left(d x +c \right)}{15}}{d}"," ",0,"1/d*(a^8*(-1/15*sin(d*x+c)^7*cos(d*x+c)^8-7/195*sin(d*x+c)^5*cos(d*x+c)^8-7/429*sin(d*x+c)^3*cos(d*x+c)^8-7/1287*sin(d*x+c)*cos(d*x+c)^8+1/1287*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-8*I*a^8*(-1/15*sin(d*x+c)^6*cos(d*x+c)^9-2/65*sin(d*x+c)^4*cos(d*x+c)^9-8/715*sin(d*x+c)^2*cos(d*x+c)^9-16/6435*cos(d*x+c)^9)-28*a^8*(-1/15*sin(d*x+c)^5*cos(d*x+c)^10-1/39*sin(d*x+c)^3*cos(d*x+c)^10-1/143*sin(d*x+c)*cos(d*x+c)^10+1/1287*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))+56*I*a^8*(-1/15*sin(d*x+c)^4*cos(d*x+c)^11-4/195*sin(d*x+c)^2*cos(d*x+c)^11-8/2145*cos(d*x+c)^11)+70*a^8*(-1/15*sin(d*x+c)^3*cos(d*x+c)^12-1/65*cos(d*x+c)^12*sin(d*x+c)+1/715*(256/63+cos(d*x+c)^10+10/9*cos(d*x+c)^8+80/63*cos(d*x+c)^6+32/21*cos(d*x+c)^4+128/63*cos(d*x+c)^2)*sin(d*x+c))-56*I*a^8*(-1/15*sin(d*x+c)^2*cos(d*x+c)^13-2/195*cos(d*x+c)^13)-28*a^8*(-1/15*cos(d*x+c)^14*sin(d*x+c)+1/195*(1024/231+cos(d*x+c)^12+12/11*cos(d*x+c)^10+40/33*cos(d*x+c)^8+320/231*cos(d*x+c)^6+128/77*cos(d*x+c)^4+512/231*cos(d*x+c)^2)*sin(d*x+c))-8/15*I*a^8*cos(d*x+c)^15+1/15*a^8*(2048/429+cos(d*x+c)^14+14/13*cos(d*x+c)^12+168/143*cos(d*x+c)^10+560/429*cos(d*x+c)^8+640/429*cos(d*x+c)^6+256/143*cos(d*x+c)^4+1024/429*cos(d*x+c)^2)*sin(d*x+c))","B"
99,1,87,93,0.387000," ","int(sec(d*x+c)^10/(a+I*a*tan(d*x+c)),x)","\frac{\tan \left(d x +c \right)-\frac{i \left(\tan^{8}\left(d x +c \right)\right)}{8}+\frac{\left(\tan^{7}\left(d x +c \right)\right)}{7}-\frac{i \left(\tan^{6}\left(d x +c \right)\right)}{2}+\frac{3 \left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{3 i \left(\tan^{4}\left(d x +c \right)\right)}{4}+\tan^{3}\left(d x +c \right)-\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-1/8*I*tan(d*x+c)^8+1/7*tan(d*x+c)^7-1/2*I*tan(d*x+c)^6+3/5*tan(d*x+c)^5-3/4*I*tan(d*x+c)^4+tan(d*x+c)^3-1/2*I*tan(d*x+c)^2)","A"
100,1,68,70,0.345000," ","int(sec(d*x+c)^8/(a+I*a*tan(d*x+c)),x)","\frac{\tan \left(d x +c \right)-\frac{i \left(\tan^{6}\left(d x +c \right)\right)}{6}+\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{2}+\frac{2 \left(\tan^{3}\left(d x +c \right)\right)}{3}-\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-1/6*I*tan(d*x+c)^6+1/5*tan(d*x+c)^5-1/2*I*tan(d*x+c)^4+2/3*tan(d*x+c)^3-1/2*I*tan(d*x+c)^2)","A"
101,1,47,47,0.379000," ","int(sec(d*x+c)^6/(a+I*a*tan(d*x+c)),x)","\frac{\tan \left(d x +c \right)-\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{4}+\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-1/4*I*tan(d*x+c)^4+1/3*tan(d*x+c)^3-1/2*I*tan(d*x+c)^2)","A"
102,1,26,31,0.347000," ","int(sec(d*x+c)^4/(a+I*a*tan(d*x+c)),x)","\frac{\tan \left(d x +c \right)-\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-1/2*I*tan(d*x+c)^2)","A"
103,1,23,22,0.259000," ","int(sec(d*x+c)^2/(a+I*a*tan(d*x+c)),x)","-\frac{i \ln \left(a +i a \tan \left(d x +c \right)\right)}{a d}"," ",0,"-I/a/d*ln(a+I*a*tan(d*x+c))","A"
104,1,59,27,0.107000," ","int(1/(a+I*a*tan(d*x+c)),x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{4 d a}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{4 d a}+\frac{1}{2 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/4*I/d/a*ln(tan(d*x+c)+I)-1/4*I/d/a*ln(tan(d*x+c)-I)+1/2/d/a/(tan(d*x+c)-I)","B"
105,1,98,68,0.419000," ","int(cos(d*x+c)^2/(a+I*a*tan(d*x+c)),x)","\frac{3 i \ln \left(\tan \left(d x +c \right)+i\right)}{16 d a}+\frac{1}{8 a d \left(\tan \left(d x +c \right)+i\right)}-\frac{3 i \ln \left(\tan \left(d x +c \right)-i\right)}{16 d a}-\frac{i}{8 a d \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{4 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"3/16*I/a/d*ln(tan(d*x+c)+I)+1/8/a/d/(tan(d*x+c)+I)-3/16*I/a/d*ln(tan(d*x+c)-I)-1/8*I/a/d/(tan(d*x+c)-I)^2+1/4/d/a/(tan(d*x+c)-I)","A"
106,1,137,112,0.420000," ","int(cos(d*x+c)^4/(a+I*a*tan(d*x+c)),x)","\frac{i}{32 a d \left(\tan \left(d x +c \right)+i\right)^{2}}+\frac{5 i \ln \left(\tan \left(d x +c \right)+i\right)}{32 d a}+\frac{1}{8 a d \left(\tan \left(d x +c \right)+i\right)}-\frac{5 i \ln \left(\tan \left(d x +c \right)-i\right)}{32 d a}-\frac{3 i}{32 a d \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{24 a d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{3}{16 d a \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/32*I/a/d/(tan(d*x+c)+I)^2+5/32*I/a/d*ln(tan(d*x+c)+I)+1/8/a/d/(tan(d*x+c)+I)-5/32*I/a/d*ln(tan(d*x+c)-I)-3/32*I/a/d/(tan(d*x+c)-I)^2-1/24/a/d/(tan(d*x+c)-I)^3+3/16/d/a/(tan(d*x+c)-I)","A"
107,1,430,75,0.357000," ","int(sec(d*x+c)^7/(a+I*a*tan(d*x+c)),x)","\frac{5 i}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3 i}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{5}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 i}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{3 i}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{i}{5 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 a d}+\frac{5 i}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{i}{5 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}-\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{7}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3 i}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 a d}"," ",0,"5/8*I/a/d/(tan(1/2*d*x+1/2*c)-1)^2+7/8/a/d/(tan(1/2*d*x+1/2*c)-1)^2+3/8*I/a/d/(tan(1/2*d*x+1/2*c)-1)+5/8/a/d/(tan(1/2*d*x+1/2*c)-1)+3/4*I/a/d/(tan(1/2*d*x+1/2*c)-1)^3+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^3-3/8*I/a/d/(tan(1/2*d*x+1/2*c)+1)+1/4/a/d/(tan(1/2*d*x+1/2*c)-1)^4-1/5*I/a/d/(tan(1/2*d*x+1/2*c)+1)^5-3/8/a/d*ln(tan(1/2*d*x+1/2*c)-1)+5/8*I/a/d/(tan(1/2*d*x+1/2*c)+1)^2+5/8/a/d/(tan(1/2*d*x+1/2*c)+1)+1/2*I/a/d/(tan(1/2*d*x+1/2*c)-1)^4+1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^3+1/5*I/a/d/(tan(1/2*d*x+1/2*c)-1)^5-1/4/a/d/(tan(1/2*d*x+1/2*c)+1)^4+1/2*I/a/d/(tan(1/2*d*x+1/2*c)+1)^4-7/8/a/d/(tan(1/2*d*x+1/2*c)+1)^2-3/4*I/a/d/(tan(1/2*d*x+1/2*c)+1)^3+3/8/a/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
108,1,258,53,0.357000," ","int(sec(d*x+c)^5/(a+I*a*tan(d*x+c)),x)","\frac{i}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a d}-\frac{i}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a d}"," ",0,"1/3*I/a/d/(tan(1/2*d*x+1/2*c)-1)^3+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^2+1/2*I/a/d/(tan(1/2*d*x+1/2*c)-1)^2+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)+1/2*I/a/d/(tan(1/2*d*x+1/2*c)-1)-1/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)-1/3*I/a/d/(tan(1/2*d*x+1/2*c)+1)^3+1/2/a/d/(tan(1/2*d*x+1/2*c)+1)-1/2*I/a/d/(tan(1/2*d*x+1/2*c)+1)-1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2+1/2*I/a/d/(tan(1/2*d*x+1/2*c)+1)^2+1/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
109,1,85,30,0.352000," ","int(sec(d*x+c)^3/(a+I*a*tan(d*x+c)),x)","\frac{i}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a d}-\frac{i}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}"," ",0,"I/a/d/(tan(1/2*d*x+1/2*c)-1)-1/a/d*ln(tan(1/2*d*x+1/2*c)-1)-I/a/d/(tan(1/2*d*x+1/2*c)+1)+1/a/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
110,1,23,26,0.198000," ","int(sec(d*x+c)/(a+I*a*tan(d*x+c)),x)","\frac{2}{d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}"," ",0,"2/d/a/(tan(1/2*d*x+1/2*c)-I)","A"
111,1,75,41,0.443000," ","int(cos(d*x+c)/(a+I*a*tan(d*x+c)),x)","\frac{\frac{2}{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+4 i}-\frac{2}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{3}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d a}"," ",0,"2/d/a*(1/4/(tan(1/2*d*x+1/2*c)+I)-1/3/(tan(1/2*d*x+1/2*c)-I)^3+1/2*I/(tan(1/2*d*x+1/2*c)-I)^2+3/4/(tan(1/2*d*x+1/2*c)-I))","A"
112,1,141,59,0.420000," ","int(cos(d*x+c)^3/(a+I*a*tan(d*x+c)),x)","\frac{-\frac{i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}-\frac{1}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{5}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}-\frac{i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{3 i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{2}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{5}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{11}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d a}"," ",0,"2/d/a*(-1/8*I/(tan(1/2*d*x+1/2*c)+I)^2-1/12/(tan(1/2*d*x+1/2*c)+I)^3+5/16/(tan(1/2*d*x+1/2*c)+I)-1/2*I/(tan(1/2*d*x+1/2*c)-I)^4+3/4*I/(tan(1/2*d*x+1/2*c)-I)^2+1/5/(tan(1/2*d*x+1/2*c)-I)^5-5/6/(tan(1/2*d*x+1/2*c)-I)^3+11/16/(tan(1/2*d*x+1/2*c)-I))","B"
113,1,207,75,0.468000," ","int(cos(d*x+c)^5/(a+I*a*tan(d*x+c)),x)","\frac{\frac{i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{4}}-\frac{i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}+\frac{1}{10 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{5}}-\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{11}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}-\frac{2}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}+\frac{15 i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{11 i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{21}{10 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{11}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{21}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d a}"," ",0,"2/d/a*(1/8*I/(tan(1/2*d*x+1/2*c)+I)^4-1/4*I/(tan(1/2*d*x+1/2*c)+I)^2+1/20/(tan(1/2*d*x+1/2*c)+I)^5-1/4/(tan(1/2*d*x+1/2*c)+I)^3+11/32/(tan(1/2*d*x+1/2*c)+I)-1/7/(tan(1/2*d*x+1/2*c)-I)^7+1/2*I/(tan(1/2*d*x+1/2*c)-I)^6+15/16*I/(tan(1/2*d*x+1/2*c)-I)^2-11/8*I/(tan(1/2*d*x+1/2*c)-I)^4+21/20/(tan(1/2*d*x+1/2*c)-I)^5-11/8/(tan(1/2*d*x+1/2*c)-I)^3+21/32/(tan(1/2*d*x+1/2*c)-I))","B"
114,1,78,70,0.414000," ","int(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^2,x)","\frac{\tan \left(d x +c \right)-\frac{\left(\tan^{7}\left(d x +c \right)\right)}{7}-\frac{i \left(\tan^{6}\left(d x +c \right)\right)}{3}-\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}-i \left(\tan^{4}\left(d x +c \right)\right)+\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-i \left(\tan^{2}\left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/d/a^2*(tan(d*x+c)-1/7*tan(d*x+c)^7-1/3*I*tan(d*x+c)^6-1/5*tan(d*x+c)^5-I*tan(d*x+c)^4+1/3*tan(d*x+c)^3-I*tan(d*x+c)^2)","A"
115,1,47,47,0.348000," ","int(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^2,x)","\frac{\tan \left(d x +c \right)-\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{2}-i \left(\tan^{2}\left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/d/a^2*(tan(d*x+c)-1/5*tan(d*x+c)^5-1/2*I*tan(d*x+c)^4-I*tan(d*x+c)^2)","A"
116,1,36,23,0.361000," ","int(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^2,x)","\frac{\tan \left(d x +c \right)-\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-i \left(\tan^{2}\left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/d/a^2*(tan(d*x+c)-1/3*tan(d*x+c)^3-I*tan(d*x+c)^2)","A"
117,1,35,37,0.360000," ","int(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{2} d}-\frac{\tan \left(d x +c \right)}{a^{2} d}"," ",0,"-2*I/a^2/d*ln(tan(d*x+c)-I)-tan(d*x+c)/a^2/d","A"
118,1,24,24,0.267000," ","int(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x)","\frac{i}{a d \left(a +i a \tan \left(d x +c \right)\right)}"," ",0,"I/a/d/(a+I*a*tan(d*x+c))","A"
119,1,79,51,0.105000," ","int(1/(a+I*a*tan(d*x+c))^2,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{8 a^{2} d}-\frac{i}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{4 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/8*I/d/a^2*ln(tan(d*x+c)+I)-1/8*I/d/a^2*ln(tan(d*x+c)-I)-1/4*I/d/a^2/(tan(d*x+c)-I)^2+1/4/d/a^2/(tan(d*x+c)-I)","A"
120,1,117,96,0.435000," ","int(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{8 d \,a^{2}}+\frac{1}{16 a^{2} d \left(\tan \left(d x +c \right)+i\right)}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{8 a^{2} d}-\frac{i}{8 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{12 a^{2} d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{3}{16 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/8*I/d/a^2*ln(tan(d*x+c)+I)+1/16/a^2/d/(tan(d*x+c)+I)-1/8*I/d/a^2*ln(tan(d*x+c)-I)-1/8*I/a^2/d/(tan(d*x+c)-I)^2-1/12/a^2/d/(tan(d*x+c)-I)^3+3/16/d/a^2/(tan(d*x+c)-I)","A"
121,1,157,139,0.434000," ","int(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x)","\frac{i}{64 a^{2} d \left(\tan \left(d x +c \right)+i\right)^{2}}+\frac{15 i \ln \left(\tan \left(d x +c \right)+i\right)}{128 d \,a^{2}}+\frac{5}{64 a^{2} d \left(\tan \left(d x +c \right)+i\right)}-\frac{15 i \ln \left(\tan \left(d x +c \right)-i\right)}{128 a^{2} d}+\frac{i}{32 a^{2} d \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{3 i}{32 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{16 a^{2} d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{5}{32 d \,a^{2} \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/64*I/a^2/d/(tan(d*x+c)+I)^2+15/128*I/a^2/d*ln(tan(d*x+c)+I)+5/64/a^2/d/(tan(d*x+c)+I)-15/128*I/a^2/d*ln(tan(d*x+c)-I)+1/32*I/a^2/d/(tan(d*x+c)-I)^4-3/32*I/a^2/d/(tan(d*x+c)-I)^2-1/16/a^2/d/(tan(d*x+c)-I)^3+5/32/d/a^2/(tan(d*x+c)-I)","A"
122,1,514,112,0.384000," ","int(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^2,x)","-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{5 i}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{9}{16 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3 i}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{9}{16 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 i}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{6 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{3 i}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}+\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{1}{6 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{6}}-\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{16 a^{2} d}+\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{2 i}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{9}{16 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1}{6 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3 i}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{5 i}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{9}{16 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{2 i}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}+\frac{1}{6 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{16 a^{2} d}"," ",0,"-1/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)^4+5/4*I/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+9/16/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2+3/4*I/a^2/d/(tan(1/2*d*x+1/2*c)-1)+9/16/a^2/d/(tan(1/2*d*x+1/2*c)-1)-3/4*I/a^2/d/(tan(1/2*d*x+1/2*c)+1)-1/6/d/a^2/(tan(1/2*d*x+1/2*c)-1)^3-3/2*I/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-1/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)^5+I/a^2/d/(tan(1/2*d*x+1/2*c)-1)^4-1/6/a^2/d/(tan(1/2*d*x+1/2*c)-1)^6-7/16/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)+1/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4-2/5*I/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5+9/16/a^2/d/(tan(1/2*d*x+1/2*c)+1)+I/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4-1/6/d/a^2/(tan(1/2*d*x+1/2*c)+1)^3+3/2*I/a^2/d/(tan(1/2*d*x+1/2*c)-1)^3-1/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5+5/4*I/a^2/d/(tan(1/2*d*x+1/2*c)-1)^2-9/16/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2+2/5*I/a^2/d/(tan(1/2*d*x+1/2*c)-1)^5+1/6/a^2/d/(tan(1/2*d*x+1/2*c)+1)^6+7/16/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
123,1,342,90,0.385000," ","int(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^2,x)","\frac{3}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{8 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 a^{2} d}+\frac{3}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 i}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{8 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{2 i}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 a^{2} d}"," ",0,"3/8/a^2/d/(tan(1/2*d*x+1/2*c)-1)+I/a^2/d/(tan(1/2*d*x+1/2*c)-1)+1/8/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2+I/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2-1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^3-I/a^2/d/(tan(1/2*d*x+1/2*c)+1)-1/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)^4-5/8/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)+3/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)-2/3*I/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-1/8/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2+2/3*I/a^2/d/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^3+I/a^2/d/(tan(1/2*d*x+1/2*c)-1)^2+1/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4+5/8/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
124,1,170,68,0.367000," ","int(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x)","-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a^{2} d}-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a^{2} d}"," ",0,"-1/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)+2*I/a^2/d/(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2-3/2/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)-1/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)-2*I/a^2/d/(tan(1/2*d*x+1/2*c)+1)+1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2+3/2/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
125,1,63,46,0.414000," ","int(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x)","\frac{4}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a^{2} d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a^{2} d}"," ",0,"4/a^2/d/(tan(1/2*d*x+1/2*c)-I)+1/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)-1/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)","A"
126,1,57,57,0.215000," ","int(sec(d*x+c)/(a+I*a*tan(d*x+c))^2,x)","\frac{\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}-\frac{4}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{2 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}}{a^{2} d}"," ",0,"2/d/a^2*(1/(tan(1/2*d*x+1/2*c)-I)-2/3/(tan(1/2*d*x+1/2*c)-I)^3+I/(tan(1/2*d*x+1/2*c)-I)^2)","A"
127,1,108,63,0.422000," ","int(cos(d*x+c)/(a+I*a*tan(d*x+c))^2,x)","\frac{\frac{2}{8 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+8 i}-\frac{2 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{5 i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{4}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{3}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{7}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{a^{2} d}"," ",0,"2/d/a^2*(1/8/(tan(1/2*d*x+1/2*c)+I)-I/(tan(1/2*d*x+1/2*c)-I)^4+5/4*I/(tan(1/2*d*x+1/2*c)-I)^2+2/5/(tan(1/2*d*x+1/2*c)-I)^5-3/2/(tan(1/2*d*x+1/2*c)-I)^3+7/8/(tan(1/2*d*x+1/2*c)-I))","A"
128,1,174,79,0.428000," ","int(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x)","\frac{-\frac{i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}-\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}+\frac{2 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{5 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{23 i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{4}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{55}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{13}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{a^{2} d}"," ",0,"2/d/a^2*(-1/16*I/(tan(1/2*d*x+1/2*c)+I)^2-1/24/(tan(1/2*d*x+1/2*c)+I)^3+3/16/(tan(1/2*d*x+1/2*c)+I)+I/(tan(1/2*d*x+1/2*c)-I)^6-5/2*I/(tan(1/2*d*x+1/2*c)-I)^4+23/16*I/(tan(1/2*d*x+1/2*c)-I)^2-2/7/(tan(1/2*d*x+1/2*c)-I)^7+2/(tan(1/2*d*x+1/2*c)-I)^5-55/24/(tan(1/2*d*x+1/2*c)-I)^3+13/16/(tan(1/2*d*x+1/2*c)-I))","B"
129,1,240,95,0.420000," ","int(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x)","\frac{\frac{i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{4}}-\frac{9 i}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}+\frac{1}{20 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{5}}-\frac{13}{48 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{29}{64 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}-\frac{2 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{51 i}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{49 i}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{35 i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{4}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}-\frac{5}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{49}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{49}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{99}{64 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{a^{2} d}"," ",0,"2/d/a^2*(1/16*I/(tan(1/2*d*x+1/2*c)+I)^4-9/64*I/(tan(1/2*d*x+1/2*c)+I)^2+1/40/(tan(1/2*d*x+1/2*c)+I)^5-13/96/(tan(1/2*d*x+1/2*c)+I)^3+29/128/(tan(1/2*d*x+1/2*c)+I)-I/(tan(1/2*d*x+1/2*c)-I)^8+51/32*I/(tan(1/2*d*x+1/2*c)-I)^2+49/12*I/(tan(1/2*d*x+1/2*c)-I)^6-35/8*I/(tan(1/2*d*x+1/2*c)-I)^4+2/9/(tan(1/2*d*x+1/2*c)-I)^9-5/2/(tan(1/2*d*x+1/2*c)-I)^7+49/10/(tan(1/2*d*x+1/2*c)-I)^5-49/16/(tan(1/2*d*x+1/2*c)-I)^3+99/128/(tan(1/2*d*x+1/2*c)-I))","B"
130,1,89,93,0.452000," ","int(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^3,x)","\frac{\tan \left(d x +c \right)+\frac{i \left(\tan^{10}\left(d x +c \right)\right)}{10}-\frac{\left(\tan^{9}\left(d x +c \right)\right)}{3}-\frac{8 \left(\tan^{7}\left(d x +c \right)\right)}{7}-i \left(\tan^{6}\left(d x +c \right)\right)-\frac{6 \left(\tan^{5}\left(d x +c \right)\right)}{5}-2 i \left(\tan^{4}\left(d x +c \right)\right)-\frac{3 i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d \,a^{3}}"," ",0,"1/d/a^3*(tan(d*x+c)+1/10*I*tan(d*x+c)^10-1/3*tan(d*x+c)^9-8/7*tan(d*x+c)^7-I*tan(d*x+c)^6-6/5*tan(d*x+c)^5-2*I*tan(d*x+c)^4-3/2*I*tan(d*x+c)^2)","A"
131,1,89,70,0.388000," ","int(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^3,x)","\frac{\tan \left(d x +c \right)+\frac{i \left(\tan^{8}\left(d x +c \right)\right)}{8}-\frac{3 \left(\tan^{7}\left(d x +c \right)\right)}{7}-\frac{i \left(\tan^{6}\left(d x +c \right)\right)}{6}-\left(\tan^{5}\left(d x +c \right)\right)-\frac{5 i \left(\tan^{4}\left(d x +c \right)\right)}{4}-\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\frac{3 i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d \,a^{3}}"," ",0,"1/d/a^3*(tan(d*x+c)+1/8*I*tan(d*x+c)^8-3/7*tan(d*x+c)^7-1/6*I*tan(d*x+c)^6-tan(d*x+c)^5-5/4*I*tan(d*x+c)^4-1/3*tan(d*x+c)^3-3/2*I*tan(d*x+c)^2)","A"
132,1,68,47,0.384000," ","int(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^3,x)","\frac{\tan \left(d x +c \right)+\frac{i \left(\tan^{6}\left(d x +c \right)\right)}{6}-\frac{3 \left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{2}-\frac{2 \left(\tan^{3}\left(d x +c \right)\right)}{3}-\frac{3 i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d \,a^{3}}"," ",0,"1/d/a^3*(tan(d*x+c)+1/6*I*tan(d*x+c)^6-3/5*tan(d*x+c)^5-1/2*I*tan(d*x+c)^4-2/3*tan(d*x+c)^3-3/2*I*tan(d*x+c)^2)","A"
133,1,47,23,0.394000," ","int(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^3,x)","\frac{\tan \left(d x +c \right)+\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{4}-\left(\tan^{3}\left(d x +c \right)\right)-\frac{3 i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d \,a^{3}}"," ",0,"1/d/a^3*(tan(d*x+c)+1/4*I*tan(d*x+c)^4-tan(d*x+c)^3-3/2*I*tan(d*x+c)^2)","A"
134,1,52,54,0.384000," ","int(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^3,x)","-\frac{3 \tan \left(d x +c \right)}{a^{3} d}+\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2 a^{3} d}-\frac{4 i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{3} d}"," ",0,"-3*tan(d*x+c)/a^3/d+1/2*I*tan(d*x+c)^2/a^3/d-4*I/a^3/d*ln(tan(d*x+c)-I)","A"
135,1,40,47,0.433000," ","int(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x)","\frac{2}{a^{3} d \left(\tan \left(d x +c \right)-i\right)}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{3} d}"," ",0,"2/a^3/d/(tan(d*x+c)-I)+I/a^3/d*ln(tan(d*x+c)-I)","A"
136,1,24,23,0.260000," ","int(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x)","\frac{i}{2 a d \left(a +i a \tan \left(d x +c \right)\right)^{2}}"," ",0,"1/2*I/a/d/(a+I*a*tan(d*x+c))^2","A"
137,1,98,74,0.109000," ","int(1/(a+I*a*tan(d*x+c))^3,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{16 d \,a^{3}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{16 a^{3} d}-\frac{i}{8 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{6 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{1}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/16*I/d/a^3*ln(tan(d*x+c)+I)-1/16*I/a^3/d*ln(tan(d*x+c)-I)-1/8*I/d/a^3/(tan(d*x+c)-I)^2-1/6/d/a^3/(tan(d*x+c)-I)^3+1/8/a^3/d/(tan(d*x+c)-I)","A"
138,1,137,119,0.414000," ","int(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x)","\frac{5 i \ln \left(\tan \left(d x +c \right)+i\right)}{64 d \,a^{3}}+\frac{1}{32 a^{3} d \left(\tan \left(d x +c \right)+i\right)}-\frac{5 i \ln \left(\tan \left(d x +c \right)-i\right)}{64 a^{3} d}+\frac{i}{16 a^{3} d \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{3 i}{32 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{12 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{1}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"5/64*I/a^3/d*ln(tan(d*x+c)+I)+1/32/a^3/d/(tan(d*x+c)+I)-5/64*I/a^3/d*ln(tan(d*x+c)-I)+1/16*I/a^3/d/(tan(d*x+c)-I)^4-3/32*I/a^3/d/(tan(d*x+c)-I)^2-1/12/d/a^3/(tan(d*x+c)-I)^3+1/8/a^3/d/(tan(d*x+c)-I)","A"
139,1,176,165,0.421000," ","int(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x)","\frac{i}{128 a^{3} d \left(\tan \left(d x +c \right)+i\right)^{2}}+\frac{21 i \ln \left(\tan \left(d x +c \right)+i\right)}{256 d \,a^{3}}+\frac{3}{64 a^{3} d \left(\tan \left(d x +c \right)+i\right)}-\frac{21 i \ln \left(\tan \left(d x +c \right)-i\right)}{256 a^{3} d}+\frac{3 i}{64 a^{3} d \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{5 i}{64 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{40 a^{3} d \left(\tan \left(d x +c \right)-i\right)^{5}}-\frac{1}{16 d \,a^{3} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{15}{128 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/128*I/a^3/d/(tan(d*x+c)+I)^2+21/256*I/a^3/d*ln(tan(d*x+c)+I)+3/64/a^3/d/(tan(d*x+c)+I)-21/256*I/a^3/d*ln(tan(d*x+c)-I)+3/64*I/a^3/d/(tan(d*x+c)-I)^4-5/64*I/a^3/d/(tan(d*x+c)-I)^2+1/40/a^3/d/(tan(d*x+c)-I)^5-1/16/d/a^3/(tan(d*x+c)-I)^3+15/128/a^3/d/(tan(d*x+c)-I)","A"
140,1,430,106,0.412000," ","int(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^3,x)","-\frac{i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{7 i}{12 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{3}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{13 i}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{5}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{i}{5 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 a^{3} d}+\frac{11 i}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{i}{5 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}+\frac{3}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{11 i}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{7 i}{12 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{13 i}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 a^{3} d}"," ",0,"-1/2*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4+1/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)+7/12*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^3-3/4/a^3/d/(tan(1/2*d*x+1/2*c)-1)^4+13/8*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)-5/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2-1/2*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^4-3/2/a^3/d/(tan(1/2*d*x+1/2*c)-1)^3+1/5*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5-7/8/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)+11/8*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2+5/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-1/5*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^5+3/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4+11/8*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2+1/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)-7/12*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3-3/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3-13/8*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)+7/8/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
141,1,258,84,0.397000," ","int(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^3,x)","-\frac{i}{3 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{7 i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a^{3} d}+\frac{i}{3 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{7 i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a^{3} d}"," ",0,"-1/3*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^3-3/2/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2-1/2*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2-3/2/a^3/d/(tan(1/2*d*x+1/2*c)-1)+7/2*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)-5/2/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)+1/3*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3+3/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-1/2*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-3/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)-7/2*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)+5/2/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
142,1,108,62,0.392000," ","int(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x)","-\frac{i}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a^{3} d}+\frac{i}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a^{3} d}+\frac{8}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}"," ",0,"-I/a^3/d/(tan(1/2*d*x+1/2*c)-1)+3/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)+I/a^3/d/(tan(1/2*d*x+1/2*c)+1)-3/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)+8/a^3/d/(tan(1/2*d*x+1/2*c)-I)","A"
143,1,57,28,0.454000," ","int(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x)","\frac{\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}-\frac{8}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}}{a^{3} d}"," ",0,"2/d/a^3*(1/(tan(1/2*d*x+1/2*c)-I)-4/3/(tan(1/2*d*x+1/2*c)-I)^3+2*I/(tan(1/2*d*x+1/2*c)-I)^2)","A"
144,1,90,86,0.226000," ","int(sec(d*x+c)/(a+I*a*tan(d*x+c))^3,x)","\frac{\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}-\frac{16}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{8}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}}{d \,a^{3}}"," ",0,"2/d/a^3*(2*I/(tan(1/2*d*x+1/2*c)-I)^2+1/(tan(1/2*d*x+1/2*c)-I)-8/3/(tan(1/2*d*x+1/2*c)-I)^3+4/5/(tan(1/2*d*x+1/2*c)-I)^5-2*I/(tan(1/2*d*x+1/2*c)-I)^4)","A"
145,1,141,89,0.410000," ","int(cos(d*x+c)/(a+I*a*tan(d*x+c))^3,x)","\frac{\frac{2}{16 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+16 i}+\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{9 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{17 i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{8}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{38}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{15}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{15}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{3}}"," ",0,"2/d/a^3*(1/16/(tan(1/2*d*x+1/2*c)+I)+2*I/(tan(1/2*d*x+1/2*c)-I)^6-9/2*I/(tan(1/2*d*x+1/2*c)-I)^4+17/8*I/(tan(1/2*d*x+1/2*c)-I)^2-4/7/(tan(1/2*d*x+1/2*c)-I)^7+19/5/(tan(1/2*d*x+1/2*c)-I)^5-15/4/(tan(1/2*d*x+1/2*c)-I)^3+15/16/(tan(1/2*d*x+1/2*c)-I))","A"
146,1,207,107,0.426000," ","int(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x)","\frac{-\frac{i}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}-\frac{1}{24 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{7}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}+\frac{46 i}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{9 i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{59 i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{8}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}-\frac{68}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{35}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{19}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{57}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{3}}"," ",0,"2/d/a^3*(-1/32*I/(tan(1/2*d*x+1/2*c)+I)^2-1/48/(tan(1/2*d*x+1/2*c)+I)^3+7/64/(tan(1/2*d*x+1/2*c)+I)+23/3*I/(tan(1/2*d*x+1/2*c)-I)^6-2*I/(tan(1/2*d*x+1/2*c)-I)^8+9/4*I/(tan(1/2*d*x+1/2*c)-I)^2-59/8*I/(tan(1/2*d*x+1/2*c)-I)^4+4/9/(tan(1/2*d*x+1/2*c)-I)^9-34/7/(tan(1/2*d*x+1/2*c)-I)^7+35/4/(tan(1/2*d*x+1/2*c)-I)^5-19/4/(tan(1/2*d*x+1/2*c)-I)^3+57/64/(tan(1/2*d*x+1/2*c)-I))","A"
147,1,273,123,0.419000," ","int(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x)","\frac{-\frac{23 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{10}}+\frac{1}{40 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{5}}-\frac{7}{48 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{37}{128 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}+\frac{217 i}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}+\frac{303 i}{64 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{5 i}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}+\frac{i}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{4}}-\frac{169 i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}-\frac{8}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{11}}+\frac{106}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}-\frac{33}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{623}{20 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{365}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{219}{128 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{3}}"," ",0,"2/d/a^3*(-23/2*I/(tan(1/2*d*x+1/2*c)-I)^8+2*I/(tan(1/2*d*x+1/2*c)-I)^10+1/80/(tan(1/2*d*x+1/2*c)+I)^5-7/96/(tan(1/2*d*x+1/2*c)+I)^3+37/256/(tan(1/2*d*x+1/2*c)+I)+217/12*I/(tan(1/2*d*x+1/2*c)-I)^6+303/128*I/(tan(1/2*d*x+1/2*c)-I)^2-5/64*I/(tan(1/2*d*x+1/2*c)+I)^2+1/32*I/(tan(1/2*d*x+1/2*c)+I)^4-169/16*I/(tan(1/2*d*x+1/2*c)-I)^4-4/11/(tan(1/2*d*x+1/2*c)-I)^11+53/9/(tan(1/2*d*x+1/2*c)-I)^9-33/2/(tan(1/2*d*x+1/2*c)-I)^7+623/40/(tan(1/2*d*x+1/2*c)-I)^5-365/64/(tan(1/2*d*x+1/2*c)-I)^3+219/256/(tan(1/2*d*x+1/2*c)-I))","B"
148,1,99,70,0.415000," ","int(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^4,x)","\frac{\tan \left(d x +c \right)+\frac{\left(\tan^{9}\left(d x +c \right)\right)}{9}+\frac{i \left(\tan^{8}\left(d x +c \right)\right)}{2}-\frac{4 \left(\tan^{7}\left(d x +c \right)\right)}{7}+\frac{2 i \left(\tan^{6}\left(d x +c \right)\right)}{3}-2 \left(\tan^{5}\left(d x +c \right)\right)-i \left(\tan^{4}\left(d x +c \right)\right)-\frac{4 \left(\tan^{3}\left(d x +c \right)\right)}{3}-2 i \left(\tan^{2}\left(d x +c \right)\right)}{d \,a^{4}}"," ",0,"1/d/a^4*(tan(d*x+c)+1/9*tan(d*x+c)^9+1/2*I*tan(d*x+c)^8-4/7*tan(d*x+c)^7+2/3*I*tan(d*x+c)^6-2*tan(d*x+c)^5-I*tan(d*x+c)^4-4/3*tan(d*x+c)^3-2*I*tan(d*x+c)^2)","A"
149,1,67,47,0.388000," ","int(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^4,x)","\frac{\tan \left(d x +c \right)+\frac{\left(\tan^{7}\left(d x +c \right)\right)}{7}+\frac{2 i \left(\tan^{6}\left(d x +c \right)\right)}{3}-\left(\tan^{5}\left(d x +c \right)\right)-\frac{5 \left(\tan^{3}\left(d x +c \right)\right)}{3}-2 i \left(\tan^{2}\left(d x +c \right)\right)}{d \,a^{4}}"," ",0,"1/d/a^4*(tan(d*x+c)+1/7*tan(d*x+c)^7+2/3*I*tan(d*x+c)^6-tan(d*x+c)^5-5/3*tan(d*x+c)^3-2*I*tan(d*x+c)^2)","A"
150,1,57,23,0.376000," ","int(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^4,x)","\frac{\tan \left(d x +c \right)+\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}+i \left(\tan^{4}\left(d x +c \right)\right)-2 \left(\tan^{3}\left(d x +c \right)\right)-2 i \left(\tan^{2}\left(d x +c \right)\right)}{d \,a^{4}}"," ",0,"1/d/a^4*(tan(d*x+c)+1/5*tan(d*x+c)^5+I*tan(d*x+c)^4-2*tan(d*x+c)^3-2*I*tan(d*x+c)^2)","B"
151,1,68,83,0.398000," ","int(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^4,x)","-\frac{7 \tan \left(d x +c \right)}{a^{4} d}+\frac{\tan^{3}\left(d x +c \right)}{3 a^{4} d}+\frac{2 i \left(\tan^{2}\left(d x +c \right)\right)}{a^{4} d}-\frac{8 i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{4} d}"," ",0,"-7*tan(d*x+c)/a^4/d+1/3/a^4/d*tan(d*x+c)^3+2*I/a^4/d*tan(d*x+c)^2-8*I/a^4/d*ln(tan(d*x+c)-I)","A"
152,1,53,60,0.389000," ","int(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^4,x)","\frac{\tan \left(d x +c \right)}{a^{4} d}+\frac{4}{a^{4} d \left(\tan \left(d x +c \right)-i\right)}+\frac{4 i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{4} d}"," ",0,"tan(d*x+c)/a^4/d+4/a^4/d/(tan(d*x+c)-I)+4*I/a^4/d*ln(tan(d*x+c)-I)","A"
153,1,36,28,0.449000," ","int(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x)","\frac{-\frac{1}{\tan \left(d x +c \right)-i}-\frac{i}{\left(\tan \left(d x +c \right)-i\right)^{2}}}{d \,a^{4}}"," ",0,"1/d/a^4*(-1/(tan(d*x+c)-I)-I/(tan(d*x+c)-I)^2)","A"
154,1,24,23,0.266000," ","int(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x)","\frac{i}{3 a d \left(a +i a \tan \left(d x +c \right)\right)^{3}}"," ",0,"1/3*I/a/d/(a+I*a*tan(d*x+c))^3","A"
155,1,118,98,0.109000," ","int(1/(a+I*a*tan(d*x+c))^4,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{32 d \,a^{4}}+\frac{i}{8 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{32 a^{4} d}-\frac{i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{12 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{1}{16 a^{4} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/32*I/d/a^4*ln(tan(d*x+c)+I)+1/8*I/d/a^4/(tan(d*x+c)-I)^4-1/32*I/d/a^4*ln(tan(d*x+c)-I)-1/16*I/d/a^4/(tan(d*x+c)-I)^2-1/12/d/a^4/(tan(d*x+c)-I)^3+1/16/a^4/d/(tan(d*x+c)-I)","A"
156,1,156,143,0.428000," ","int(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x)","\frac{3 i \ln \left(\tan \left(d x +c \right)+i\right)}{64 d \,a^{4}}+\frac{1}{64 a^{4} d \left(\tan \left(d x +c \right)+i\right)}-\frac{3 i \ln \left(\tan \left(d x +c \right)-i\right)}{64 a^{4} d}+\frac{i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{i}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{20 a^{4} d \left(\tan \left(d x +c \right)-i\right)^{5}}-\frac{1}{16 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{5}{64 a^{4} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"3/64*I/a^4/d*ln(tan(d*x+c)+I)+1/64/a^4/d/(tan(d*x+c)+I)-3/64*I/a^4/d*ln(tan(d*x+c)-I)+1/16*I/a^4/d/(tan(d*x+c)-I)^4-1/16*I/d/a^4/(tan(d*x+c)-I)^2+1/20/a^4/d/(tan(d*x+c)-I)^5-1/16/d/a^4/(tan(d*x+c)-I)^3+5/64/a^4/d/(tan(d*x+c)-I)","A"
157,1,196,190,0.430000," ","int(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x)","\frac{i}{256 a^{4} d \left(\tan \left(d x +c \right)+i\right)^{2}}+\frac{7 i \ln \left(\tan \left(d x +c \right)+i\right)}{128 d \,a^{4}}+\frac{7}{256 a^{4} d \left(\tan \left(d x +c \right)+i\right)}-\frac{7 i \ln \left(\tan \left(d x +c \right)-i\right)}{128 a^{4} d}+\frac{3 i}{64 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{i}{48 a^{4} d \left(\tan \left(d x +c \right)-i\right)^{6}}-\frac{15 i}{256 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{3}{80 a^{4} d \left(\tan \left(d x +c \right)-i\right)^{5}}-\frac{5}{96 d \,a^{4} \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{21}{256 a^{4} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/256*I/a^4/d/(tan(d*x+c)+I)^2+7/128*I/a^4/d*ln(tan(d*x+c)+I)+7/256/a^4/d/(tan(d*x+c)+I)-7/128*I/a^4/d*ln(tan(d*x+c)-I)+3/64*I/a^4/d/(tan(d*x+c)-I)^4-1/48*I/a^4/d/(tan(d*x+c)-I)^6-15/256*I/a^4/d/(tan(d*x+c)-I)^2+3/80/a^4/d/(tan(d*x+c)-I)^5-5/96/d/a^4/(tan(d*x+c)-I)^3+21/256/a^4/d/(tan(d*x+c)-I)","A"
158,1,342,121,0.418000," ","int(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^4,x)","\frac{1}{2 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{4 i}{3 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{25}{8 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{2 i}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{27}{8 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{6 i}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{4 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{35 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 d \,a^{4}}+\frac{25}{8 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{4 i}{3 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{1}{2 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{6 i}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{27}{8 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 i}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{4 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{35 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 d \,a^{4}}"," ",0,"1/2/a^4/d/(tan(1/2*d*x+1/2*c)-1)^3+4/3*I/a^4/d/(tan(1/2*d*x+1/2*c)+1)^3-25/8/a^4/d/(tan(1/2*d*x+1/2*c)-1)^2-2*I/a^4/d/(tan(1/2*d*x+1/2*c)+1)^2-27/8/a^4/d/(tan(1/2*d*x+1/2*c)-1)-6*I/a^4/d/(tan(1/2*d*x+1/2*c)+1)+1/4/a^4/d/(tan(1/2*d*x+1/2*c)-1)^4-35/8/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)+25/8/a^4/d/(tan(1/2*d*x+1/2*c)+1)^2-4/3*I/a^4/d/(tan(1/2*d*x+1/2*c)-1)^3+1/2/a^4/d/(tan(1/2*d*x+1/2*c)+1)^3+6*I/a^4/d/(tan(1/2*d*x+1/2*c)-1)-27/8/a^4/d/(tan(1/2*d*x+1/2*c)+1)-2*I/a^4/d/(tan(1/2*d*x+1/2*c)-1)^2-1/4/a^4/d/(tan(1/2*d*x+1/2*c)+1)^4+35/8/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)","B"
159,1,192,99,0.417000," ","int(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^4,x)","\frac{1}{2 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{4 i}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{2 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,a^{4}}+\frac{1}{2 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{4 i}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{2 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,a^{4}}+\frac{16}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}"," ",0,"1/2/a^4/d/(tan(1/2*d*x+1/2*c)-1)-4*I/a^4/d/(tan(1/2*d*x+1/2*c)-1)+1/2/a^4/d/(tan(1/2*d*x+1/2*c)-1)^2+15/2/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)+1/2/a^4/d/(tan(1/2*d*x+1/2*c)+1)+4*I/a^4/d/(tan(1/2*d*x+1/2*c)+1)-1/2/a^4/d/(tan(1/2*d*x+1/2*c)+1)^2-15/2/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)+16/a^4/d/(tan(1/2*d*x+1/2*c)-I)","A"
160,1,86,76,0.467000," ","int(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x)","-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{4}}+\frac{8 i}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{16}{3 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}"," ",0,"-1/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)+8*I/a^4/d/(tan(1/2*d*x+1/2*c)-I)^2-16/3/a^4/d/(tan(1/2*d*x+1/2*c)-I)^3","A"
161,1,90,60,0.469000," ","int(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x)","\frac{\frac{6 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{8 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}-\frac{28}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{16}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}}{a^{4} d}"," ",0,"2/d/a^4*(3*I/(tan(1/2*d*x+1/2*c)-I)^2-4*I/(tan(1/2*d*x+1/2*c)-I)^4+1/(tan(1/2*d*x+1/2*c)-I)-14/3/(tan(1/2*d*x+1/2*c)-I)^3+8/5/(tan(1/2*d*x+1/2*c)-I)^5)","A"
162,1,123,116,0.227000," ","int(sec(d*x+c)/(a+I*a*tan(d*x+c))^4,x)","\frac{\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}+\frac{72}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{16}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}-\frac{16 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{6 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{12}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{8 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}}{d \,a^{4}}"," ",0,"2/d/a^4*(1/(tan(1/2*d*x+1/2*c)-I)+36/5/(tan(1/2*d*x+1/2*c)-I)^5-8/7/(tan(1/2*d*x+1/2*c)-I)^7-8*I/(tan(1/2*d*x+1/2*c)-I)^4+3*I/(tan(1/2*d*x+1/2*c)-I)^2-6/(tan(1/2*d*x+1/2*c)-I)^3+4*I/(tan(1/2*d*x+1/2*c)-I)^6)","A"
163,1,174,118,0.428000," ","int(cos(d*x+c)/(a+I*a*tan(d*x+c))^4,x)","\frac{\frac{2}{32 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+32 i}+\frac{86 i}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{8 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}-\frac{49 i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{49 i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{16}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}-\frac{132}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{31}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{173}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{31}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{4}}"," ",0,"2/d/a^4*(1/32/(tan(1/2*d*x+1/2*c)+I)+43/3*I/(tan(1/2*d*x+1/2*c)-I)^6-4*I/(tan(1/2*d*x+1/2*c)-I)^8-49/4*I/(tan(1/2*d*x+1/2*c)-I)^4+49/16*I/(tan(1/2*d*x+1/2*c)-I)^2+8/9/(tan(1/2*d*x+1/2*c)-I)^9-66/7/(tan(1/2*d*x+1/2*c)-I)^7+31/2/(tan(1/2*d*x+1/2*c)-I)^5-173/24/(tan(1/2*d*x+1/2*c)-I)^3+31/32/(tan(1/2*d*x+1/2*c)-I))","A"
164,1,240,138,0.437000," ","int(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x)","\frac{-\frac{i}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}-\frac{1}{48 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{2}{16 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+16 i}+\frac{8 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{10}}-\frac{67 i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}-\frac{44 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{385 i}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}+\frac{201 i}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{16}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{11}}+\frac{208}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}-\frac{61}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{105}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{267}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{15}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{4}}"," ",0,"2/d/a^4*(-1/64*I/(tan(1/2*d*x+1/2*c)+I)^2-1/96/(tan(1/2*d*x+1/2*c)+I)^3+1/16/(tan(1/2*d*x+1/2*c)+I)+4*I/(tan(1/2*d*x+1/2*c)-I)^10-67/4*I/(tan(1/2*d*x+1/2*c)-I)^4-22*I/(tan(1/2*d*x+1/2*c)-I)^8+385/12*I/(tan(1/2*d*x+1/2*c)-I)^6+201/64*I/(tan(1/2*d*x+1/2*c)-I)^2-8/11/(tan(1/2*d*x+1/2*c)-I)^11+104/9/(tan(1/2*d*x+1/2*c)-I)^9-61/2/(tan(1/2*d*x+1/2*c)-I)^7+105/4/(tan(1/2*d*x+1/2*c)-I)^5-267/32/(tan(1/2*d*x+1/2*c)-I)^3+15/16/(tan(1/2*d*x+1/2*c)-I))","A"
165,1,306,154,0.482000," ","int(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x)","\frac{\frac{i}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{4}}-\frac{11 i}{128 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}+\frac{1}{80 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{5}}-\frac{5}{64 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{23}{128 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}-\frac{1375 i}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}-\frac{135 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{62 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{10}}+\frac{465 i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{8 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{12}}+\frac{825 i}{128 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{16}{13 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{13}}-\frac{300}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{11}}+\frac{104}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}-\frac{279}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{6291}{80 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{1207}{64 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{233}{128 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{4}}"," ",0,"2/d/a^4*(1/64*I/(tan(1/2*d*x+1/2*c)+I)^4-11/256*I/(tan(1/2*d*x+1/2*c)+I)^2+1/160/(tan(1/2*d*x+1/2*c)+I)^5-5/128/(tan(1/2*d*x+1/2*c)+I)^3+23/256/(tan(1/2*d*x+1/2*c)+I)-1375/64*I/(tan(1/2*d*x+1/2*c)-I)^4-135/2*I/(tan(1/2*d*x+1/2*c)-I)^8+31*I/(tan(1/2*d*x+1/2*c)-I)^10+465/8*I/(tan(1/2*d*x+1/2*c)-I)^6-4*I/(tan(1/2*d*x+1/2*c)-I)^12+825/256*I/(tan(1/2*d*x+1/2*c)-I)^2+8/13/(tan(1/2*d*x+1/2*c)-I)^13-150/11/(tan(1/2*d*x+1/2*c)-I)^11+52/(tan(1/2*d*x+1/2*c)-I)^9-279/4/(tan(1/2*d*x+1/2*c)-I)^7+6291/160/(tan(1/2*d*x+1/2*c)-I)^5-1207/128/(tan(1/2*d*x+1/2*c)-I)^3+233/256/(tan(1/2*d*x+1/2*c)-I))","A"
166,1,120,127,0.505000," ","int(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^8,x)","\frac{129 \tan \left(d x +c \right)}{a^{8} d}+\frac{\tan^{5}\left(d x +c \right)}{5 a^{8} d}+\frac{2 i \left(\tan^{4}\left(d x +c \right)\right)}{a^{8} d}-\frac{10 \left(\tan^{3}\left(d x +c \right)\right)}{a^{8} d}-\frac{36 i \left(\tan^{2}\left(d x +c \right)\right)}{a^{8} d}+\frac{64}{a^{8} d \left(\tan \left(d x +c \right)-i\right)}+\frac{192 i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{8} d}"," ",0,"129*tan(d*x+c)/a^8/d+1/5*tan(d*x+c)^5/a^8/d+2*I*tan(d*x+c)^4/a^8/d-10*tan(d*x+c)^3/a^8/d-36*I*tan(d*x+c)^2/a^8/d+64/a^8/d/(tan(d*x+c)-I)+192*I/a^8/d*ln(tan(d*x+c)-I)","A"
167,1,107,118,0.450000," ","int(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^8,x)","-\frac{31 \tan \left(d x +c \right)}{a^{8} d}+\frac{\tan^{3}\left(d x +c \right)}{3 a^{8} d}+\frac{4 i \left(\tan^{2}\left(d x +c \right)\right)}{a^{8} d}-\frac{16 i}{a^{8} d \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{80}{a^{8} d \left(\tan \left(d x +c \right)-i\right)}-\frac{80 i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{8} d}"," ",0,"-31*tan(d*x+c)/a^8/d+1/3*tan(d*x+c)^3/a^8/d+4*I*tan(d*x+c)^2/a^8/d-16*I/a^8/d/(tan(d*x+c)-I)^2-80/a^8/d/(tan(d*x+c)-I)-80*I/a^8/d*ln(tan(d*x+c)-I)","A"
168,1,92,107,0.443000," ","int(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^8,x)","\frac{\tan \left(d x +c \right)}{a^{8} d}+\frac{16 i}{a^{8} d \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{24}{a^{8} d \left(\tan \left(d x +c \right)-i\right)}-\frac{16}{3 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{8 i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{8} d}"," ",0,"tan(d*x+c)/a^8/d+16*I/a^8/d/(tan(d*x+c)-I)^2+24/a^8/d/(tan(d*x+c)-I)-16/3/a^8/d/(tan(d*x+c)-I)^3+8*I/a^8/d*ln(tan(d*x+c)-I)","A"
169,1,63,38,0.527000," ","int(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^8,x)","\frac{-\frac{1}{\tan \left(d x +c \right)-i}+\frac{4}{\left(\tan \left(d x +c \right)-i\right)^{3}}-\frac{3 i}{\left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{2 i}{\left(\tan \left(d x +c \right)-i\right)^{4}}}{d \,a^{8}}"," ",0,"1/d/a^8*(-1/(tan(d*x+c)-I)+4/(tan(d*x+c)-I)^3-3*I/(tan(d*x+c)-I)^2+2*I/(tan(d*x+c)-I)^4)","A"
170,1,49,71,0.523000," ","int(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^8,x)","\frac{-\frac{i}{\left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{1}{3 \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{4}{5 \left(\tan \left(d x +c \right)-i\right)^{5}}}{d \,a^{8}}"," ",0,"1/d/a^8*(-I/(tan(d*x+c)-I)^4-1/3/(tan(d*x+c)-I)^3+4/5/(tan(d*x+c)-I)^5)","A"
171,1,36,47,0.488000," ","int(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^8,x)","\frac{-\frac{i}{3 \left(\tan \left(d x +c \right)-i\right)^{6}}-\frac{1}{5 \left(\tan \left(d x +c \right)-i\right)^{5}}}{d \,a^{8}}"," ",0,"1/d/a^8*(-1/3*I/(tan(d*x+c)-I)^6-1/5/(tan(d*x+c)-I)^5)","A"
172,1,24,23,0.291000," ","int(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^8,x)","\frac{i}{7 a d \left(a +i a \tan \left(d x +c \right)\right)^{7}}"," ",0,"1/7*I/a/d/(a+I*a*tan(d*x+c))^7","A"
173,1,196,195,0.112000," ","int(1/(a+I*a*tan(d*x+c))^8,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{512 d \,a^{8}}+\frac{i}{16 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{8}}+\frac{i}{128 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{512 a^{8} d}-\frac{i}{48 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{6}}-\frac{i}{256 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{28 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{7}}+\frac{1}{80 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{5}}-\frac{1}{192 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{1}{256 a^{8} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/512*I/d/a^8*ln(tan(d*x+c)+I)+1/16*I/d/a^8/(tan(d*x+c)-I)^8+1/128*I/d/a^8/(tan(d*x+c)-I)^4-1/512*I/d/a^8*ln(tan(d*x+c)-I)-1/48*I/d/a^8/(tan(d*x+c)-I)^6-1/256*I/d/a^8/(tan(d*x+c)-I)^2-1/28/d/a^8/(tan(d*x+c)-I)^7+1/80/d/a^8/(tan(d*x+c)-I)^5-1/192/a^8/d/(tan(d*x+c)-I)^3+1/256/a^8/d/(tan(d*x+c)-I)","A"
174,1,234,236,0.452000," ","int(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^8,x)","\frac{5 i \ln \left(\tan \left(d x +c \right)+i\right)}{1024 d \,a^{8}}+\frac{1}{1024 a^{8} d \left(\tan \left(d x +c \right)+i\right)}-\frac{5 i \ln \left(\tan \left(d x +c \right)-i\right)}{1024 a^{8} d}+\frac{3 i}{256 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{i}{32 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{8}}-\frac{i}{48 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{6}}-\frac{i}{128 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{36 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{9}}-\frac{3}{112 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{7}}+\frac{1}{64 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{5}}-\frac{7}{768 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{9}{1024 a^{8} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"5/1024*I/a^8/d*ln(tan(d*x+c)+I)+1/1024/a^8/d/(tan(d*x+c)+I)-5/1024*I/a^8/d*ln(tan(d*x+c)-I)+3/256*I/a^8/d/(tan(d*x+c)-I)^4+1/32*I/a^8/d/(tan(d*x+c)-I)^8-1/48*I/d/a^8/(tan(d*x+c)-I)^6-1/128*I/a^8/d/(tan(d*x+c)-I)^2+1/36/a^8/d/(tan(d*x+c)-I)^9-3/112/d/a^8/(tan(d*x+c)-I)^7+1/64/d/a^8/(tan(d*x+c)-I)^5-7/768/a^8/d/(tan(d*x+c)-I)^3+9/1024/a^8/d/(tan(d*x+c)-I)","A"
175,1,274,283,0.487000," ","int(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^8,x)","\frac{i}{4096 a^{8} d \left(\tan \left(d x +c \right)+i\right)^{2}}+\frac{33 i \ln \left(\tan \left(d x +c \right)+i\right)}{4096 d \,a^{8}}+\frac{11}{4096 a^{8} d \left(\tan \left(d x +c \right)+i\right)}-\frac{33 i \ln \left(\tan \left(d x +c \right)-i\right)}{4096 a^{8} d}+\frac{7 i}{512 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{4}}+\frac{3 i}{128 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{8}}-\frac{i}{80 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{10}}-\frac{5 i}{256 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{6}}-\frac{45 i}{4096 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{48 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{9}}-\frac{5}{224 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{7}}+\frac{21}{1280 d \,a^{8} \left(\tan \left(d x +c \right)-i\right)^{5}}-\frac{3}{256 a^{8} d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{55}{4096 a^{8} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/4096*I/a^8/d/(tan(d*x+c)+I)^2+33/4096*I/a^8/d*ln(tan(d*x+c)+I)+11/4096/a^8/d/(tan(d*x+c)+I)-33/4096*I/a^8/d*ln(tan(d*x+c)-I)+7/512*I/a^8/d/(tan(d*x+c)-I)^4+3/128*I/a^8/d/(tan(d*x+c)-I)^8-1/80*I/a^8/d/(tan(d*x+c)-I)^10-5/256*I/a^8/d/(tan(d*x+c)-I)^6-45/4096*I/a^8/d/(tan(d*x+c)-I)^2+1/48/a^8/d/(tan(d*x+c)-I)^9-5/224/d/a^8/(tan(d*x+c)-I)^7+21/1280/d/a^8/(tan(d*x+c)-I)^5-3/256/a^8/d/(tan(d*x+c)-I)^3+55/4096/a^8/d/(tan(d*x+c)-I)","A"
176,1,409,187,0.466000," ","int(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^8,x)","\frac{1}{2 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{4 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{121}{8 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{76 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{123}{8 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{4 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{4 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{1155 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 a^{8} d}+\frac{121}{8 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{76 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{2 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{8 i}{3 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{123}{8 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{8 i}{3 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{4 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1155 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 a^{8} d}+\frac{128 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{256}{3 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}-\frac{256}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}"," ",0,"1/2/a^8/d/(tan(1/2*d*x+1/2*c)-1)^3-4*I/a^8/d/(tan(1/2*d*x+1/2*c)+1)^2-121/8/a^8/d/(tan(1/2*d*x+1/2*c)-1)^2-76*I/a^8/d/(tan(1/2*d*x+1/2*c)+1)-123/8/a^8/d/(tan(1/2*d*x+1/2*c)-1)-4*I/a^8/d/(tan(1/2*d*x+1/2*c)-1)^2+1/4/a^8/d/(tan(1/2*d*x+1/2*c)-1)^4-1155/8/a^8/d*ln(tan(1/2*d*x+1/2*c)-1)+121/8/a^8/d/(tan(1/2*d*x+1/2*c)+1)^2+76*I/a^8/d/(tan(1/2*d*x+1/2*c)-1)+1/2/a^8/d/(tan(1/2*d*x+1/2*c)+1)^3-8/3*I/a^8/d/(tan(1/2*d*x+1/2*c)-1)^3-123/8/a^8/d/(tan(1/2*d*x+1/2*c)+1)+8/3*I/a^8/d/(tan(1/2*d*x+1/2*c)+1)^3-1/4/a^8/d/(tan(1/2*d*x+1/2*c)+1)^4+1155/8/a^8/d*ln(tan(1/2*d*x+1/2*c)+1)+128*I/a^8/d/(tan(1/2*d*x+1/2*c)-I)^2-256/3/a^8/d/(tan(1/2*d*x+1/2*c)-I)^3-256/a^8/d/(tan(1/2*d*x+1/2*c)-I)","B"
177,1,282,165,0.456000," ","int(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^8,x)","\frac{1}{2 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{2 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{63 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a^{8} d}+\frac{1}{2 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{8 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{2 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{63 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a^{8} d}-\frac{32 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{128 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{256}{5 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{64}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{64}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}"," ",0,"1/2/a^8/d/(tan(1/2*d*x+1/2*c)-1)-8*I/a^8/d/(tan(1/2*d*x+1/2*c)-1)+1/2/a^8/d/(tan(1/2*d*x+1/2*c)-1)^2+63/2/a^8/d*ln(tan(1/2*d*x+1/2*c)-1)+1/2/a^8/d/(tan(1/2*d*x+1/2*c)+1)+8*I/a^8/d/(tan(1/2*d*x+1/2*c)+1)-1/2/a^8/d/(tan(1/2*d*x+1/2*c)+1)^2-63/2/a^8/d*ln(tan(1/2*d*x+1/2*c)+1)-32*I/a^8/d/(tan(1/2*d*x+1/2*c)-I)^2-128*I/a^8/d/(tan(1/2*d*x+1/2*c)-I)^4+256/5/a^8/d/(tan(1/2*d*x+1/2*c)-I)^5-64/a^8/d/(tan(1/2*d*x+1/2*c)-I)^3+64/a^8/d/(tan(1/2*d*x+1/2*c)-I)","A"
178,1,176,142,0.516000," ","int(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^8,x)","-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a^{8} d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a^{8} d}+\frac{128 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}+\frac{16 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{128 i}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}-\frac{256}{7 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{896}{5 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{160}{3 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}"," ",0,"-1/a^8/d*ln(tan(1/2*d*x+1/2*c)-1)+1/a^8/d*ln(tan(1/2*d*x+1/2*c)+1)+128*I/a^8/d/(tan(1/2*d*x+1/2*c)-I)^6+16*I/a^8/d/(tan(1/2*d*x+1/2*c)-I)^2-128*I/a^8/d/(tan(1/2*d*x+1/2*c)-I)^4-256/7/a^8/d/(tan(1/2*d*x+1/2*c)-I)^7+896/5/a^8/d/(tan(1/2*d*x+1/2*c)-I)^5-160/3/a^8/d/(tan(1/2*d*x+1/2*c)-I)^3","A"
179,1,156,60,0.515000," ","int(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^8,x)","\frac{-\frac{172}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{256}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}-\frac{128 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{272}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{152 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{14 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{992 i}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{1856}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}}{a^{8} d}"," ",0,"2/d/a^8*(-86/3/(tan(1/2*d*x+1/2*c)-I)^3+128/9/(tan(1/2*d*x+1/2*c)-I)^9-64*I/(tan(1/2*d*x+1/2*c)-I)^8+136/(tan(1/2*d*x+1/2*c)-I)^5-76*I/(tan(1/2*d*x+1/2*c)-I)^4+7*I/(tan(1/2*d*x+1/2*c)-I)^2+496/3*I/(tan(1/2*d*x+1/2*c)-I)^6-928/7/(tan(1/2*d*x+1/2*c)-I)^7+1/(tan(1/2*d*x+1/2*c)-I))","B"
180,1,189,122,0.517000," ","int(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^8,x)","\frac{-\frac{4752}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{14 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{176 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}-\frac{256}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{11}}+\frac{584 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}+\frac{1864}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}+\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}-\frac{576 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{1024}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}+\frac{128 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{10}}-\frac{60}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}}{a^{8} d}"," ",0,"2/d/a^8*(-2376/7/(tan(1/2*d*x+1/2*c)-I)^7+7*I/(tan(1/2*d*x+1/2*c)-I)^2-88*I/(tan(1/2*d*x+1/2*c)-I)^4-128/11/(tan(1/2*d*x+1/2*c)-I)^11+292*I/(tan(1/2*d*x+1/2*c)-I)^6+932/5/(tan(1/2*d*x+1/2*c)-I)^5+1/(tan(1/2*d*x+1/2*c)-I)-288*I/(tan(1/2*d*x+1/2*c)-I)^8+512/3/(tan(1/2*d*x+1/2*c)-I)^9+64*I/(tan(1/2*d*x+1/2*c)-I)^10-30/(tan(1/2*d*x+1/2*c)-I)^3)","A"
181,1,222,189,0.541000," ","int(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^8,x)","\frac{\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}+\frac{864 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{10}}+\frac{14 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{480}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{4544}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{11}}-\frac{200 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{2672 i}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}+\frac{256}{13 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{13}}-\frac{128 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{12}}-\frac{188}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}-\frac{1472 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}-\frac{9056}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{11680}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}}{a^{8} d}"," ",0,"2/d/a^8*(1/(tan(1/2*d*x+1/2*c)-I)+432*I/(tan(1/2*d*x+1/2*c)-I)^10+7*I/(tan(1/2*d*x+1/2*c)-I)^2+240/(tan(1/2*d*x+1/2*c)-I)^5-2272/11/(tan(1/2*d*x+1/2*c)-I)^11-100*I/(tan(1/2*d*x+1/2*c)-I)^4+1336/3*I/(tan(1/2*d*x+1/2*c)-I)^6+128/13/(tan(1/2*d*x+1/2*c)-I)^13-64*I/(tan(1/2*d*x+1/2*c)-I)^12-94/3/(tan(1/2*d*x+1/2*c)-I)^3-736*I/(tan(1/2*d*x+1/2*c)-I)^8-4528/7/(tan(1/2*d*x+1/2*c)-I)^7+5840/9/(tan(1/2*d*x+1/2*c)-I)^9)","A"
182,1,255,237,0.251000," ","int(sec(d*x+c)/(a+I*a*tan(d*x+c))^8,x)","\frac{\frac{15008 i}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{10}}-\frac{2944 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{29792}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}+\frac{14 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{224 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{3752 i}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{23744}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{11}}-\frac{2128}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}-\frac{256}{15 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{15}}-\frac{196}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{2968}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}+\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}+\frac{128 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{14}}+\frac{6272}{13 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{13}}-\frac{3584 i}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{12}}}{d \,a^{8}}"," ",0,"2/d/a^8*(7504/5*I/(tan(1/2*d*x+1/2*c)-I)^10-1472*I/(tan(1/2*d*x+1/2*c)-I)^8+14896/9/(tan(1/2*d*x+1/2*c)-I)^9+7*I/(tan(1/2*d*x+1/2*c)-I)^2-112*I/(tan(1/2*d*x+1/2*c)-I)^4+1876/3*I/(tan(1/2*d*x+1/2*c)-I)^6-11872/11/(tan(1/2*d*x+1/2*c)-I)^11-1064/(tan(1/2*d*x+1/2*c)-I)^7-128/15/(tan(1/2*d*x+1/2*c)-I)^15-98/3/(tan(1/2*d*x+1/2*c)-I)^3+1484/5/(tan(1/2*d*x+1/2*c)-I)^5+1/(tan(1/2*d*x+1/2*c)-I)+64*I/(tan(1/2*d*x+1/2*c)-I)^14+3136/13/(tan(1/2*d*x+1/2*c)-I)^13-1792/3*I/(tan(1/2*d*x+1/2*c)-I)^12)","A"
183,1,306,239,0.466000," ","int(cos(d*x+c)/(a+I*a*tan(d*x+c))^8,x)","\frac{\frac{2}{512 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+512 i}-\frac{5384 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{12}}-\frac{10241 i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{1793 i}{128 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{128 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{16}}+\frac{13313 i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{7937 i}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{1568 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{14}}+\frac{38218 i}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{10}}+\frac{256}{17 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{17}}-\frac{2752}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{15}}+\frac{42800}{13 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{13}}-\frac{77908}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{11}}+\frac{6847}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}-\frac{12799}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{57083}{80 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{4351}{64 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{511}{256 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{8}}"," ",0,"2/d/a^8*(1/512/(tan(1/2*d*x+1/2*c)+I)-2692*I/(tan(1/2*d*x+1/2*c)-I)^12-10241/4*I/(tan(1/2*d*x+1/2*c)-I)^8+1793/256*I/(tan(1/2*d*x+1/2*c)-I)^2-64*I/(tan(1/2*d*x+1/2*c)-I)^16+13313/16*I/(tan(1/2*d*x+1/2*c)-I)^6-7937/64*I/(tan(1/2*d*x+1/2*c)-I)^4+784*I/(tan(1/2*d*x+1/2*c)-I)^14+19109/5*I/(tan(1/2*d*x+1/2*c)-I)^10+128/17/(tan(1/2*d*x+1/2*c)-I)^17-1376/5/(tan(1/2*d*x+1/2*c)-I)^15+21400/13/(tan(1/2*d*x+1/2*c)-I)^13-38954/11/(tan(1/2*d*x+1/2*c)-I)^11+6847/2/(tan(1/2*d*x+1/2*c)-I)^9-12799/8/(tan(1/2*d*x+1/2*c)-I)^7+57083/160/(tan(1/2*d*x+1/2*c)-I)^5-4351/128/(tan(1/2*d*x+1/2*c)-I)^3+511/512/(tan(1/2*d*x+1/2*c)-I))","A"
184,1,372,267,0.480000," ","int(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^8,x)","\frac{\frac{128 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{18}}-\frac{1}{768 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{3}{256 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}-\frac{32525 i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{8}}+\frac{32417 i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{10}}+\frac{7181 i}{512 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{i}{512 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}-\frac{1984 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{16}}-\frac{50936 i}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{12}}-\frac{2177 i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{8856 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{14}}+\frac{204605 i}{96 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{256}{19 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{19}}+\frac{10496}{17 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{17}}-\frac{14192}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{15}}+\frac{175016}{13 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{13}}-\frac{18011}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{11}}+\frac{12430}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{9}}-\frac{72425}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{26871}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{54229}{768 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{509}{256 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{8}}"," ",0,"2/d/a^8*(64*I/(tan(1/2*d*x+1/2*c)-I)^18-1/1536/(tan(1/2*d*x+1/2*c)+I)^3+3/512/(tan(1/2*d*x+1/2*c)+I)-32525/8*I/(tan(1/2*d*x+1/2*c)-I)^8+32417/4*I/(tan(1/2*d*x+1/2*c)-I)^10+7181/1024*I/(tan(1/2*d*x+1/2*c)-I)^2-1/1024*I/(tan(1/2*d*x+1/2*c)+I)^2-992*I/(tan(1/2*d*x+1/2*c)-I)^16-25468/3*I/(tan(1/2*d*x+1/2*c)-I)^12-2177/16*I/(tan(1/2*d*x+1/2*c)-I)^4+4428*I/(tan(1/2*d*x+1/2*c)-I)^14+204605/192*I/(tan(1/2*d*x+1/2*c)-I)^6-128/19/(tan(1/2*d*x+1/2*c)-I)^19+5248/17/(tan(1/2*d*x+1/2*c)-I)^17-7096/3/(tan(1/2*d*x+1/2*c)-I)^15+87508/13/(tan(1/2*d*x+1/2*c)-I)^13-18011/2/(tan(1/2*d*x+1/2*c)-I)^11+6215/(tan(1/2*d*x+1/2*c)-I)^9-72425/32/(tan(1/2*d*x+1/2*c)-I)^7+26871/64/(tan(1/2*d*x+1/2*c)-I)^5-54229/1536/(tan(1/2*d*x+1/2*c)-I)^3+509/512/(tan(1/2*d*x+1/2*c)-I))","A"
185,1,365,130,0.937000," ","int((e*sec(d*x+c))^(7/2)*(a+I*a*tan(d*x+c)),x)","-\frac{2 a \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(21 i \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+21 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+21 \left(\cos^{4}\left(d x +c \right)\right)-14 \left(\cos^{3}\left(d x +c \right)\right)-5 i \sin \left(d x +c \right)-7 \cos \left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{35 d \sin \left(d x +c \right)^{5}}"," ",0,"-2/35*a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(21*I*sin(d*x+c)*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*sin(d*x+c)*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+21*I*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+21*cos(d*x+c)^4-14*cos(d*x+c)^3-5*I*sin(d*x+c)-7*cos(d*x+c))*(e/cos(d*x+c))^(7/2)/sin(d*x+c)^5","B"
186,1,192,105,0.832000," ","int((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c)),x)","\frac{2 a \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 i\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{15 d \sin \left(d x +c \right)^{4}}"," ",0,"2/15*a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*cos(d*x+c)*sin(d*x+c)+3*I)*(e/cos(d*x+c))^(5/2)/sin(d*x+c)^4","A"
187,1,351,105,0.819000," ","int((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c)),x)","\frac{2 a \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+i \sin \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right)^{5}}"," ",0,"2/3*a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+I*sin(d*x+c)-3*cos(d*x+c)^2+3*cos(d*x+c))*(e/cos(d*x+c))^(3/2)/sin(d*x+c)^5","B"
188,1,164,79,0.894000," ","int((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c)),x)","\frac{2 i a \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+1\right)}{d \sin \left(d x +c \right)^{4}}"," ",0,"2*I*a/d*(e/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*((1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+1)/sin(d*x+c)^4","B"
189,1,910,79,0.908000," ","int((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(1/2),x)","-\frac{a \left(-1+\cos \left(d x +c \right)\right) \left(4 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-4 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+8 i \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-8 i \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-4 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-4 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+i \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1\right)}{\sin \left(d x +c \right)^{2}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-i \cos \left(d x +c \right) \ln \left(-\frac{2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1}{\sin \left(d x +c \right)^{2}}\right) \sin \left(d x +c \right)-4 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-4 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \cos \left(d x +c \right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\right)}{2 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}}"," ",0,"-1/2*a/d*(-1+cos(d*x+c))*(4*I*sin(d*x+c)*cos(d*x+c)^2*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-4*I*sin(d*x+c)*cos(d*x+c)^2*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+8*I*sin(d*x+c)*cos(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-8*I*sin(d*x+c)*cos(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-4*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-4*I*sin(d*x+c)*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+I*ln(-2*(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)*cos(d*x+c)*sin(d*x+c)-I*cos(d*x+c)*ln(-(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)*sin(d*x+c)-4*I*sin(d*x+c)*cos(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-4*cos(d*x+c)^3*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*cos(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2))/sin(d*x+c)^3/cos(d*x+c)/(e/cos(d*x+c))^(1/2)/(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)","B"
190,1,170,107,0.779000," ","int((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(3/2),x)","\frac{2 a \left(i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-i \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{2} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"2/3*a/d*(I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*cos(d*x+c)^2+cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^2/(e/cos(d*x+c))^(3/2)","A"
191,1,341,107,0.815000," ","int((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(5/2),x)","\frac{2 a \left(3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-\left(\cos^{4}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right)}{5 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"2/5*a/d*(3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*sin(d*x+c)*cos(d*x+c)^3-cos(d*x+c)^4-2*cos(d*x+c)^2+3*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^3/(e/cos(d*x+c))^(5/2)","B"
192,1,187,132,0.835000," ","int((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(7/2),x)","\frac{2 a \left(-3 i \left(\cos^{4}\left(d x +c \right)\right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{21 d \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)^{4}}"," ",0,"2/21*a/d*(-3*I*cos(d*x+c)^4+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+3*cos(d*x+c)^3*sin(d*x+c)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*cos(d*x+c)*sin(d*x+c))/(e/cos(d*x+c))^(7/2)/cos(d*x+c)^4","A"
193,1,374,143,0.898000," ","int((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^2,x)","-\frac{2 a^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(21 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+21 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-10 i \cos \left(d x +c \right) \sin \left(d x +c \right)+21 \left(\cos^{3}\left(d x +c \right)\right)-24 \left(\cos^{2}\left(d x +c \right)\right)+3\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{15 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}"," ",0,"-2/15*a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(21*I*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+21*I*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-10*I*cos(d*x+c)*sin(d*x+c)+21*cos(d*x+c)^3-24*cos(d*x+c)^2+3)*(e/cos(d*x+c))^(3/2)/sin(d*x+c)^5/cos(d*x+c)","B"
194,1,201,115,0.911000," ","int((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^2,x)","\frac{2 a^{2} \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+6 i \cos \left(d x +c \right)-\sin \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{4}}"," ",0,"2/3*a^2/d*(e/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+6*I*cos(d*x+c)-sin(d*x+c))*(1+cos(d*x+c))^2/cos(d*x+c)/sin(d*x+c)^4","A"
195,1,1099,123,0.964000," ","int((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(1/2),x)","\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(-12 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)+6 i \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+6 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-6 i \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-6 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \left(\cos^{5}\left(d x +c \right)\right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+12 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+i \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1\right)}{\sin \left(d x +c \right)^{2}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-i \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1}{\sin \left(d x +c \right)^{2}}\right) \sin \left(d x +c \right)+6 \left(\cos^{4}\left(d x +c \right)\right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+4 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}-4 \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+12 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+12 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-8 \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)+2 \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}\right)}{d \left(1+\cos \left(d x +c \right)\right)^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)^{3} \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"a^2/d*(-1+cos(d*x+c))*(12*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)*sin(d*x+c)-6*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-12*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-6*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+12*I*cos(d*x+c)^3*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+4*cos(d*x+c)^5*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+I*ln(-2*(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)*cos(d*x+c)^2*sin(d*x+c)-I*cos(d*x+c)^2*ln(-(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)*sin(d*x+c)+4*I*cos(d*x+c)^4*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+6*cos(d*x+c)^4*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+6*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)*sin(d*x+c)-4*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^3+6*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+12*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^2*sin(d*x+c)-8*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^2+2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2))/(1+cos(d*x+c))^2/cos(d*x+c)/sin(d*x+c)^3/(e/cos(d*x+c))^(1/2)/(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)","B"
196,1,173,99,0.836000," ","int((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(3/2),x)","-\frac{2 a^{2} \left(i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+2 i \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{2} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/3*a^2/d*(I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+2*I*cos(d*x+c)^2-2*cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^2/(e/cos(d*x+c))^(3/2)","A"
197,1,343,99,0.814000," ","int((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(5/2),x)","-\frac{2 a^{2} \left(i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+2 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+2 \left(\cos^{4}\left(d x +c \right)\right)-\left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/5*a^2/d*(I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+2*I*cos(d*x+c)^3*sin(d*x+c)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+2*cos(d*x+c)^4-cos(d*x+c)^2-cos(d*x+c))/cos(d*x+c)^3/sin(d*x+c)/(e/cos(d*x+c))^(5/2)","B"
198,1,189,126,0.850000," ","int((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(7/2),x)","-\frac{2 a^{2} \left(2 i \left(\cos^{4}\left(d x +c \right)\right)-i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-\cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{4} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}"," ",0,"-2/7*a^2/d*(2*I*cos(d*x+c)^4-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-2*cos(d*x+c)^3*sin(d*x+c)-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^4/(e/cos(d*x+c))^(7/2)","A"
199,1,353,126,0.940000," ","int((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(9/2),x)","-\frac{2 a^{2} \left(2 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 \left(\cos^{6}\left(d x +c \right)\right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-\left(\cos^{4}\left(d x +c \right)\right)+2 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{5} \sin \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}}}"," ",0,"-2/9*a^2/d*(2*I*cos(d*x+c)^5*sin(d*x+c)+2*cos(d*x+c)^6-3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-cos(d*x+c)^4+2*cos(d*x+c)^2-3*cos(d*x+c))/cos(d*x+c)^5/sin(d*x+c)/(e/cos(d*x+c))^(9/2)","B"
200,1,205,153,1.062000," ","int((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(11/2),x)","-\frac{2 a^{2} \left(6 i \left(\cos^{6}\left(d x +c \right)\right)-6 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-5 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{33 d \cos \left(d x +c \right)^{6} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}}}"," ",0,"-2/33*a^2/d*(6*I*cos(d*x+c)^6-6*cos(d*x+c)^5*sin(d*x+c)-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-3*cos(d*x+c)^3*sin(d*x+c)-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-5*cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^6/(e/cos(d*x+c))^(11/2)","A"
201,1,402,201,1.089000," ","int((e*sec(d*x+c))^(7/2)*(a+I*a*tan(d*x+c))^3,x)","-\frac{2 a^{3} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(231 i \left(\cos^{6}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-231 i \left(\cos^{6}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+231 i \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-231 i \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+231 \left(\cos^{6}\left(d x +c \right)\right)-154 \left(\cos^{5}\left(d x +c \right)\right)-132 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-154 \left(\cos^{3}\left(d x +c \right)\right)+21 i \sin \left(d x +c \right)+77 \cos \left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{231 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5}}"," ",0,"-2/231*a^3/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(231*I*cos(d*x+c)^6*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-231*I*cos(d*x+c)^6*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+231*I*cos(d*x+c)^5*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-231*I*cos(d*x+c)^5*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+231*cos(d*x+c)^6-154*cos(d*x+c)^5-132*I*cos(d*x+c)^2*sin(d*x+c)-154*cos(d*x+c)^3+21*I*sin(d*x+c)+77*cos(d*x+c))*(e/cos(d*x+c))^(7/2)/cos(d*x+c)^2/sin(d*x+c)^5","A"
202,1,229,174,1.028000," ","int((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^3,x)","\frac{2 a^{3} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(195 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+195 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+195 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+252 i \left(\cos^{2}\left(d x +c \right)\right)-135 \cos \left(d x +c \right) \sin \left(d x +c \right)-35 i\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{315 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{4}}"," ",0,"2/315*a^3/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(195*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^5*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+195*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+195*cos(d*x+c)^3*sin(d*x+c)+252*I*cos(d*x+c)^2-135*cos(d*x+c)*sin(d*x+c)-35*I)*(e/cos(d*x+c))^(5/2)/cos(d*x+c)^2/sin(d*x+c)^4","A"
203,1,392,174,0.987000," ","int((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^3,x)","\frac{2 a^{3} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(231 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+231 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+140 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-231 \left(\cos^{4}\left(d x +c \right)\right)+294 \left(\cos^{3}\left(d x +c \right)\right)-15 i \sin \left(d x +c \right)-63 \cos \left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{105 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5}}"," ",0,"2/105*a^3/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(231*I*cos(d*x+c)^4*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-231*I*cos(d*x+c)^4*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+231*I*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-231*I*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+140*I*cos(d*x+c)^2*sin(d*x+c)-231*cos(d*x+c)^4+294*cos(d*x+c)^3-15*I*sin(d*x+c)-63*cos(d*x+c))*(e/cos(d*x+c))^(3/2)/cos(d*x+c)^2/sin(d*x+c)^5","B"
204,1,213,146,0.983000," ","int((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^3,x)","\frac{2 a^{3} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{3}\left(d x +c \right)\right)+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+20 i \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right) \sin \left(d x +c \right)-i\right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}}{5 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{4}}"," ",0,"2/5*a^3/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2+20*I*cos(d*x+c)^2-5*cos(d*x+c)*sin(d*x+c)-I)*(e/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)^4","A"
205,1,1564,134,1.016000," ","int((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(1/2),x)","-\frac{2 a^{3} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(126 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1}{\sin \left(d x +c \right)^{2}}\right)+21 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+37 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+3 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1\right)}{\sin \left(d x +c \right)^{2}}\right)+84 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-84 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-84 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+12 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+21 i \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+12 \left(\cos^{6}\left(d x +c \right)\right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}-21 i \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+15 \left(\cos^{5}\left(d x +c \right)\right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+3 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)-18 \left(\cos^{4}\left(d x +c \right)\right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}-126 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+84 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+36 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}-24 \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+15 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)+9 \cos \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}\right)}{3 d \left(1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5} \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"-2/3*a^3/d*(-1+cos(d*x+c))^2*(-126*I*cos(d*x+c)^3*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*cos(d*x+c)^3*sin(d*x+c)*ln(-(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)-21*I*cos(d*x+c)^5*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+84*I*cos(d*x+c)^2*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+37*I*cos(d*x+c)^3*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+3*I*cos(d*x+c)^3*sin(d*x+c)*ln(-2*(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)+21*I*cos(d*x+c)*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-84*I*cos(d*x+c)^4*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+126*I*cos(d*x+c)^3*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+21*I*cos(d*x+c)^5*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*cos(d*x+c)*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*sin(d*x+c)+12*cos(d*x+c)^6*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+12*I*cos(d*x+c)^5*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+15*cos(d*x+c)^5*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+84*I*cos(d*x+c)^4*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-18*cos(d*x+c)^4*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+3*I*cos(d*x+c)*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+36*I*cos(d*x+c)^4*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-84*I*cos(d*x+c)^2*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-24*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^3+15*I*cos(d*x+c)^2*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+6*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^2+9*cos(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2))/(1+cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5/(e/cos(d*x+c))^(1/2)/(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)","B"
206,1,175,120,0.962000," ","int((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(3/2),x)","-\frac{2 a^{3} \left(5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+4 i \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 i\right)}{3 d \cos \left(d x +c \right)^{2} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/3*a^3/d*(5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+4*I*cos(d*x+c)^2-4*cos(d*x+c)*sin(d*x+c)+3*I)/cos(d*x+c)^2/(e/cos(d*x+c))^(3/2)","A"
207,1,1086,120,0.956000," ","int((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(5/2),x)","-\frac{a^{3} \left(1+\cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-24 i \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-12 i \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+16 i \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+24 i \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-12 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+16 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \left(\cos^{5}\left(d x +c \right)\right)-20 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+12 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sin \left(d x +c \right)+5 i \cos \left(d x +c \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1\right)}{\sin \left(d x +c \right)^{2}}\right) \sin \left(d x +c \right)+16 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \left(\cos^{4}\left(d x +c \right)\right)-20 i \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-28 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+16 i \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \cos \left(d x +c \right) \ln \left(-\frac{2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1}{\sin \left(d x +c \right)^{2}}\right) \sin \left(d x +c \right)+12 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-16 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+12 \cos \left(d x +c \right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\right)}{10 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)^{5} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}}"," ",0,"-1/10*a^3/d*(1+cos(d*x+c))*(-1+cos(d*x+c))^2*(-24*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)+12*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*sin(d*x+c)-12*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+24*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)*sin(d*x+c)+12*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+16*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^5+16*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^4*sin(d*x+c)-20*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)*sin(d*x+c)+5*I*cos(d*x+c)*ln(-2*(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)*sin(d*x+c)+16*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^4-20*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^2*sin(d*x+c)-28*cos(d*x+c)^3*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+16*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^3*sin(d*x+c)-12*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-5*I*cos(d*x+c)*ln(-(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)*sin(d*x+c)-16*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+12*cos(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2))/cos(d*x+c)^3/sin(d*x+c)^5/(e/cos(d*x+c))^(5/2)/(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)","B"
208,1,199,132,0.900000," ","int((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(7/2),x)","-\frac{2 a^{3} \left(12 i \left(\cos^{4}\left(d x +c \right)\right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-12 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-7 i \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{21 d \cos \left(d x +c \right)^{4} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}"," ",0,"-2/21*a^3/d*(12*I*cos(d*x+c)^4+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-12*cos(d*x+c)^3*sin(d*x+c)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-7*I*cos(d*x+c)^2+cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^4/(e/cos(d*x+c))^(7/2)","A"
209,1,370,132,0.975000," ","int((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(9/2),x)","-\frac{2 a^{3} \left(20 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+20 \left(\cos^{6}\left(d x +c \right)\right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-9 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-19 \left(\cos^{4}\left(d x +c \right)\right)+2 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)\right)}{45 d \cos \left(d x +c \right)^{5} \sin \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}}}"," ",0,"-2/45*a^3/d*(20*I*cos(d*x+c)^5*sin(d*x+c)+20*cos(d*x+c)^6+3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-9*I*cos(d*x+c)^3*sin(d*x+c)+3*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-19*cos(d*x+c)^4+2*cos(d*x+c)^2-3*cos(d*x+c))/cos(d*x+c)^5/sin(d*x+c)/(e/cos(d*x+c))^(9/2)","B"
210,1,216,159,1.003000," ","int((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(11/2),x)","-\frac{2 a^{3} \left(28 i \left(\cos^{6}\left(d x +c \right)\right)-28 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-11 i \left(\cos^{4}\left(d x +c \right)\right)-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-5 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{77 d \cos \left(d x +c \right)^{6} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}}}"," ",0,"-2/77*a^3/d*(28*I*cos(d*x+c)^6-28*cos(d*x+c)^5*sin(d*x+c)-11*I*cos(d*x+c)^4-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-3*cos(d*x+c)^3*sin(d*x+c)-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-5*cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^6/(e/cos(d*x+c))^(11/2)","A"
211,1,380,159,1.160000," ","int((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(13/2),x)","-\frac{2 a^{3} \left(36 i \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)+36 \left(\cos^{8}\left(d x +c \right)\right)-13 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-31 \left(\cos^{6}\left(d x +c \right)\right)+21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+2 \left(\cos^{4}\left(d x +c \right)\right)+14 \left(\cos^{2}\left(d x +c \right)\right)-21 \cos \left(d x +c \right)\right)}{117 d \cos \left(d x +c \right)^{7} \sin \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{13}{2}}}"," ",0,"-2/117*a^3/d*(36*I*cos(d*x+c)^7*sin(d*x+c)+36*cos(d*x+c)^8-13*I*cos(d*x+c)^5*sin(d*x+c)+21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-21*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-31*cos(d*x+c)^6+21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-21*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2*cos(d*x+c)^4+14*cos(d*x+c)^2-21*cos(d*x+c))/cos(d*x+c)^7/sin(d*x+c)/(e/cos(d*x+c))^(13/2)","B"
212,1,232,186,1.212000," ","int((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(15/2),x)","-\frac{2 a^{3} \left(44 i \left(\cos^{8}\left(d x +c \right)\right)-44 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-15 i \left(\cos^{6}\left(d x +c \right)\right)-7 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-15 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{165 d \cos \left(d x +c \right)^{8} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{15}{2}}}"," ",0,"-2/165*a^3/d*(44*I*cos(d*x+c)^8-44*sin(d*x+c)*cos(d*x+c)^7-15*I*cos(d*x+c)^6-7*cos(d*x+c)^5*sin(d*x+c)-15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-9*cos(d*x+c)^3*sin(d*x+c)-15*cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^8/(e/cos(d*x+c))^(15/2)","A"
213,1,401,208,1.006000," ","int((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^4,x)","-\frac{2 a^{4} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(231 i \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-231 i \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+231 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-168 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+231 \left(\cos^{5}\left(d x +c \right)\right)-322 \left(\cos^{4}\left(d x +c \right)\right)+36 i \cos \left(d x +c \right) \sin \left(d x +c \right)+98 \left(\cos^{2}\left(d x +c \right)\right)-7\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{63 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)^{5}}"," ",0,"-2/63*a^4/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(231*I*cos(d*x+c)^5*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-231*I*cos(d*x+c)^5*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+231*I*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-231*I*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-168*I*cos(d*x+c)^3*sin(d*x+c)+231*cos(d*x+c)^5-322*cos(d*x+c)^4+36*I*cos(d*x+c)*sin(d*x+c)+98*cos(d*x+c)^2-7)*(e/cos(d*x+c))^(3/2)/cos(d*x+c)^3/sin(d*x+c)^5","A"
214,1,230,180,0.999000," ","int((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^4,x)","\frac{2 a^{4} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(195 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+195 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{3}\left(d x +c \right)\right)+280 i \left(\cos^{3}\left(d x +c \right)\right)-85 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-28 i \cos \left(d x +c \right)+5 \sin \left(d x +c \right)\right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}}{35 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)^{4}}"," ",0,"2/35*a^4/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(195*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+195*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+280*I*cos(d*x+c)^3-85*cos(d*x+c)^2*sin(d*x+c)-28*I*cos(d*x+c)+5*sin(d*x+c))*(e/cos(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)^4","A"
215,1,1618,179,1.049000," ","int((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(1/2),x)","-\frac{2 a^{4} \left(-1+\cos \left(d x +c \right)\right)^{3} \left(-20 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)-360 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}-108 \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)-105 \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)+231 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+924 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-924 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-120 i \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+30 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1}{\sin \left(d x +c \right)^{2}}\right)-30 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-\left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-2 \sqrt{-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-1\right)}{\sin \left(d x +c \right)^{2}}\right)-60 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+924 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-924 i \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-120 \left(\cos^{7}\left(d x +c \right)\right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+3 \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}-180 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}-380 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+231 \left(\cos^{4}\left(d x +c \right)\right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+219 \left(\cos^{5}\left(d x +c \right)\right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+9 \cos \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}-129 \left(\cos^{6}\left(d x +c \right)\right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}+1386 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+231 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-1386 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)\right)}{15 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)^{7} \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \left(-\frac{\cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"-2/15*a^4/d*(-1+cos(d*x+c))^3*(231*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^6*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-231*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^6*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+924*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-924*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+1386*I*cos(d*x+c)^4*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-1386*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+924*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-924*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+231*I*cos(d*x+c)^2*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-231*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-120*cos(d*x+c)^7*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-120*I*cos(d*x+c)^6*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-360*I*cos(d*x+c)^5*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-380*I*cos(d*x+c)^4*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-180*I*cos(d*x+c)^3*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+30*I*cos(d*x+c)^4*sin(d*x+c)*ln(-(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)-30*I*cos(d*x+c)^4*sin(d*x+c)*ln(-2*(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)-60*I*cos(d*x+c)^2*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-20*I*cos(d*x+c)*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+3*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-129*cos(d*x+c)^6*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+219*cos(d*x+c)^5*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+231*cos(d*x+c)^4*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-108*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^3-105*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^2+9*cos(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2))/cos(d*x+c)^3/sin(d*x+c)^7/(e/cos(d*x+c))^(1/2)/(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)","B"
216,1,200,155,0.969000," ","int((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(3/2),x)","-\frac{2 a^{4} \left(15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+8 i \left(\cos^{3}\left(d x +c \right)\right)-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+12 i \cos \left(d x +c \right)-\sin \left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/3*a^4/d*(15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+8*I*cos(d*x+c)^3-8*cos(d*x+c)^2*sin(d*x+c)+12*I*cos(d*x+c)-sin(d*x+c))/cos(d*x+c)^3/(e/cos(d*x+c))^(3/2)","A"
217,1,2196,160,1.073000," ","int((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"1/10*a^4/d*(-1+cos(d*x+c))^3*(32*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^6*sin(d*x+c)+96*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^5*sin(d*x+c)+16*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^4*sin(d*x+c)-208*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^3*sin(d*x+c)-240*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^2*sin(d*x+c)-80*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)*sin(d*x+c)-20*I*cos(d*x+c)^2*ln(-(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)*sin(d*x+c)+20*I*cos(d*x+c)^2*ln(-2*(2*cos(d*x+c)^2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-cos(d*x+c)^2+2*cos(d*x+c)-2*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-1)/sin(d*x+c)^2)*sin(d*x+c)+63*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-84*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-21*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^6*sin(d*x+c)-231*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^4*sin(d*x+c)+32*cos(d*x+c)^7*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-20*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+96*cos(d*x+c)^6*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-172*cos(d*x+c)^4*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-56*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^3+96*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^2+24*cos(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-84*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^4*sin(d*x+c)-21*I*cos(d*x+c)^5*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-336*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3*sin(d*x+c)-84*I*cos(d*x+c)^4*sin(d*x+c)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+189*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*sin(d*x+c)-504*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*sin(d*x+c)-126*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3*sin(d*x+c)+210*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)-336*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)-84*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*sin(d*x+c)-84*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3*sin(d*x+c)-21*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)*sin(d*x+c)-126*I*(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^5*sin(d*x+c))/cos(d*x+c)^3/sin(d*x+c)^7/(e/cos(d*x+c))^(5/2)/(-cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)","B"
218,1,200,133,0.925000," ","int((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(7/2),x)","-\frac{2 a^{4} \left(24 i \left(\cos^{4}\left(d x +c \right)\right)-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-24 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-28 i \left(\cos^{2}\left(d x +c \right)\right)+16 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{21 d \cos \left(d x +c \right)^{4} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}"," ",0,"-2/21*a^4/d*(24*I*cos(d*x+c)^4-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-24*cos(d*x+c)^3*sin(d*x+c)-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-28*I*cos(d*x+c)^2+16*cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^4/(e/cos(d*x+c))^(7/2)","A"
219,1,370,133,0.965000," ","int((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(9/2),x)","-\frac{2 a^{4} \left(40 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+40 \left(\cos^{6}\left(d x +c \right)\right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-36 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-56 \left(\cos^{4}\left(d x +c \right)\right)+13 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right)}{45 d \cos \left(d x +c \right)^{5} \sin \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}}}"," ",0,"-2/45*a^4/d*(40*I*cos(d*x+c)^5*sin(d*x+c)+40*cos(d*x+c)^6-3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-36*I*cos(d*x+c)^3*sin(d*x+c)-3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-56*cos(d*x+c)^4+13*cos(d*x+c)^2+3*cos(d*x+c))/cos(d*x+c)^5/sin(d*x+c)/(e/cos(d*x+c))^(9/2)","B"
220,1,215,160,1.033000," ","int((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(11/2),x)","-\frac{2 a^{4} \left(56 i \left(\cos^{6}\left(d x +c \right)\right)-56 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-44 i \left(\cos^{4}\left(d x +c \right)\right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+16 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+\cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{77 d \cos \left(d x +c \right)^{6} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}}}"," ",0,"-2/77*a^4/d*(56*I*cos(d*x+c)^6-56*cos(d*x+c)^5*sin(d*x+c)-44*I*cos(d*x+c)^4+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+16*cos(d*x+c)^3*sin(d*x+c)+cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^6/(e/cos(d*x+c))^(11/2)","A"
221,1,380,160,1.141000," ","int((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(13/2),x)","-\frac{2 a^{4} \left(72 i \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)+72 \left(\cos^{8}\left(d x +c \right)\right)-52 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-88 \left(\cos^{6}\left(d x +c \right)\right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+17 \left(\cos^{4}\left(d x +c \right)\right)+2 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)\right)}{117 d \cos \left(d x +c \right)^{7} \sin \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{13}{2}}}"," ",0,"-2/117*a^4/d*(72*I*cos(d*x+c)^7*sin(d*x+c)+72*cos(d*x+c)^8-52*I*cos(d*x+c)^5*sin(d*x+c)+3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-88*cos(d*x+c)^6+3*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+17*cos(d*x+c)^4+2*cos(d*x+c)^2-3*cos(d*x+c))/cos(d*x+c)^7/sin(d*x+c)/(e/cos(d*x+c))^(13/2)","B"
222,1,232,187,1.149000," ","int((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(15/2),x)","-\frac{2 a^{4} \left(88 i \left(\cos^{8}\left(d x +c \right)\right)-88 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-60 i \left(\cos^{6}\left(d x +c \right)\right)+16 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-5 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{165 d \cos \left(d x +c \right)^{8} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{15}{2}}}"," ",0,"-2/165*a^4/d*(88*I*cos(d*x+c)^8-88*sin(d*x+c)*cos(d*x+c)^7-60*I*cos(d*x+c)^6+16*cos(d*x+c)^5*sin(d*x+c)-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-3*cos(d*x+c)^3*sin(d*x+c)-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-5*cos(d*x+c)*sin(d*x+c))/cos(d*x+c)^8/(e/cos(d*x+c))^(15/2)","A"
223,1,375,143,1.161000," ","int((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c)),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(21 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+21 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 \left(\cos^{4}\left(d x +c \right)\right)+14 \left(\cos^{3}\left(d x +c \right)\right)-5 i \sin \left(d x +c \right)+7 \cos \left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{35 a d \sin \left(d x +c \right)^{5}}"," ",0,"2/35/a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(21*I*cos(d*x+c)^4*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*cos(d*x+c)^4*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+21*I*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*cos(d*x+c)^4+14*cos(d*x+c)^3-5*I*sin(d*x+c)+7*cos(d*x+c))*(e/cos(d*x+c))^(11/2)*cos(d*x+c)^2/sin(d*x+c)^5","B"
224,1,202,116,1.089000," ","int((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c)),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{15 a d \sin \left(d x +c \right)^{4}}"," ",0,"2/15/a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(5*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*cos(d*x+c)*sin(d*x+c)-3*I)*(e/cos(d*x+c))^(9/2)*cos(d*x+c)^2/sin(d*x+c)^4","A"
225,1,361,116,1.087000," ","int((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c)),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right)-i \sin \left(d x +c \right)+3 \cos \left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{3 a d \sin \left(d x +c \right)^{5}}"," ",0,"2/3/a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*cos(d*x+c)^2-I*sin(d*x+c)+3*cos(d*x+c))*(e/cos(d*x+c))^(7/2)*cos(d*x+c)^2/sin(d*x+c)^5","B"
226,1,174,89,1.082000," ","int((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c)),x)","\frac{2 i \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-1\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{a d \sin \left(d x +c \right)^{4}}"," ",0,"2*I/a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*((1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-1)*(e/cos(d*x+c))^(5/2)*cos(d*x+c)^2/sin(d*x+c)^4","A"
227,1,347,89,1.236000," ","int((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-i \cos \left(d x +c \right) \sin \left(d x +c \right)+\cos^{2}\left(d x +c \right)-\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)}{a d \sin \left(d x +c \right)^{5}}"," ",0,"-2/a/d*(-1+cos(d*x+c))^2*(-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*cos(d*x+c)*sin(d*x+c)+cos(d*x+c)^2-cos(d*x+c))*(1+cos(d*x+c))^2*(e/cos(d*x+c))^(3/2)*cos(d*x+c)/sin(d*x+c)^5","B"
228,1,192,94,1.095000," ","int((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c)),x)","\frac{2 \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+i \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{3 a d \sin \left(d x +c \right)^{4}}"," ",0,"2/3/a/d*(e/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*cos(d*x+c)^2+cos(d*x+c)*sin(d*x+c))/sin(d*x+c)^4","B"
229,1,358,94,1.630000," ","int(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c)),x)","\frac{2 \left(3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-\left(\cos^{4}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{e}{\cos \left(d x +c \right)}}}{5 a d \sin \left(d x +c \right)^{5} e}"," ",0,"2/5/a/d*(3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*cos(d*x+c)^3*sin(d*x+c)-cos(d*x+c)^4-2*cos(d*x+c)^2+3*cos(d*x+c))*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(e/cos(d*x+c))^(1/2)/sin(d*x+c)^5/e","B"
230,1,218,124,1.276000," ","int(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c)),x)","\frac{2 \cos \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(3 i \left(\cos^{4}\left(d x +c \right)\right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{21 a d \,e^{3} \sin \left(d x +c \right)^{4}}"," ",0,"2/21/a/d*cos(d*x+c)*(e/cos(d*x+c))^(3/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(3*I*cos(d*x+c)^4+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*cos(d*x+c)^3*sin(d*x+c)+5*cos(d*x+c)*sin(d*x+c))/e^3/sin(d*x+c)^4","A"
231,1,376,124,1.552000," ","int(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c)),x)","\frac{2 \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(5 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-5 \left(\cos^{6}\left(d x +c \right)\right)+21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-2 \left(\cos^{4}\left(d x +c \right)\right)-14 \left(\cos^{2}\left(d x +c \right)\right)+21 \cos \left(d x +c \right)\right)}{45 a d \,e^{5} \sin \left(d x +c \right)^{5}}"," ",0,"2/45/a/d*cos(d*x+c)^2*(e/cos(d*x+c))^(5/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(5*I*cos(d*x+c)^5*sin(d*x+c)+21*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-21*I*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-5*cos(d*x+c)^6+21*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-2*cos(d*x+c)^4-14*cos(d*x+c)^2+21*cos(d*x+c))/e^5/sin(d*x+c)^5","B"
232,1,236,151,1.401000," ","int(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c)),x)","\frac{2 \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(\cos^{3}\left(d x +c \right)\right) \left(7 i \left(\cos^{6}\left(d x +c \right)\right)+7 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+15 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{77 a d \,e^{7} \sin \left(d x +c \right)^{4}}"," ",0,"2/77/a/d*(e/cos(d*x+c))^(7/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*cos(d*x+c)^3*(7*I*cos(d*x+c)^6+7*cos(d*x+c)^5*sin(d*x+c)+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+9*cos(d*x+c)^3*sin(d*x+c)+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+15*cos(d*x+c)*sin(d*x+c))/e^7/sin(d*x+c)^4","A"
233,1,384,185,1.338000," ","int((e*sec(d*x+c))^(15/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(231 i \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-231 i \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+231 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+231 \left(\cos^{5}\left(d x +c \right)\right)-154 \left(\cos^{4}\left(d x +c \right)\right)+90 i \cos \left(d x +c \right) \sin \left(d x +c \right)-112 \left(\cos^{2}\left(d x +c \right)\right)+35\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{15}{2}} \left(\cos^{3}\left(d x +c \right)\right)}{315 a^{2} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/315/a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(231*I*cos(d*x+c)^5*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-231*I*cos(d*x+c)^5*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+231*I*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-231*I*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+231*cos(d*x+c)^5-154*cos(d*x+c)^4+90*I*cos(d*x+c)*sin(d*x+c)-112*cos(d*x+c)^2+35)*(e/cos(d*x+c))^(15/2)*cos(d*x+c)^3/sin(d*x+c)^5","B"
234,1,219,158,1.251000," ","int((e*sec(d*x+c))^(13/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(15 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-14 i \cos \left(d x +c \right)-5 \sin \left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \left(\cos^{3}\left(d x +c \right)\right)}{35 a^{2} d \sin \left(d x +c \right)^{4}}"," ",0,"2/35/a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(15*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3+15*cos(d*x+c)^2*sin(d*x+c)-14*I*cos(d*x+c)-5*sin(d*x+c))*(e/cos(d*x+c))^(13/2)*cos(d*x+c)^3/sin(d*x+c)^4","A"
235,1,374,158,1.288000," ","int((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(21 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+21 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+21 \left(\cos^{3}\left(d x +c \right)\right)+10 i \cos \left(d x +c \right) \sin \left(d x +c \right)-24 \left(\cos^{2}\left(d x +c \right)\right)+3\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \left(\cos^{3}\left(d x +c \right)\right)}{15 a^{2} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/15/a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(21*I*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+21*I*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+21*cos(d*x+c)^3+10*I*cos(d*x+c)*sin(d*x+c)-24*cos(d*x+c)^2+3)*(e/cos(d*x+c))^(11/2)*cos(d*x+c)^3/sin(d*x+c)^5","B"
236,1,201,131,1.177000," ","int((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-6 i \cos \left(d x +c \right)-\sin \left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{3}\left(d x +c \right)\right)}{3 a^{2} d \sin \left(d x +c \right)^{4}}"," ",0,"2/3/a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(5*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-6*I*cos(d*x+c)-sin(d*x+c))*(e/cos(d*x+c))^(9/2)*cos(d*x+c)^3/sin(d*x+c)^4","A"
237,1,352,131,1.217000," ","int((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\cos^{3}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-2 i \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)+1\right)}{a^{2} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/a^2/d*(e/cos(d*x+c))^(7/2)*(-1+cos(d*x+c))^2*cos(d*x+c)^3*(1+cos(d*x+c))^2*(-3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-3*cos(d*x+c)+1)/sin(d*x+c)^5","B"
238,1,201,104,1.131000," ","int((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{2 \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+2 i \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{3 a^{2} d \sin \left(d x +c \right)^{4}}"," ",0,"2/3/a^2/d*cos(d*x+c)^2*(e/cos(d*x+c))^(5/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+2*I*cos(d*x+c)^2+2*cos(d*x+c)*sin(d*x+c))/sin(d*x+c)^4","A"
239,1,361,104,1.176000," ","int((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 \left(i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-2 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+2 \left(\cos^{4}\left(d x +c \right)\right)-\left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)\right) \cos \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{5 a^{2} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/5/a^2/d*(I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-2*I*cos(d*x+c)^3*sin(d*x+c)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+2*cos(d*x+c)^4-cos(d*x+c)^2-cos(d*x+c))*cos(d*x+c)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(e/cos(d*x+c))^(3/2)/sin(d*x+c)^5","B"
240,1,180,126,0.999000," ","int((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{2 \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \left(i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+2 i \left(\cos^{4}\left(d x +c \right)\right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+\cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{7 a^{2} d}"," ",0,"2/7/a^2/d*(e/cos(d*x+c))^(1/2)*(I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+2*I*cos(d*x+c)^4+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+2*cos(d*x+c)^3*sin(d*x+c)+cos(d*x+c)*sin(d*x+c))","A"
241,1,366,126,1.424000," ","int(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{2 \left(2 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-2 \left(\cos^{6}\left(d x +c \right)\right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+\cos^{4}\left(d x +c \right)-2 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{e}{\cos \left(d x +c \right)}}}{9 a^{2} d \sin \left(d x +c \right)^{5} e}"," ",0,"2/9/a^2/d*(2*I*cos(d*x+c)^5*sin(d*x+c)+3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-2*cos(d*x+c)^6+3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+cos(d*x+c)^4-2*cos(d*x+c)^2+3*cos(d*x+c))*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(e/cos(d*x+c))^(1/2)/sin(d*x+c)^5/e","B"
242,1,234,156,1.398000," ","int(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{2 \cos \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(6 i \left(\cos^{6}\left(d x +c \right)\right)+6 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{33 a^{2} d \,e^{3} \sin \left(d x +c \right)^{4}}"," ",0,"2/33/a^2/d*cos(d*x+c)*(e/cos(d*x+c))^(3/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(6*I*cos(d*x+c)^6+6*cos(d*x+c)^5*sin(d*x+c)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*cos(d*x+c)^3*sin(d*x+c)+5*cos(d*x+c)*sin(d*x+c))/e^3/sin(d*x+c)^4","A"
243,1,386,156,1.601000," ","int(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(-10 i \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)+10 \left(\cos^{8}\left(d x +c \right)\right)-5 \left(\cos^{6}\left(d x +c \right)\right)+21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+2 \left(\cos^{4}\left(d x +c \right)\right)+14 \left(\cos^{2}\left(d x +c \right)\right)-21 \cos \left(d x +c \right)\right)}{65 a^{2} d \,e^{5} \sin \left(d x +c \right)^{5}}"," ",0,"-2/65/a^2/d*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*cos(d*x+c)^2*(e/cos(d*x+c))^(5/2)*(-10*I*cos(d*x+c)^7*sin(d*x+c)+10*cos(d*x+c)^8-5*cos(d*x+c)^6+21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-21*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-21*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2*cos(d*x+c)^4+14*cos(d*x+c)^2-21*cos(d*x+c))/e^5/sin(d*x+c)^5","B"
244,1,252,183,1.550000," ","int(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{2 \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(14 i \left(\cos^{8}\left(d x +c \right)\right)+14 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+7 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+15 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{105 a^{2} d \,e^{7} \sin \left(d x +c \right)^{4}}"," ",0,"2/105/a^2/d*cos(d*x+c)^3*(e/cos(d*x+c))^(7/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(14*I*cos(d*x+c)^8+14*sin(d*x+c)*cos(d*x+c)^7+7*cos(d*x+c)^5*sin(d*x+c)+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+9*cos(d*x+c)^3*sin(d*x+c)+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+15*cos(d*x+c)*sin(d*x+c))/e^7/sin(d*x+c)^4","A"
245,1,392,179,1.408000," ","int((e*sec(d*x+c))^(15/2)/(a+I*a*tan(d*x+c))^3,x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(231 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+231 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+231 \left(\cos^{4}\left(d x +c \right)\right)+140 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-294 \left(\cos^{3}\left(d x +c \right)\right)-15 i \sin \left(d x +c \right)+63 \cos \left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{15}{2}} \left(\cos^{4}\left(d x +c \right)\right)}{105 a^{3} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/105/a^3/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(231*I*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-231*I*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+231*I*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-231*I*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+231*cos(d*x+c)^4+140*I*cos(d*x+c)^2*sin(d*x+c)-294*cos(d*x+c)^3-15*I*sin(d*x+c)+63*cos(d*x+c))*(e/cos(d*x+c))^(15/2)*cos(d*x+c)^4/sin(d*x+c)^5","B"
246,1,213,152,1.340000," ","int((e*sec(d*x+c))^(13/2)/(a+I*a*tan(d*x+c))^3,x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(15 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-20 i \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right) \sin \left(d x +c \right)+i\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \left(\cos^{4}\left(d x +c \right)\right)}{5 a^{3} d \sin \left(d x +c \right)^{4}}"," ",0,"2/5/a^3/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^3+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2-20*I*cos(d*x+c)^2-5*cos(d*x+c)*sin(d*x+c)+I)*(e/cos(d*x+c))^(13/2)*cos(d*x+c)^4/sin(d*x+c)^4","A"
247,1,388,152,1.360000," ","int((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^3,x)","-\frac{2 \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(21 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-12 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+12 \left(\cos^{3}\left(d x +c \right)\right)-21 \left(\cos^{2}\left(d x +c \right)\right)-i \sin \left(d x +c \right)+9 \cos \left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{3 a^{3} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/3/a^3/d*(e/cos(d*x+c))^(11/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-21*I*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-21*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-12*I*cos(d*x+c)^2*sin(d*x+c)+12*cos(d*x+c)^3-21*cos(d*x+c)^2-I*sin(d*x+c)+9*cos(d*x+c))*cos(d*x+c)^4/sin(d*x+c)^5","B"
248,1,203,125,1.325000," ","int((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^3,x)","\frac{2 \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+4 i \left(\cos^{2}\left(d x +c \right)\right)+4 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 i\right)}{3 a^{3} d \sin \left(d x +c \right)^{4}}"," ",0,"2/3/a^3/d*cos(d*x+c)^4*(e/cos(d*x+c))^(9/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+4*I*cos(d*x+c)^2+4*cos(d*x+c)*sin(d*x+c)+3*I)/sin(d*x+c)^4","A"
249,1,378,125,1.316000," ","int((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^3,x)","-\frac{2 \left(-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-4 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+4 \left(\cos^{4}\left(d x +c \right)\right)+5 i \cos \left(d x +c \right) \sin \left(d x +c \right)-7 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(d x +c \right)\right)}{5 a^{3} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/5/a^3/d*(-3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-4*I*cos(d*x+c)^3*sin(d*x+c)-3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+4*cos(d*x+c)^4+5*I*cos(d*x+c)*sin(d*x+c)-7*cos(d*x+c)^2+3*cos(d*x+c))*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(e/cos(d*x+c))^(7/2)*cos(d*x+c)^3/sin(d*x+c)^5","B"
250,1,227,140,1.283000," ","int((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^3,x)","-\frac{2 \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(\cos^{2}\left(d x +c \right)\right) \left(i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-12 i \left(\cos^{4}\left(d x +c \right)\right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-12 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+7 i \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{21 a^{3} d \sin \left(d x +c \right)^{4}}"," ",0,"-2/21/a^3/d*(e/cos(d*x+c))^(5/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*cos(d*x+c)^2*(I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-12*I*cos(d*x+c)^4+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-12*cos(d*x+c)^3*sin(d*x+c)+7*I*cos(d*x+c)^2+cos(d*x+c)*sin(d*x+c))/sin(d*x+c)^4","A"
251,1,388,140,1.338000," ","int((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^3,x)","\frac{2 \left(20 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-20 \left(\cos^{6}\left(d x +c \right)\right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-9 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+19 \left(\cos^{4}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)}{45 a^{3} d \sin \left(d x +c \right)^{5}}"," ",0,"2/45/a^3/d*(20*I*cos(d*x+c)^5*sin(d*x+c)+3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-20*cos(d*x+c)^6+3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-9*I*cos(d*x+c)^3*sin(d*x+c)+19*cos(d*x+c)^4-2*cos(d*x+c)^2+3*cos(d*x+c))*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(e/cos(d*x+c))^(3/2)*cos(d*x+c)/sin(d*x+c)^5","B"
252,1,236,156,1.448000," ","int((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^3,x)","\frac{2 \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(28 i \left(\cos^{6}\left(d x +c \right)\right)+28 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-11 i \left(\cos^{4}\left(d x +c \right)\right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{77 a^{3} d \sin \left(d x +c \right)^{4}}"," ",0,"2/77/a^3/d*(e/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(28*I*cos(d*x+c)^6+28*cos(d*x+c)^5*sin(d*x+c)-11*I*cos(d*x+c)^4+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*cos(d*x+c)^3*sin(d*x+c)+5*cos(d*x+c)*sin(d*x+c))/sin(d*x+c)^4","A"
253,1,395,156,1.725000," ","int(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^3,x)","\frac{2 \left(36 i \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)-36 \left(\cos^{8}\left(d x +c \right)\right)-13 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+31 \left(\cos^{6}\left(d x +c \right)\right)+21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-2 \left(\cos^{4}\left(d x +c \right)\right)-14 \left(\cos^{2}\left(d x +c \right)\right)+21 \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{e}{\cos \left(d x +c \right)}}}{117 a^{3} d \sin \left(d x +c \right)^{5} e}"," ",0,"2/117/a^3/d*(36*I*cos(d*x+c)^7*sin(d*x+c)-36*cos(d*x+c)^8-13*I*cos(d*x+c)^5*sin(d*x+c)+21*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+31*cos(d*x+c)^6+21*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*cos(d*x+c)^4-14*cos(d*x+c)^2+21*cos(d*x+c))*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(e/cos(d*x+c))^(1/2)/sin(d*x+c)^5/e","B"
254,1,261,186,1.601000," ","int(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^3,x)","\frac{2 \cos \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(44 i \left(\cos^{8}\left(d x +c \right)\right)+44 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-15 i \left(\cos^{6}\left(d x +c \right)\right)+7 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+15 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{165 a^{3} d \,e^{3} \sin \left(d x +c \right)^{4}}"," ",0,"2/165/a^3/d*cos(d*x+c)*(e/cos(d*x+c))^(3/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(44*I*cos(d*x+c)^8+44*sin(d*x+c)*cos(d*x+c)^7-15*I*cos(d*x+c)^6+7*cos(d*x+c)^5*sin(d*x+c)+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+9*cos(d*x+c)^3*sin(d*x+c)+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+15*cos(d*x+c)*sin(d*x+c))/e^3/sin(d*x+c)^4","A"
255,1,401,194,1.486000," ","int((e*sec(d*x+c))^(15/2)/(a+I*a*tan(d*x+c))^4,x)","\frac{2 \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{15}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(231 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+231 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-231 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+120 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-120 \left(\cos^{4}\left(d x +c \right)\right)+20 i \cos \left(d x +c \right) \sin \left(d x +c \right)+231 \left(\cos^{3}\left(d x +c \right)\right)-114 \left(\cos^{2}\left(d x +c \right)\right)+3\right) \left(\cos^{5}\left(d x +c \right)\right)}{15 a^{4} d \sin \left(d x +c \right)^{5}}"," ",0,"2/15/a^4/d*(e/cos(d*x+c))^(15/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(231*I*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-231*I*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+231*I*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-231*I*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+120*I*cos(d*x+c)^3*sin(d*x+c)-120*cos(d*x+c)^4+20*I*cos(d*x+c)*sin(d*x+c)+231*cos(d*x+c)^3-114*cos(d*x+c)^2+3)*cos(d*x+c)^5/sin(d*x+c)^5","B"
256,1,228,167,1.434000," ","int((e*sec(d*x+c))^(13/2)/(a+I*a*tan(d*x+c))^4,x)","-\frac{2 \left(\cos^{5}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+15 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-8 i \left(\cos^{3}\left(d x +c \right)\right)-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-12 i \cos \left(d x +c \right)-\sin \left(d x +c \right)\right)}{3 a^{4} d \sin \left(d x +c \right)^{4}}"," ",0,"-2/3/a^4/d*cos(d*x+c)^5*(e/cos(d*x+c))^(13/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)^2+15*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-8*I*cos(d*x+c)^3-8*cos(d*x+c)^2*sin(d*x+c)-12*I*cos(d*x+c)-sin(d*x+c))/sin(d*x+c)^4","A"
257,1,379,167,1.437000," ","int((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^4,x)","-\frac{2 \left(21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-21 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-8 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-21 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+8 \left(\cos^{4}\left(d x +c \right)\right)+20 i \cos \left(d x +c \right) \sin \left(d x +c \right)-24 \left(\cos^{2}\left(d x +c \right)\right)+21 \cos \left(d x +c \right)-5\right) \left(\cos^{5}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2}}{5 a^{4} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/5/a^4/d*(21*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-8*I*cos(d*x+c)^3*sin(d*x+c)+21*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-21*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*cos(d*x+c)^4+20*I*cos(d*x+c)*sin(d*x+c)-24*cos(d*x+c)^2+21*cos(d*x+c)-5)*cos(d*x+c)^5*(e/cos(d*x+c))^(11/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2/sin(d*x+c)^5","B"
258,1,228,140,1.372000," ","int((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^4,x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+24 i \left(\cos^{4}\left(d x +c \right)\right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+24 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-28 i \left(\cos^{2}\left(d x +c \right)\right)-16 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{21 a^{4} d \sin \left(d x +c \right)^{4}}"," ",0,"2/21/a^4/d*(1+cos(d*x+c))^2*cos(d*x+c)^4*(e/cos(d*x+c))^(9/2)*(-1+cos(d*x+c))^2*(5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+24*I*cos(d*x+c)^4+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+24*cos(d*x+c)^3*sin(d*x+c)-28*I*cos(d*x+c)^2-16*cos(d*x+c)*sin(d*x+c))/sin(d*x+c)^4","A"
259,1,390,140,1.411000," ","int((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^4,x)","-\frac{2 \left(-40 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+40 \left(\cos^{6}\left(d x +c \right)\right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+36 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-56 \left(\cos^{4}\left(d x +c \right)\right)+13 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(d x +c \right)\right)}{45 a^{4} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/45/a^4/d*(-40*I*cos(d*x+c)^5*sin(d*x+c)+40*cos(d*x+c)^6+3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+36*I*cos(d*x+c)^3*sin(d*x+c)+3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-56*cos(d*x+c)^4+13*cos(d*x+c)^2+3*cos(d*x+c))*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(e/cos(d*x+c))^(7/2)*cos(d*x+c)^3/sin(d*x+c)^5","B"
260,1,243,167,1.385000," ","int((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^4,x)","-\frac{2 \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(\cos^{2}\left(d x +c \right)\right) \left(-56 i \left(\cos^{6}\left(d x +c \right)\right)-56 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+44 i \left(\cos^{4}\left(d x +c \right)\right)+i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+16 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+\cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{77 a^{4} d \sin \left(d x +c \right)^{4}}"," ",0,"-2/77/a^4/d*(e/cos(d*x+c))^(5/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*cos(d*x+c)^2*(-56*I*cos(d*x+c)^6-56*cos(d*x+c)^5*sin(d*x+c)+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+44*I*cos(d*x+c)^4+I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+16*cos(d*x+c)^3*sin(d*x+c)+cos(d*x+c)*sin(d*x+c))/sin(d*x+c)^4","A"
261,1,398,167,1.419000," ","int((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^4,x)","-\frac{2 \left(-72 i \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)+72 \left(\cos^{8}\left(d x +c \right)\right)+52 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-88 \left(\cos^{6}\left(d x +c \right)\right)+3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+17 \left(\cos^{4}\left(d x +c \right)\right)+2 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)}{117 a^{4} d \sin \left(d x +c \right)^{5}}"," ",0,"-2/117/a^4/d*(-72*I*cos(d*x+c)^7*sin(d*x+c)+72*cos(d*x+c)^8+52*I*cos(d*x+c)^5*sin(d*x+c)-88*cos(d*x+c)^6+3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+3*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+17*cos(d*x+c)^4+2*cos(d*x+c)^2-3*cos(d*x+c))*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(e/cos(d*x+c))^(3/2)*cos(d*x+c)/sin(d*x+c)^5","B"
262,1,252,189,1.356000," ","int((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^4,x)","\frac{2 \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(88 i \left(\cos^{8}\left(d x +c \right)\right)+88 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-60 i \left(\cos^{6}\left(d x +c \right)\right)-16 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+5 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{165 a^{4} d \sin \left(d x +c \right)^{4}}"," ",0,"2/165/a^4/d*(e/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(88*I*cos(d*x+c)^8+88*sin(d*x+c)*cos(d*x+c)^7-60*I*cos(d*x+c)^6-16*cos(d*x+c)^5*sin(d*x+c)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+5*I*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*cos(d*x+c)^3*sin(d*x+c)+5*cos(d*x+c)*sin(d*x+c))/sin(d*x+c)^4","A"
263,0,0,50,0.581000," ","int((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e)),x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}} \left(a +i a \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e)),x)","F"
264,0,0,50,0.590000," ","int((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e)),x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(a +i a \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e)),x)","F"
265,0,0,50,0.588000," ","int((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x)","\int \frac{a +i a \tan \left(f x +e \right)}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x)","F"
266,0,0,50,0.625000," ","int((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x)","\int \frac{a +i a \tan \left(f x +e \right)}{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x)","F"
267,0,0,52,0.626000," ","int((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e))^2,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}} \left(a +i a \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e))^2,x)","F"
268,0,0,52,0.622000," ","int((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e))^2,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(a +i a \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e))^2,x)","F"
269,0,0,65,0.588000," ","int((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{2}}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x)","F"
270,0,0,65,0.652000," ","int((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x)","\int \frac{\left(a +i a \tan \left(f x +e \right)\right)^{2}}{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x)","F"
271,0,0,63,0.936000," ","int((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}}}{a +i a \tan \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x)","F"
272,0,0,63,0.998000," ","int((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}{a +i a \tan \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x)","F"
273,0,0,52,0.882000," ","int(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x)","\int \frac{1}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(a +i a \tan \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x)","F"
274,0,0,52,0.889000," ","int(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x)","\int \frac{1}{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}} \left(a +i a \tan \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x)","F"
275,0,0,67,1.076000," ","int((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}}}{\left(a +i a \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x)","F"
276,0,0,67,1.078000," ","int((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}{\left(a +i a \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x)","F"
277,0,0,52,1.032000," ","int(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x)","\int \frac{1}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(a +i a \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x)","F"
278,0,0,52,1.036000," ","int(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x)","\int \frac{1}{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}} \left(a +i a \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x)","F"
279,1,141,93,4.755000," ","int(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 \left(1024 i \left(\cos^{7}\left(d x +c \right)\right)-1024 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+128 i \left(\cos^{5}\left(d x +c \right)\right)-640 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+56 i \left(\cos^{3}\left(d x +c \right)\right)-504 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+33 i \cos \left(d x +c \right)-429 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{6435 d \cos \left(d x +c \right)^{7}}"," ",0,"-2/6435/d*(1024*I*cos(d*x+c)^7-1024*sin(d*x+c)*cos(d*x+c)^6+128*I*cos(d*x+c)^5-640*sin(d*x+c)*cos(d*x+c)^4+56*I*cos(d*x+c)^3-504*cos(d*x+c)^2*sin(d*x+c)+33*I*cos(d*x+c)-429*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^7","A"
280,1,114,70,1.432000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 \left(128 i \left(\cos^{5}\left(d x +c \right)\right)-128 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+16 i \left(\cos^{3}\left(d x +c \right)\right)-80 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+7 i \cos \left(d x +c \right)-63 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{693 d \cos \left(d x +c \right)^{5}}"," ",0,"-2/693/d*(128*I*cos(d*x+c)^5-128*sin(d*x+c)*cos(d*x+c)^4+16*I*cos(d*x+c)^3-80*cos(d*x+c)^2*sin(d*x+c)+7*I*cos(d*x+c)-63*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^5","A"
281,1,87,47,1.415000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 \left(8 i \left(\cos^{3}\left(d x +c \right)\right)-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+i \cos \left(d x +c \right)-5 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{35 d \cos \left(d x +c \right)^{3}}"," ",0,"-2/35/d*(8*I*cos(d*x+c)^3-8*cos(d*x+c)^2*sin(d*x+c)+I*cos(d*x+c)-5*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3","A"
282,1,24,23,0.243000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d a}"," ",0,"-2/3*I*(a+I*a*tan(d*x+c))^(3/2)/d/a","A"
283,1,397,94,1.289000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(3 i \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+3 i \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+3 \sin \left(d x +c \right) \cos \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-8 i \left(\cos^{4}\left(d x +c \right)\right)-4 i \left(\cos^{3}\left(d x +c \right)\right)+8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+12 i \left(\cos^{2}\left(d x +c \right)\right)-12 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)}"," ",0,"1/16/d*(3*I*sin(d*x+c)*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)+3*I*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+3*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+3*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-8*I*cos(d*x+c)^4-4*I*cos(d*x+c)^3+8*cos(d*x+c)^3*sin(d*x+c)+12*I*cos(d*x+c)^2-12*cos(d*x+c)^2*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)","B"
284,1,741,154,1.350000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(128 i \left(\cos^{7}\left(d x +c \right)\right)-105 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-1680 i \left(\cos^{4}\left(d x +c \right)\right)-315 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+224 i \left(\cos^{6}\left(d x +c \right)\right)-315 \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+560 i \left(\cos^{5}\left(d x +c \right)\right)-105 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)-315 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-105 i \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)-768 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-105 i \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+896 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+768 i \left(\cos^{8}\left(d x +c \right)\right)-1120 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-315 i \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+1680 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3072 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{3}}"," ",0,"-1/3072/d*(128*I*cos(d*x+c)^7-105*cos(d*x+c)^3*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-1680*I*cos(d*x+c)^4-315*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+224*I*cos(d*x+c)^6-315*cos(d*x+c)*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+560*I*cos(d*x+c)^5-105*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*sin(d*x+c)-315*I*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-105*I*cos(d*x+c)^3*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-768*sin(d*x+c)*cos(d*x+c)^7-105*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*sin(d*x+c)+896*sin(d*x+c)*cos(d*x+c)^6-315*I*cos(d*x+c)*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-1120*cos(d*x+c)^5*sin(d*x+c)+768*I*cos(d*x+c)^8+1680*sin(d*x+c)*cos(d*x+c)^4)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^3","B"
285,1,1085,214,1.431000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(-73920 i \left(\cos^{7}\left(d x +c \right)\right)+147840 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+3465 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+101376 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)+3465 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \sin \left(d x +c \right)+17325 \sin \left(d x +c \right) \cos \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+3465 i \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}+17325 i \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}+34650 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}+34650 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}+17325 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+34650 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+34650 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+81920 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)-118272 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)-221760 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+17325 i \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}+221760 i \left(\cos^{6}\left(d x +c \right)\right)-90112 \sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)-29568 i \left(\cos^{8}\left(d x +c \right)\right)-8192 i \left(\cos^{11}\left(d x +c \right)\right)-11264 i \left(\cos^{10}\left(d x +c \right)\right)-16896 i \left(\cos^{9}\left(d x +c \right)\right)-81920 i \left(\cos^{12}\left(d x +c \right)\right)+3465 \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{491520 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{5}}"," ",0,"1/491520/d*(3465*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)-81920*I*cos(d*x+c)^12-8192*I*cos(d*x+c)^11-11264*I*cos(d*x+c)^10-16896*I*cos(d*x+c)^9-29568*I*cos(d*x+c)^8-73920*I*cos(d*x+c)^7+221760*I*cos(d*x+c)^6+81920*sin(d*x+c)*cos(d*x+c)^11+101376*sin(d*x+c)*cos(d*x+c)^9-118272*sin(d*x+c)*cos(d*x+c)^8-90112*sin(d*x+c)*cos(d*x+c)^10+3465*sin(d*x+c)*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+17325*sin(d*x+c)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+34650*sin(d*x+c)*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+34650*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+17325*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+3465*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+147840*sin(d*x+c)*cos(d*x+c)^7-221760*sin(d*x+c)*cos(d*x+c)^6+17325*I*sin(d*x+c)*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*2^(1/2)+3465*I*sin(d*x+c)*cos(d*x+c)^5*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*2^(1/2)+17325*I*sin(d*x+c)*cos(d*x+c)^4*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*2^(1/2)+34650*I*sin(d*x+c)*cos(d*x+c)^3*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*2^(1/2)+34650*I*sin(d*x+c)*cos(d*x+c)^2*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*2^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^5","B"
286,1,141,123,1.959000," ","int(sec(d*x+c)^7*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(1024 i \left(\cos^{7}\left(d x +c \right)\right)+1024 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-128 i \left(\cos^{5}\left(d x +c \right)\right)+384 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-40 i \left(\cos^{3}\left(d x +c \right)\right)+280 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-21 i \cos \left(d x +c \right)+231 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3003 d \cos \left(d x +c \right)^{6}}"," ",0,"2/3003/d*(1024*I*cos(d*x+c)^7+1024*sin(d*x+c)*cos(d*x+c)^6-128*I*cos(d*x+c)^5+384*sin(d*x+c)*cos(d*x+c)^4-40*I*cos(d*x+c)^3+280*cos(d*x+c)^2*sin(d*x+c)-21*I*cos(d*x+c)+231*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^6","A"
287,1,114,92,1.279000," ","int(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(128 i \left(\cos^{5}\left(d x +c \right)\right)+128 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-16 i \left(\cos^{3}\left(d x +c \right)\right)+48 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \cos \left(d x +c \right)+35 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{315 d \cos \left(d x +c \right)^{4}}"," ",0,"2/315/d*(128*I*cos(d*x+c)^5+128*sin(d*x+c)*cos(d*x+c)^4-16*I*cos(d*x+c)^3+48*cos(d*x+c)^2*sin(d*x+c)-5*I*cos(d*x+c)+35*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4","A"
288,1,87,61,1.190000," ","int(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(8 i \left(\cos^{3}\left(d x +c \right)\right)+8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-i \cos \left(d x +c \right)+3 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{15 d \cos \left(d x +c \right)^{2}}"," ",0,"2/15/d*(8*I*cos(d*x+c)^3+8*cos(d*x+c)^2*sin(d*x+c)-I*cos(d*x+c)+3*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2","A"
289,1,50,27,0.885000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(i \cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d}"," ",0,"2/d*(I*cos(d*x+c)+sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)","A"
290,1,217,68,1.123000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-\sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+2 i \left(\cos^{2}\left(d x +c \right)\right)-2 i \cos \left(d x +c \right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right)}"," ",0,"-1/2/d*(I*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+2*I*cos(d*x+c)^2-2*I*cos(d*x+c)-2*cos(d*x+c)*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)","B"
291,1,569,123,1.344000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(15 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+30 i \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-15 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}+15 i \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)-30 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}-15 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)+64 i \left(\cos^{6}\left(d x +c \right)\right)+16 i \left(\cos^{5}\left(d x +c \right)\right)-64 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+40 i \left(\cos^{4}\left(d x +c \right)\right)+80 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-120 i \left(\cos^{3}\left(d x +c \right)\right)-120 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{192 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/192/d*(15*I*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+30*I*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-15*cos(d*x+c)^2*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)+15*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)-30*cos(d*x+c)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)-15*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)+64*I*cos(d*x+c)^6+16*I*cos(d*x+c)^5-64*cos(d*x+c)^5*sin(d*x+c)+40*I*cos(d*x+c)^4+80*sin(d*x+c)*cos(d*x+c)^4-120*I*cos(d*x+c)^3-120*cos(d*x+c)^3*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^2","B"
292,1,913,180,1.319000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(1344 i \left(\cos^{7}\left(d x +c \right)\right)-315 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+1260 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}-1260 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+512 i \left(\cos^{9}\left(d x +c \right)\right)-1890 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+315 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}-1260 \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+1890 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}-315 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}\, \sin \left(d x +c \right)+3360 i \left(\cos^{6}\left(d x +c \right)\right)+315 i \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}\, \sin \left(d x +c \right)-4096 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-10080 i \left(\cos^{5}\left(d x +c \right)\right)+4608 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)+1260 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}-5376 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+768 i \left(\cos^{8}\left(d x +c \right)\right)+6720 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+4096 i \left(\cos^{10}\left(d x +c \right)\right)-10080 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{20480 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{4}}"," ",0,"-1/20480/d*(1344*I*cos(d*x+c)^7-315*cos(d*x+c)^4*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+512*I*cos(d*x+c)^9-1260*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+3360*I*cos(d*x+c)^6-1890*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-10080*I*cos(d*x+c)^5-1260*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+1890*I*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)-315*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)*sin(d*x+c)+768*I*cos(d*x+c)^8+315*I*cos(d*x+c)^4*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)-4096*sin(d*x+c)*cos(d*x+c)^9+1260*I*cos(d*x+c)^3*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)+4608*sin(d*x+c)*cos(d*x+c)^8+1260*I*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)-5376*sin(d*x+c)*cos(d*x+c)^7+4096*I*cos(d*x+c)^10+6720*sin(d*x+c)*cos(d*x+c)^6+315*I*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)*sin(d*x+c)-10080*cos(d*x+c)^5*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^4","B"
293,1,152,93,6.800000," ","int(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \left(2048 i \left(\cos^{8}\left(d x +c \right)\right)-2048 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+256 i \left(\cos^{6}\left(d x +c \right)\right)-1280 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+112 i \left(\cos^{4}\left(d x +c \right)\right)-1008 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+66 i \left(\cos^{2}\left(d x +c \right)\right)-858 \cos \left(d x +c \right) \sin \left(d x +c \right)-715 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{12155 d \cos \left(d x +c \right)^{8}}"," ",0,"-2/12155/d*(2048*I*cos(d*x+c)^8-2048*sin(d*x+c)*cos(d*x+c)^7+256*I*cos(d*x+c)^6-1280*cos(d*x+c)^5*sin(d*x+c)+112*I*cos(d*x+c)^4-1008*cos(d*x+c)^3*sin(d*x+c)+66*I*cos(d*x+c)^2-858*cos(d*x+c)*sin(d*x+c)-715*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^8*a","A"
294,1,125,70,1.716000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \left(256 i \left(\cos^{6}\left(d x +c \right)\right)-256 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+32 i \left(\cos^{4}\left(d x +c \right)\right)-160 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+14 i \left(\cos^{2}\left(d x +c \right)\right)-126 \cos \left(d x +c \right) \sin \left(d x +c \right)-99 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{1287 d \cos \left(d x +c \right)^{6}}"," ",0,"-2/1287/d*(256*I*cos(d*x+c)^6-256*cos(d*x+c)^5*sin(d*x+c)+32*I*cos(d*x+c)^4-160*cos(d*x+c)^3*sin(d*x+c)+14*I*cos(d*x+c)^2-126*cos(d*x+c)*sin(d*x+c)-99*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^6*a","A"
295,1,98,47,1.160000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \left(16 i \left(\cos^{4}\left(d x +c \right)\right)-16 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 i \left(\cos^{2}\left(d x +c \right)\right)-10 \cos \left(d x +c \right) \sin \left(d x +c \right)-7 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{63 d \cos \left(d x +c \right)^{4}}"," ",0,"-2/63/d*(16*I*cos(d*x+c)^4-16*cos(d*x+c)^3*sin(d*x+c)+2*I*cos(d*x+c)^2-10*cos(d*x+c)*sin(d*x+c)-7*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4*a","B"
296,1,24,23,0.185000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d a}"," ",0,"-2/5*I*(a+I*a*tan(d*x+c))^(5/2)/d/a","A"
297,1,398,73,1.267000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(-i \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}-\sin \left(d x +c \right) \cos \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+8 i \left(\cos^{4}\left(d x +c \right)\right)-8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 i \left(\cos^{3}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 i \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{8 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)}"," ",0,"-1/8/d*(-I*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)-2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+8*I*cos(d*x+c)^4-8*cos(d*x+c)^3*sin(d*x+c)-4*I*cos(d*x+c)^3+4*cos(d*x+c)^2*sin(d*x+c)-4*I*cos(d*x+c)^2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)*a","B"
298,1,742,133,1.322000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(128 i \left(\cos^{7}\left(d x +c \right)\right)+240 i \left(\cos^{4}\left(d x +c \right)\right)+15 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+15 i \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+45 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-32 i \left(\cos^{6}\left(d x +c \right)\right)+45 \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+15 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)-80 i \left(\cos^{5}\left(d x +c \right)\right)+15 i \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)+256 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+45 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-128 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-256 i \left(\cos^{8}\left(d x +c \right)\right)+160 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+45 i \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-240 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{512 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{3}}"," ",0,"1/512/d*(128*I*cos(d*x+c)^7+240*I*cos(d*x+c)^4+15*cos(d*x+c)^3*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-32*I*cos(d*x+c)^6+45*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-80*I*cos(d*x+c)^5+45*cos(d*x+c)*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+15*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*sin(d*x+c)+15*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-256*I*cos(d*x+c)^8+256*sin(d*x+c)*cos(d*x+c)^7+15*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*sin(d*x+c)-128*sin(d*x+c)*cos(d*x+c)^6+45*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+160*cos(d*x+c)^5*sin(d*x+c)+45*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-240*sin(d*x+c)*cos(d*x+c)^4)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^3*a","B"
299,1,1086,193,1.514000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(1575 i \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}}-6720 i \left(\cos^{7}\left(d x +c \right)\right)+13440 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+315 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+9216 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)+315 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \sin \left(d x +c \right)+1575 \sin \left(d x +c \right) \cos \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+315 i \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}+3150 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}+3150 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}+1575 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+16384 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)-10752 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)-20160 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+1575 i \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}+20160 i \left(\cos^{6}\left(d x +c \right)\right)-8192 \sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)-2688 i \left(\cos^{8}\left(d x +c \right)\right)+3150 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+3150 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+8192 i \left(\cos^{11}\left(d x +c \right)\right)-1024 i \left(\cos^{10}\left(d x +c \right)\right)-1536 i \left(\cos^{9}\left(d x +c \right)\right)-16384 i \left(\cos^{12}\left(d x +c \right)\right)+315 \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{49152 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{5}}"," ",0,"1/49152/d*(315*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)^5*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)+1575*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)^4*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)+315*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)+16384*sin(d*x+c)*cos(d*x+c)^11+9216*sin(d*x+c)*cos(d*x+c)^9-10752*sin(d*x+c)*cos(d*x+c)^8-8192*sin(d*x+c)*cos(d*x+c)^10+315*sin(d*x+c)*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+1575*sin(d*x+c)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+3150*sin(d*x+c)*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+3150*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+1575*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+13440*sin(d*x+c)*cos(d*x+c)^7-20160*sin(d*x+c)*cos(d*x+c)^6+3150*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)^3*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)-16384*I*cos(d*x+c)^12+8192*I*cos(d*x+c)^11-1024*I*cos(d*x+c)^10-1536*I*cos(d*x+c)^9-2688*I*cos(d*x+c)^8-6720*I*cos(d*x+c)^7+20160*I*cos(d*x+c)^6+3150*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)+1575*I*2^(1/2)*sin(d*x+c)*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)+315*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^5*a","B"
300,1,125,123,1.309000," ","int(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \left(512 i \left(\cos^{6}\left(d x +c \right)\right)+512 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-64 i \left(\cos^{4}\left(d x +c \right)\right)+192 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-20 i \left(\cos^{2}\left(d x +c \right)\right)+140 \cos \left(d x +c \right) \sin \left(d x +c \right)+105 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{1155 d \cos \left(d x +c \right)^{5}}"," ",0,"2/1155/d*(512*I*cos(d*x+c)^6+512*cos(d*x+c)^5*sin(d*x+c)-64*I*cos(d*x+c)^4+192*cos(d*x+c)^3*sin(d*x+c)-20*I*cos(d*x+c)^2+140*cos(d*x+c)*sin(d*x+c)+105*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^5*a","A"
301,1,98,92,1.121000," ","int(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \left(64 i \left(\cos^{4}\left(d x +c \right)\right)+64 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-8 i \left(\cos^{2}\left(d x +c \right)\right)+24 \cos \left(d x +c \right) \sin \left(d x +c \right)+15 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{105 d \cos \left(d x +c \right)^{3}}"," ",0,"2/105/d*(64*I*cos(d*x+c)^4+64*cos(d*x+c)^3*sin(d*x+c)-8*I*cos(d*x+c)^2+24*cos(d*x+c)*sin(d*x+c)+15*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3*a","A"
302,1,71,57,1.021000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \left(4 i \left(\cos^{2}\left(d x +c \right)\right)+4 \cos \left(d x +c \right) \sin \left(d x +c \right)+i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{3 d \cos \left(d x +c \right)}"," ",0,"2/3/d*(4*I*cos(d*x+c)^2+4*cos(d*x+c)*sin(d*x+c)+I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)*a","A"
303,1,42,27,1.040000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 i \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) a}{d}"," ",0,"-2*I/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*a","A"
304,1,570,97,1.387000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(3 i \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}+6 i \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-6 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}+3 i \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)+32 i \left(\cos^{6}\left(d x +c \right)\right)-16 i \left(\cos^{5}\left(d x +c \right)\right)-32 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 i \left(\cos^{4}\left(d x +c \right)\right)+16 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-24 i \left(\cos^{3}\left(d x +c \right)\right)-24 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{48 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/48/d*(3*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-3*cos(d*x+c)^2*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)+6*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-6*cos(d*x+c)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)+3*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)-3*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)+32*I*cos(d*x+c)^6-16*I*cos(d*x+c)^5-32*cos(d*x+c)^5*sin(d*x+c)+8*I*cos(d*x+c)^4+16*sin(d*x+c)*cos(d*x+c)^4-24*I*cos(d*x+c)^3-24*cos(d*x+c)^3*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^2*a","B"
305,1,914,155,1.419000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(448 i \left(\cos^{7}\left(d x +c \right)\right)+420 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}-105 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+1120 i \left(\cos^{6}\left(d x +c \right)\right)-420 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-3360 i \left(\cos^{5}\left(d x +c \right)\right)-630 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+105 i \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}\, \sin \left(d x +c \right)-420 \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-105 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}\, \sin \left(d x +c \right)+420 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+630 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}-3072 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)+256 i \left(\cos^{8}\left(d x +c \right)\right)+1536 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)+3072 i \left(\cos^{10}\left(d x +c \right)\right)-1792 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+105 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+2240 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-1536 i \left(\cos^{9}\left(d x +c \right)\right)-3360 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{7680 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{4}}"," ",0,"-1/7680/d*(448*I*cos(d*x+c)^7+1120*I*cos(d*x+c)^6-105*cos(d*x+c)^4*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+105*I*cos(d*x+c)^4*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-420*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-3360*I*cos(d*x+c)^5-630*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+420*I*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-420*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-105*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)*sin(d*x+c)+420*I*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+630*I*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-3072*sin(d*x+c)*cos(d*x+c)^9+256*I*cos(d*x+c)^8+1536*sin(d*x+c)*cos(d*x+c)^8+3072*I*cos(d*x+c)^10-1792*sin(d*x+c)*cos(d*x+c)^7+105*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*sin(d*x+c)+2240*sin(d*x+c)*cos(d*x+c)^6-1536*I*cos(d*x+c)^9-3360*cos(d*x+c)^5*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^4*a","B"
306,1,171,93,18.975000," ","int(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 \left(4096 i \left(\cos^{9}\left(d x +c \right)\right)-4096 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)+512 i \left(\cos^{7}\left(d x +c \right)\right)-2560 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+224 i \left(\cos^{5}\left(d x +c \right)\right)-2016 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+132 i \left(\cos^{3}\left(d x +c \right)\right)-1716 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2535 i \cos \left(d x +c \right)+1105 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{20995 d \cos \left(d x +c \right)^{9}}"," ",0,"-2/20995/d*(4096*I*cos(d*x+c)^9-4096*sin(d*x+c)*cos(d*x+c)^8+512*I*cos(d*x+c)^7-2560*sin(d*x+c)*cos(d*x+c)^6+224*I*cos(d*x+c)^5-2016*sin(d*x+c)*cos(d*x+c)^4+132*I*cos(d*x+c)^3-1716*cos(d*x+c)^2*sin(d*x+c)-2535*I*cos(d*x+c)+1105*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^9*a^2","A"
307,1,144,70,2.815000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 \left(512 i \left(\cos^{7}\left(d x +c \right)\right)-512 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+64 i \left(\cos^{5}\left(d x +c \right)\right)-320 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+28 i \left(\cos^{3}\left(d x +c \right)\right)-252 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-341 i \cos \left(d x +c \right)+143 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{2145 d \cos \left(d x +c \right)^{7}}"," ",0,"-2/2145/d*(512*I*cos(d*x+c)^7-512*sin(d*x+c)*cos(d*x+c)^6+64*I*cos(d*x+c)^5-320*sin(d*x+c)*cos(d*x+c)^4+28*I*cos(d*x+c)^3-252*cos(d*x+c)^2*sin(d*x+c)-341*I*cos(d*x+c)+143*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^7*a^2","B"
308,1,117,47,1.301000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(-32 i \left(\cos^{5}\left(d x +c \right)\right)+32 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-4 i \left(\cos^{3}\left(d x +c \right)\right)+20 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+23 i \cos \left(d x +c \right)-9 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{99 d \cos \left(d x +c \right)^{5}}"," ",0,"2/99/d*(-32*I*cos(d*x+c)^5+32*sin(d*x+c)*cos(d*x+c)^4-4*I*cos(d*x+c)^3+20*cos(d*x+c)^2*sin(d*x+c)+23*I*cos(d*x+c)-9*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^5*a^2","B"
309,1,24,23,0.180000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d a}"," ",0,"-2/7*I*(a+I*a*tan(d*x+c))^(7/2)/d/a","A"
310,1,398,73,1.182000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+\sin \left(d x +c \right) \cos \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+8 i \left(\cos^{4}\left(d x +c \right)\right)-4 i \left(\cos^{3}\left(d x +c \right)\right)-8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 i \left(\cos^{2}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{4 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)}"," ",0,"-1/4/d*(I*2^(1/2)*sin(d*x+c)*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+8*I*cos(d*x+c)^4-4*I*cos(d*x+c)^3-8*cos(d*x+c)^3*sin(d*x+c)-4*I*cos(d*x+c)^2+4*cos(d*x+c)^2*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)*a^2","B"
311,1,744,110,1.339000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(128 i \left(\cos^{7}\left(d x +c \right)\right)+48 i \left(\cos^{4}\left(d x +c \right)\right)+3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+9 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+3 i \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)+9 \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)+96 i \left(\cos^{6}\left(d x +c \right)\right)-16 i \left(\cos^{5}\left(d x +c \right)\right)+256 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-256 i \left(\cos^{8}\left(d x +c \right)\right)-128 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+3 i \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+32 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+9 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-48 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{256 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{3}}"," ",0,"1/256/d*(128*I*cos(d*x+c)^7+48*I*cos(d*x+c)^4+3*cos(d*x+c)^3*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+9*I*sin(d*x+c)*cos(d*x+c)^2*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+9*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+3*I*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*sin(d*x+c)+9*cos(d*x+c)*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+3*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*sin(d*x+c)+96*I*cos(d*x+c)^6-16*I*cos(d*x+c)^5+256*sin(d*x+c)*cos(d*x+c)^7+3*I*sin(d*x+c)*cos(d*x+c)^3*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-128*sin(d*x+c)*cos(d*x+c)^6-256*I*cos(d*x+c)^8+32*cos(d*x+c)^5*sin(d*x+c)+9*I*sin(d*x+c)*cos(d*x+c)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-48*sin(d*x+c)*cos(d*x+c)^4)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^3*a^2","B"
312,1,1088,170,1.617000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(-525 i \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}}+2240 i \left(\cos^{7}\left(d x +c \right)\right)-4480 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-105 \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-105 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)-3072 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-105 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \sin \left(d x +c \right)-525 \sin \left(d x +c \right) \cos \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+16384 i \left(\cos^{12}\left(d x +c \right)\right)-105 i \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}-1050 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}-1050 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}-525 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-16384 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)+3584 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)+6720 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-525 i \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}-6720 i \left(\cos^{6}\left(d x +c \right)\right)+8192 \sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)+896 i \left(\cos^{8}\left(d x +c \right)\right)-1050 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-1050 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-8192 i \left(\cos^{11}\left(d x +c \right)\right)-5120 i \left(\cos^{10}\left(d x +c \right)\right)+512 i \left(\cos^{9}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{24576 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{5}}"," ",0,"-1/24576/d*(-105*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^5*sin(d*x+c)*2^(1/2)+16384*I*cos(d*x+c)^12-5120*I*cos(d*x+c)^10+896*I*cos(d*x+c)^8+2240*I*cos(d*x+c)^7-6720*I*cos(d*x+c)^6-525*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^4*sin(d*x+c)*2^(1/2)-105*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)-8192*I*cos(d*x+c)^11-16384*sin(d*x+c)*cos(d*x+c)^11-3072*sin(d*x+c)*cos(d*x+c)^9+3584*sin(d*x+c)*cos(d*x+c)^8+8192*sin(d*x+c)*cos(d*x+c)^10-105*sin(d*x+c)*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-525*sin(d*x+c)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-1050*sin(d*x+c)*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-1050*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-525*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-4480*sin(d*x+c)*cos(d*x+c)^7+6720*sin(d*x+c)*cos(d*x+c)^6+512*I*cos(d*x+c)^9-105*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*sin(d*x+c)-1050*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-1050*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)-525*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^5*a^2","B"
313,1,117,123,1.193000," ","int(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(256 i \left(\cos^{5}\left(d x +c \right)\right)+256 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-32 i \left(\cos^{3}\left(d x +c \right)\right)+96 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+95 i \cos \left(d x +c \right)-35 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{315 d \cos \left(d x +c \right)^{4}}"," ",0,"2/315/d*(256*I*cos(d*x+c)^5+256*sin(d*x+c)*cos(d*x+c)^4-32*I*cos(d*x+c)^3+96*cos(d*x+c)^2*sin(d*x+c)+95*I*cos(d*x+c)-35*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4*a^2","A"
314,1,90,86,0.898000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(32 i \left(\cos^{3}\left(d x +c \right)\right)+32 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+11 i \cos \left(d x +c \right)-3 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{15 d \cos \left(d x +c \right)^{2}}"," ",0,"2/15/d*(32*I*cos(d*x+c)^3+32*cos(d*x+c)^2*sin(d*x+c)+11*I*cos(d*x+c)-3*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2*a^2","A"
315,1,53,57,1.084000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 \left(3 i \cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{d}"," ",0,"-2/d*(3*I*cos(d*x+c)+sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*a^2","A"
316,1,63,29,1.254000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 \left(i \cos \left(d x +c \right)-\sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{3 d}"," ",0,"-2/3/d*(I*cos(d*x+c)-sin(d*x+c))*cos(d*x+c)^2*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*a^2","B"
317,1,916,128,1.464000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(-768 i \left(\cos^{9}\left(d x +c \right)\right)+64 i \left(\cos^{7}\left(d x +c \right)\right)-15 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+60 i \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-60 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+15 i \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}\, \sin \left(d x +c \right)-90 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+160 i \left(\cos^{6}\left(d x +c \right)\right)-60 \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-15 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}\, \sin \left(d x +c \right)+60 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}-480 i \left(\cos^{5}\left(d x +c \right)\right)-1536 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)+15 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+768 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)+90 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}-256 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-512 i \left(\cos^{8}\left(d x +c \right)\right)+320 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+1536 i \left(\cos^{10}\left(d x +c \right)\right)-480 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{1920 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{4}}"," ",0,"-1/1920/d*(-768*I*cos(d*x+c)^9+64*I*cos(d*x+c)^7-15*cos(d*x+c)^4*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+60*I*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)*sin(d*x+c)*cos(d*x+c)-60*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+90*I*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2-90*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+160*I*cos(d*x+c)^6-60*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-15*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)*sin(d*x+c)+15*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*sin(d*x+c)-480*I*cos(d*x+c)^5-1536*sin(d*x+c)*cos(d*x+c)^9+60*I*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)*sin(d*x+c)*cos(d*x+c)^3+768*sin(d*x+c)*cos(d*x+c)^8-512*I*cos(d*x+c)^8-256*sin(d*x+c)*cos(d*x+c)^7+1536*I*cos(d*x+c)^10+320*sin(d*x+c)*cos(d*x+c)^6+15*I*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)*sin(d*x+c)*cos(d*x+c)^4-480*cos(d*x+c)^5*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^4*a^2","B"
318,1,1260,188,1.846000," ","int(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\left(-40320 i \left(\cos^{7}\left(d x +c \right)\right)-40320 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-21504 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-24576 i \left(\cos^{12}\left(d x +c \right)\right)+81920 i \left(\cos^{14}\left(d x +c \right)\right)+40960 \left(\cos^{12}\left(d x +c \right)\right) \sin \left(d x +c \right)-16384 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)-315 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \sin \left(d x +c \right)+26880 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)+18432 \sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)+13440 i \left(\cos^{8}\left(d x +c \right)\right)-81920 \sin \left(d x +c \right) \left(\cos^{13}\left(d x +c \right)\right)+1890 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}+2048 i \left(\cos^{11}\left(d x +c \right)\right)+3072 i \left(\cos^{10}\left(d x +c \right)\right)+5376 i \left(\cos^{9}\left(d x +c \right)\right)+4725 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+6300 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+4725 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-40960 i \left(\cos^{13}\left(d x +c \right)\right)-1890 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}+315 i \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \sin \left(d x +c \right)+315 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right) \sqrt{2}+1890 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-315 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right) \sqrt{2}-1890 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-4725 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-6300 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-4725 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{143360 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{6}}"," ",0,"-1/143360/d*(315*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^6*2^(1/2)+1890*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^5*2^(1/2)-16384*sin(d*x+c)*cos(d*x+c)^11-21504*sin(d*x+c)*cos(d*x+c)^9+26880*sin(d*x+c)*cos(d*x+c)^8+18432*sin(d*x+c)*cos(d*x+c)^10-40320*sin(d*x+c)*cos(d*x+c)^7-81920*sin(d*x+c)*cos(d*x+c)^13+40960*sin(d*x+c)*cos(d*x+c)^12+81920*I*cos(d*x+c)^14-40960*I*cos(d*x+c)^13-24576*I*cos(d*x+c)^12+2048*I*cos(d*x+c)^11+5376*I*cos(d*x+c)^9+13440*I*cos(d*x+c)^8-40320*I*cos(d*x+c)^7-315*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*sin(d*x+c)+3072*I*cos(d*x+c)^10+1890*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+315*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*sin(d*x+c)-315*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^6*2^(1/2)-1890*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^5*2^(1/2)-4725*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)-6300*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3*2^(1/2)-4725*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2*2^(1/2)-1890*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+4725*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)+6300*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3*2^(1/2)+4725*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2*2^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^6*a^2","B"
319,1,181,93,56.570000," ","int(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \left(-8192 i \left(\cos^{10}\left(d x +c \right)\right)+8192 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-1024 i \left(\cos^{8}\left(d x +c \right)\right)+5120 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-448 i \left(\cos^{6}\left(d x +c \right)\right)+4032 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-264 i \left(\cos^{4}\left(d x +c \right)\right)+3432 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+8300 i \left(\cos^{2}\left(d x +c \right)\right)-5440 \cos \left(d x +c \right) \sin \left(d x +c \right)-1615 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{33915 d \cos \left(d x +c \right)^{10}}"," ",0,"2/33915/d*(-8192*I*cos(d*x+c)^10+8192*sin(d*x+c)*cos(d*x+c)^9-1024*I*cos(d*x+c)^8+5120*sin(d*x+c)*cos(d*x+c)^7-448*I*cos(d*x+c)^6+4032*cos(d*x+c)^5*sin(d*x+c)-264*I*cos(d*x+c)^4+3432*cos(d*x+c)^3*sin(d*x+c)+8300*I*cos(d*x+c)^2-5440*cos(d*x+c)*sin(d*x+c)-1615*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^10*a^3","A"
320,1,154,70,6.768000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{2 \left(1024 i \left(\cos^{8}\left(d x +c \right)\right)-1024 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+128 i \left(\cos^{6}\left(d x +c \right)\right)-640 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+56 i \left(\cos^{4}\left(d x +c \right)\right)-504 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-1072 i \left(\cos^{2}\left(d x +c \right)\right)+676 \cos \left(d x +c \right) \sin \left(d x +c \right)+195 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{3315 d \cos \left(d x +c \right)^{8}}"," ",0,"-2/3315/d*(1024*I*cos(d*x+c)^8-1024*sin(d*x+c)*cos(d*x+c)^7+128*I*cos(d*x+c)^6-640*cos(d*x+c)^5*sin(d*x+c)+56*I*cos(d*x+c)^4-504*cos(d*x+c)^3*sin(d*x+c)-1072*I*cos(d*x+c)^2+676*cos(d*x+c)*sin(d*x+c)+195*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^8*a^3","B"
321,1,127,47,1.672000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{2 \left(64 i \left(\cos^{6}\left(d x +c \right)\right)-64 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 i \left(\cos^{4}\left(d x +c \right)\right)-40 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-68 i \left(\cos^{2}\left(d x +c \right)\right)+40 \cos \left(d x +c \right) \sin \left(d x +c \right)+11 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{143 d \cos \left(d x +c \right)^{6}}"," ",0,"-2/143/d*(64*I*cos(d*x+c)^6-64*cos(d*x+c)^5*sin(d*x+c)+8*I*cos(d*x+c)^4-40*cos(d*x+c)^3*sin(d*x+c)-68*I*cos(d*x+c)^2+40*cos(d*x+c)*sin(d*x+c)+11*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^6*a^3","B"
322,1,24,23,0.176000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{2 i \left(a +i a \tan \left(d x +c \right)\right)^{\frac{9}{2}}}{9 d a}"," ",0,"-2/9*I*(a+I*a*tan(d*x+c))^(9/2)/d/a","A"
323,1,412,96,1.259000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 i \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+3 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+3 \sin \left(d x +c \right) \cos \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+8 i \left(\cos^{4}\left(d x +c \right)\right)-4 i \left(\cos^{3}\left(d x +c \right)\right)-8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 i \cos \left(d x +c \right)-4 \cos \left(d x +c \right) \sin \left(d x +c \right)\right) a^{3}}{2 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)}"," ",0,"-1/2/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*I*sin(d*x+c)*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)+3*I*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+3*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+3*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+8*I*cos(d*x+c)^4-4*I*cos(d*x+c)^3-8*cos(d*x+c)^3*sin(d*x+c)+4*cos(d*x+c)^2*sin(d*x+c)-4*I*cos(d*x+c)-4*cos(d*x+c)*sin(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)*a^3","B"
324,1,742,110,1.276000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{\left(i \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-128 i \left(\cos^{7}\left(d x +c \right)\right)+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+16 i \left(\cos^{4}\left(d x +c \right)\right)+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-224 i \left(\cos^{6}\left(d x +c \right)\right)+3 \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)+80 i \left(\cos^{5}\left(d x +c \right)\right)+i \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)-256 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+3 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}+128 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+3 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+96 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+256 i \left(\cos^{8}\left(d x +c \right)\right)-16 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{128 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{3}}"," ",0,"-1/128/d*(-128*I*cos(d*x+c)^7+16*I*cos(d*x+c)^4+cos(d*x+c)^3*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+3*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+3*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-224*I*cos(d*x+c)^6+3*cos(d*x+c)*2^(1/2)*sin(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*sin(d*x+c)+80*I*cos(d*x+c)^5+3*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2*2^(1/2)-256*sin(d*x+c)*cos(d*x+c)^7+I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3*2^(1/2)+128*sin(d*x+c)*cos(d*x+c)^6+256*I*cos(d*x+c)^8+96*cos(d*x+c)^5*sin(d*x+c)+I*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-16*sin(d*x+c)*cos(d*x+c)^4)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^3*a^3","B"
325,1,1088,147,1.630000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{\left(-75 i \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}}+320 i \left(\cos^{7}\left(d x +c \right)\right)-640 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-15 \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-15 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+3072 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-15 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \sin \left(d x +c \right)-75 \sin \left(d x +c \right) \cos \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+16384 i \left(\cos^{12}\left(d x +c \right)\right)-15 i \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}-150 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}-150 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}-75 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-16384 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)+512 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)+960 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-75 i \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}-960 i \left(\cos^{6}\left(d x +c \right)\right)+8192 \sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)+128 i \left(\cos^{8}\left(d x +c \right)\right)-8192 i \left(\cos^{11}\left(d x +c \right)\right)-11264 i \left(\cos^{10}\left(d x +c \right)\right)+3584 i \left(\cos^{9}\left(d x +c \right)\right)-150 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-150 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{12288 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{5}}"," ",0,"-1/12288/d*(-15*I*cos(d*x+c)^5*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-75*I*cos(d*x+c)^4*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+16384*I*cos(d*x+c)^12-15*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)-8192*I*cos(d*x+c)^11-11264*I*cos(d*x+c)^10-16384*sin(d*x+c)*cos(d*x+c)^11+3072*sin(d*x+c)*cos(d*x+c)^9+512*sin(d*x+c)*cos(d*x+c)^8+8192*sin(d*x+c)*cos(d*x+c)^10-15*sin(d*x+c)*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-75*sin(d*x+c)*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-150*sin(d*x+c)*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-150*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-75*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-640*sin(d*x+c)*cos(d*x+c)^7+960*sin(d*x+c)*cos(d*x+c)^6+3584*I*cos(d*x+c)^9+320*I*cos(d*x+c)^7-960*I*cos(d*x+c)^6+128*I*cos(d*x+c)^8-150*I*cos(d*x+c)^3*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-150*I*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-75*I*cos(d*x+c)*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-15*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^5*a^3","B"
326,1,100,115,0.932000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \left(128 i \left(\cos^{4}\left(d x +c \right)\right)+128 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+54 i \left(\cos^{2}\left(d x +c \right)\right)-22 \cos \left(d x +c \right) \sin \left(d x +c \right)-5 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{35 d \cos \left(d x +c \right)^{3}}"," ",0,"2/35/d*(128*I*cos(d*x+c)^4+128*cos(d*x+c)^3*sin(d*x+c)+54*I*cos(d*x+c)^2-22*cos(d*x+c)*sin(d*x+c)-5*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3*a^3","A"
327,1,73,86,1.097000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{2 \left(22 i \left(\cos^{2}\left(d x +c \right)\right)+10 \cos \left(d x +c \right) \sin \left(d x +c \right)+i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{3 d \cos \left(d x +c \right)}"," ",0,"-2/3/d*(22*I*cos(d*x+c)^2+10*cos(d*x+c)*sin(d*x+c)+I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)*a^3","A"
328,1,71,61,1.134000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \left(-2 i \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 i\right) \cos \left(d x +c \right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{3 d}"," ",0,"2/3/d*(-2*I*cos(d*x+c)^2+2*cos(d*x+c)*sin(d*x+c)+3*I)*cos(d*x+c)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*a^3","A"
329,1,73,29,1.517000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{2 \left(2 i \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right)-i\right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{5 d}"," ",0,"-2/5/d*(2*I*cos(d*x+c)^2-2*cos(d*x+c)*sin(d*x+c)-I)*cos(d*x+c)^3*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*a^3","B"
330,1,1260,159,1.767000," ","int(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{\left(-13440 i \left(\cos^{7}\left(d x +c \right)\right)-13440 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-105 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right) \sqrt{2}-630 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-7168 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-79872 i \left(\cos^{12}\left(d x +c \right)\right)+122880 i \left(\cos^{14}\left(d x +c \right)\right)+105 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+630 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+2100 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+18432 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)-105 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \sin \left(d x +c \right)+61440 \sin \left(d x +c \right) \left(\cos^{12}\left(d x +c \right)\right)+8960 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)+6144 \sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)+4480 i \left(\cos^{8}\left(d x +c \right)\right)-122880 \sin \left(d x +c \right) \left(\cos^{13}\left(d x +c \right)\right)+630 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}+24576 i \left(\cos^{11}\left(d x +c \right)\right)+1024 i \left(\cos^{10}\left(d x +c \right)\right)+1792 i \left(\cos^{9}\left(d x +c \right)\right)+1575 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+1575 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-61440 i \left(\cos^{13}\left(d x +c \right)\right)-630 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}+105 i \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \sin \left(d x +c \right)-1575 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-2100 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-1575 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{107520 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{6}}"," ",0,"-1/107520/d*(105*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^6*sin(d*x+c)*2^(1/2)+630*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^5*sin(d*x+c)*2^(1/2)+18432*sin(d*x+c)*cos(d*x+c)^11-7168*sin(d*x+c)*cos(d*x+c)^9+8960*sin(d*x+c)*cos(d*x+c)^8+6144*sin(d*x+c)*cos(d*x+c)^10-13440*sin(d*x+c)*cos(d*x+c)^7+122880*I*cos(d*x+c)^14-61440*I*cos(d*x+c)^13-79872*I*cos(d*x+c)^12+24576*I*cos(d*x+c)^11+1024*I*cos(d*x+c)^10+1792*I*cos(d*x+c)^9+4480*I*cos(d*x+c)^8-13440*I*cos(d*x+c)^7-122880*sin(d*x+c)*cos(d*x+c)^13+61440*sin(d*x+c)*cos(d*x+c)^12+1575*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^4*sin(d*x+c)*2^(1/2)+2100*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)+1575*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)+630*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-105*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*sin(d*x+c)-105*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^6*2^(1/2)-630*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^5*2^(1/2)-1575*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^4*2^(1/2)-2100*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3*2^(1/2)-1575*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2*2^(1/2)-630*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+105*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(13/2)*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^6*a^3","B"
331,1,1604,219,2.236000," ","int(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{\left(-27720 \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+3465 i \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+27720 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \sqrt{2}-4587520 i \left(\cos^{17}\left(d x +c \right)\right)+1638400 i \left(\cos^{15}\left(d x +c \right)\right)-1774080 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-3465 \left(\cos^{8}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-27720 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-97020 \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-194040 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+135168 i \left(\cos^{12}\left(d x +c \right)\right)+65536 i \left(\cos^{14}\left(d x +c \right)\right)-946176 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)-5570560 i \left(\cos^{16}\left(d x +c \right)\right)+811008 \sin \left(d x +c \right) \left(\cos^{12}\left(d x +c \right)\right)-242550 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-194040 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-97020 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-3465 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \sin \left(d x +c \right)+9175040 i \left(\cos^{18}\left(d x +c \right)\right)-9175040 \left(\cos^{17}\left(d x +c \right)\right) \sin \left(d x +c \right)+1182720 \sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)+3465 i \left(\cos^{8}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \sqrt{2}+27720 i \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \sqrt{2}+97020 i \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \sqrt{2}+194040 i \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \sqrt{2}+242550 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \sqrt{2}+194040 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \sqrt{2}+97020 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{17}{2}} \sqrt{2}-720896 \sin \left(d x +c \right) \left(\cos^{13}\left(d x +c \right)\right)+236544 i \left(\cos^{11}\left(d x +c \right)\right)+591360 i \left(\cos^{10}\left(d x +c \right)\right)-1774080 i \left(\cos^{9}\left(d x +c \right)\right)+90112 i \left(\cos^{13}\left(d x +c \right)\right)+4587520 \left(\cos^{16}\left(d x +c \right)\right) \sin \left(d x +c \right)+983040 \left(\cos^{15}\left(d x +c \right)\right) \sin \left(d x +c \right)+655360 \left(\cos^{14}\left(d x +c \right)\right) \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{3}}{10321920 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{8}}"," ",0,"-1/10321920/d*(3465*I*cos(d*x+c)^8*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*2^(1/2)-242550*cos(d*x+c)^4*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-194040*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-97020*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-27720*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+27720*I*cos(d*x+c)^7*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*2^(1/2)-946176*sin(d*x+c)*cos(d*x+c)^11-1774080*sin(d*x+c)*cos(d*x+c)^9+1182720*sin(d*x+c)*cos(d*x+c)^10-720896*sin(d*x+c)*cos(d*x+c)^13+811008*sin(d*x+c)*cos(d*x+c)^12-3465*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*sin(d*x+c)+97020*I*cos(d*x+c)^6*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*2^(1/2)+194040*I*cos(d*x+c)^5*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*2^(1/2)+242550*I*cos(d*x+c)^4*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*2^(1/2)+194040*I*cos(d*x+c)^3*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*2^(1/2)+97020*I*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*2^(1/2)+27720*I*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*2^(1/2)+3465*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)-3465*cos(d*x+c)^8*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-27720*cos(d*x+c)^7*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-97020*cos(d*x+c)^6*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-194040*cos(d*x+c)^5*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(17/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-9175040*cos(d*x+c)^17*sin(d*x+c)+4587520*cos(d*x+c)^16*sin(d*x+c)+983040*cos(d*x+c)^15*sin(d*x+c)+655360*cos(d*x+c)^14*sin(d*x+c)+9175040*I*cos(d*x+c)^18-4587520*I*cos(d*x+c)^17-5570560*I*cos(d*x+c)^16+1638400*I*cos(d*x+c)^15+65536*I*cos(d*x+c)^14+90112*I*cos(d*x+c)^13+135168*I*cos(d*x+c)^12+236544*I*cos(d*x+c)^11+591360*I*cos(d*x+c)^10-1774080*I*cos(d*x+c)^9)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^8*a^3","B"
332,1,1948,281,3.649000," ","int(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^(7/2),x)","\text{Expression too large to display}"," ",0,"-1/484442112/d*(11351340*I*2^(1/2)*cos(d*x+c)^5*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)-45045*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*sin(d*x+c)-9459450*2^(1/2)*cos(d*x+c)^4*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-5405400*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-2027025*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-450450*2^(1/2)*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+45045*I*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*sin(d*x+c)-45045*2^(1/2)*cos(d*x+c)^10*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-450450*2^(1/2)*cos(d*x+c)^9*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-2027025*2^(1/2)*cos(d*x+c)^8*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+5405400*I*2^(1/2)*cos(d*x+c)^7*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)+45045*I*2^(1/2)*cos(d*x+c)^10*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)+450450*I*2^(1/2)*cos(d*x+c)^9*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)+2027025*I*2^(1/2)*cos(d*x+c)^8*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)+450450*I*2^(1/2)*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)+9459450*I*2^(1/2)*cos(d*x+c)^4*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)-5405400*2^(1/2)*cos(d*x+c)^7*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-9459450*2^(1/2)*cos(d*x+c)^6*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-11351340*2^(1/2)*cos(d*x+c)^5*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+9459450*I*2^(1/2)*cos(d*x+c)^6*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)-92252160*sin(d*x+c)*cos(d*x+c)^11-49201152*sin(d*x+c)*cos(d*x+c)^13+61501440*sin(d*x+c)*cos(d*x+c)^12+5405400*I*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)+2027025*I*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(21/2)+30750720*I*cos(d*x+c)^12-92252160*I*cos(d*x+c)^11-352321536*cos(d*x+c)^21*sin(d*x+c)+176160768*cos(d*x+c)^20*sin(d*x+c)+29360128*cos(d*x+c)^19*sin(d*x+c)+29360128*cos(d*x+c)^18*sin(d*x+c)+352321536*I*cos(d*x+c)^22-176160768*I*cos(d*x+c)^21-205520896*I*cos(d*x+c)^20+58720256*I*cos(d*x+c)^19+2097152*I*cos(d*x+c)^18+2621440*I*cos(d*x+c)^17+3407872*I*cos(d*x+c)^16+4685824*I*cos(d*x+c)^15+7028736*I*cos(d*x+c)^14+12300288*I*cos(d*x+c)^13-31457280*cos(d*x+c)^17*sin(d*x+c)+34078720*cos(d*x+c)^16*sin(d*x+c)-37486592*cos(d*x+c)^15*sin(d*x+c)+42172416*cos(d*x+c)^14*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^10*a^3","B"
333,1,127,93,1.813000," ","int(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 \left(512 i \left(\cos^{6}\left(d x +c \right)\right)-512 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+64 i \left(\cos^{4}\left(d x +c \right)\right)-320 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+28 i \left(\cos^{2}\left(d x +c \right)\right)-252 \cos \left(d x +c \right) \sin \left(d x +c \right)+231 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3003 d \cos \left(d x +c \right)^{6} a}"," ",0,"-2/3003/d*(512*I*cos(d*x+c)^6-512*cos(d*x+c)^5*sin(d*x+c)+64*I*cos(d*x+c)^4-320*cos(d*x+c)^3*sin(d*x+c)+28*I*cos(d*x+c)^2-252*cos(d*x+c)*sin(d*x+c)+231*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^6/a","A"
334,1,100,70,1.289000," ","int(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 \left(64 i \left(\cos^{4}\left(d x +c \right)\right)-64 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 i \left(\cos^{2}\left(d x +c \right)\right)-40 \cos \left(d x +c \right) \sin \left(d x +c \right)+35 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{315 d \cos \left(d x +c \right)^{4} a}"," ",0,"-2/315/d*(64*I*cos(d*x+c)^4-64*cos(d*x+c)^3*sin(d*x+c)+8*I*cos(d*x+c)^2-40*cos(d*x+c)*sin(d*x+c)+35*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4/a","A"
335,1,73,47,1.197000," ","int(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 \left(4 i \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{15 d \cos \left(d x +c \right)^{2} a}"," ",0,"-2/15/d*(4*I*cos(d*x+c)^2-4*cos(d*x+c)*sin(d*x+c)+3*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/a","A"
336,1,24,23,0.204000," ","int(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 i \sqrt{a +i a \tan \left(d x +c \right)}}{d a}"," ",0,"-2*I*(a+I*a*tan(d*x+c))^(1/2)/d/a","A"
337,1,341,114,1.150000," ","int(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(32 i \left(\cos^{4}\left(d x +c \right)\right)+15 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+32 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+15 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+20 i \left(\cos^{2}\left(d x +c \right)\right)+60 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{96 d a}"," ",0,"1/96/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(32*I*cos(d*x+c)^4+15*I*cos(d*x+c)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+32*cos(d*x+c)^3*sin(d*x+c)+15*I*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+20*I*cos(d*x+c)^2+60*cos(d*x+c)*sin(d*x+c))/a","B"
338,1,368,174,1.151000," ","int(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(512 i \left(\cos^{6}\left(d x +c \right)\right)+512 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+315 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+96 i \left(\cos^{4}\left(d x +c \right)\right)+315 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+315 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+672 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+420 i \left(\cos^{2}\left(d x +c \right)\right)+1260 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{2560 d a}"," ",0,"1/2560/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(512*I*cos(d*x+c)^6+512*cos(d*x+c)^5*sin(d*x+c)+315*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)+96*I*cos(d*x+c)^4+315*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+315*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+672*cos(d*x+c)^3*sin(d*x+c)+420*I*cos(d*x+c)^2+1260*cos(d*x+c)*sin(d*x+c))/a","B"
339,1,395,234,1.289000," ","int(cos(d*x+c)^6/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(61440 i \left(\cos^{8}\left(d x +c \right)\right)+61440 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+6656 i \left(\cos^{6}\left(d x +c \right)\right)+73216 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+13728 i \left(\cos^{4}\left(d x +c \right)\right)+45045 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+45045 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+96096 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+45045 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+60060 i \left(\cos^{2}\left(d x +c \right)\right)+180180 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{430080 d a}"," ",0,"1/430080/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(61440*I*cos(d*x+c)^8+61440*sin(d*x+c)*cos(d*x+c)^7+6656*I*cos(d*x+c)^6+73216*cos(d*x+c)^5*sin(d*x+c)+13728*I*cos(d*x+c)^4+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+96096*cos(d*x+c)^3*sin(d*x+c)+45045*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+60060*I*cos(d*x+c)^2+180180*cos(d*x+c)*sin(d*x+c))/a","A"
340,1,154,123,2.957000," ","int(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(2048 i \left(\cos^{8}\left(d x +c \right)\right)+2048 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-256 i \left(\cos^{6}\left(d x +c \right)\right)+768 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-80 i \left(\cos^{4}\left(d x +c \right)\right)+560 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-42 i \left(\cos^{2}\left(d x +c \right)\right)+462 \cos \left(d x +c \right) \sin \left(d x +c \right)-429 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{6435 d \cos \left(d x +c \right)^{7} a}"," ",0,"2/6435/d*(2048*I*cos(d*x+c)^8+2048*sin(d*x+c)*cos(d*x+c)^7-256*I*cos(d*x+c)^6+768*cos(d*x+c)^5*sin(d*x+c)-80*I*cos(d*x+c)^4+560*cos(d*x+c)^3*sin(d*x+c)-42*I*cos(d*x+c)^2+462*cos(d*x+c)*sin(d*x+c)-429*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^7/a","A"
341,1,127,92,1.438000," ","int(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(256 i \left(\cos^{6}\left(d x +c \right)\right)+256 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-32 i \left(\cos^{4}\left(d x +c \right)\right)+96 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-10 i \left(\cos^{2}\left(d x +c \right)\right)+70 \cos \left(d x +c \right) \sin \left(d x +c \right)-63 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{693 d \cos \left(d x +c \right)^{5} a}"," ",0,"2/693/d*(256*I*cos(d*x+c)^6+256*cos(d*x+c)^5*sin(d*x+c)-32*I*cos(d*x+c)^4+96*cos(d*x+c)^3*sin(d*x+c)-10*I*cos(d*x+c)^2+70*cos(d*x+c)*sin(d*x+c)-63*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^5/a","A"
342,1,100,61,1.250000," ","int(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(16 i \left(\cos^{4}\left(d x +c \right)\right)+16 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-2 i \left(\cos^{2}\left(d x +c \right)\right)+6 \cos \left(d x +c \right) \sin \left(d x +c \right)-5 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{35 d \cos \left(d x +c \right)^{3} a}"," ",0,"2/35/d*(16*I*cos(d*x+c)^4+16*cos(d*x+c)^3*sin(d*x+c)-2*I*cos(d*x+c)^2+6*cos(d*x+c)*sin(d*x+c)-5*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/a","A"
343,1,73,29,1.175000," ","int(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(2 i \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)-i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3 d \cos \left(d x +c \right) a}"," ",0,"2/3/d*(2*I*cos(d*x+c)^2+2*cos(d*x+c)*sin(d*x+c)-I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/a","B"
344,1,137,41,0.981000," ","int(sec(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}}{d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) a}"," ",0,"-1/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)*2^(1/2)/a","B"
345,1,319,97,1.146000," ","int(cos(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+8 i \left(\cos^{3}\left(d x +c \right)\right)+3 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-12 i \cos \left(d x +c \right)\right)}{16 d a}"," ",0,"1/16/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*I*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+8*I*cos(d*x+c)^3+3*I*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+8*cos(d*x+c)^2*sin(d*x+c)-12*I*cos(d*x+c))/a","B"
346,1,346,156,1.119000," ","int(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(192 i \left(\cos^{5}\left(d x +c \right)\right)+105 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+192 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+105 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+105 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+56 i \left(\cos^{3}\left(d x +c \right)\right)+280 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-420 i \cos \left(d x +c \right)\right)}{768 d a}"," ",0,"1/768/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(192*I*cos(d*x+c)^5+105*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+192*sin(d*x+c)*cos(d*x+c)^4+105*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+105*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+56*I*cos(d*x+c)^3+280*cos(d*x+c)^2*sin(d*x+c)-420*I*cos(d*x+c))/a","B"
347,1,117,93,1.367000," ","int(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \left(256 i \left(\cos^{5}\left(d x +c \right)\right)-256 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+32 i \left(\cos^{3}\left(d x +c \right)\right)-160 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+245 i \cos \left(d x +c \right)+105 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{1155 d \cos \left(d x +c \right)^{5} a^{2}}"," ",0,"-2/1155/d*(256*I*cos(d*x+c)^5-256*sin(d*x+c)*cos(d*x+c)^4+32*I*cos(d*x+c)^3-160*cos(d*x+c)^2*sin(d*x+c)+245*I*cos(d*x+c)+105*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^5/a^2","A"
348,1,90,70,1.152000," ","int(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \left(32 i \left(\cos^{3}\left(d x +c \right)\right)-32 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+39 i \cos \left(d x +c \right)+15 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{105 d \cos \left(d x +c \right)^{3} a^{2}}"," ",0,"-2/105/d*(32*I*cos(d*x+c)^3-32*cos(d*x+c)^2*sin(d*x+c)+39*I*cos(d*x+c)+15*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/a^2","A"
349,1,61,47,1.109000," ","int(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \left(5 i \cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3 d \cos \left(d x +c \right) a^{2}}"," ",0,"-2/3/d*(5*I*cos(d*x+c)+sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/a^2","A"
350,1,24,23,0.188000," ","int(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 i}{a d \sqrt{a +i a \tan \left(d x +c \right)}}"," ",0,"2*I/a/d/(a+I*a*tan(d*x+c))^(1/2)","A"
351,1,368,137,1.073000," ","int(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(384 i \left(\cos^{6}\left(d x +c \right)\right)+384 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+32 i \left(\cos^{4}\left(d x +c \right)\right)+105 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+105 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+224 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+105 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+140 i \left(\cos^{2}\left(d x +c \right)\right)+420 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{960 d \,a^{2}}"," ",0,"1/960/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(384*I*cos(d*x+c)^6+384*cos(d*x+c)^5*sin(d*x+c)+32*I*cos(d*x+c)^4+105*I*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+105*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+224*cos(d*x+c)^3*sin(d*x+c)+105*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+140*I*cos(d*x+c)^2+420*cos(d*x+c)*sin(d*x+c))/a^2","B"
352,1,395,197,1.152000," ","int(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(10240 i \left(\cos^{8}\left(d x +c \right)\right)+10240 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+512 i \left(\cos^{6}\left(d x +c \right)\right)+5632 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+3465 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1056 i \left(\cos^{4}\left(d x +c \right)\right)+3465 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3465 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+7392 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+4620 i \left(\cos^{2}\left(d x +c \right)\right)+13860 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{35840 d \,a^{2}}"," ",0,"1/35840/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(10240*I*cos(d*x+c)^8+10240*sin(d*x+c)*cos(d*x+c)^7+512*I*cos(d*x+c)^6+5632*cos(d*x+c)^5*sin(d*x+c)+3465*I*2^(1/2)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+1056*I*cos(d*x+c)^4+3465*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3465*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+7392*cos(d*x+c)^3*sin(d*x+c)+4620*I*cos(d*x+c)^2+13860*cos(d*x+c)*sin(d*x+c))/a^2","A"
353,1,422,257,1.416000," ","int(cos(d*x+c)^6/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(114688 i \left(\cos^{10}\left(d x +c \right)\right)+114688 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)+4096 i \left(\cos^{8}\left(d x +c \right)\right)+61440 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+6656 i \left(\cos^{6}\left(d x +c \right)\right)+73216 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+13728 i \left(\cos^{4}\left(d x +c \right)\right)+45045 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+45045 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+96096 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+45045 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+60060 i \left(\cos^{2}\left(d x +c \right)\right)+180180 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{516096 d \,a^{2}}"," ",0,"1/516096/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(114688*I*cos(d*x+c)^10+114688*sin(d*x+c)*cos(d*x+c)^9+4096*I*cos(d*x+c)^8+61440*sin(d*x+c)*cos(d*x+c)^7+6656*I*cos(d*x+c)^6+73216*cos(d*x+c)^5*sin(d*x+c)+13728*I*cos(d*x+c)^4+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+96096*cos(d*x+c)^3*sin(d*x+c)+45045*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+60060*I*cos(d*x+c)^2+180180*cos(d*x+c)*sin(d*x+c))/a^2","A"
354,1,171,123,6.824000," ","int(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \left(4096 i \left(\cos^{9}\left(d x +c \right)\right)+4096 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)-512 i \left(\cos^{7}\left(d x +c \right)\right)+1536 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-160 i \left(\cos^{5}\left(d x +c \right)\right)+1120 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-84 i \left(\cos^{3}\left(d x +c \right)\right)+924 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-1573 i \cos \left(d x +c \right)-715 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{12155 d \cos \left(d x +c \right)^{8} a^{2}}"," ",0,"2/12155/d*(4096*I*cos(d*x+c)^9+4096*sin(d*x+c)*cos(d*x+c)^8-512*I*cos(d*x+c)^7+1536*sin(d*x+c)*cos(d*x+c)^6-160*I*cos(d*x+c)^5+1120*sin(d*x+c)*cos(d*x+c)^4-84*I*cos(d*x+c)^3+924*cos(d*x+c)^2*sin(d*x+c)-1573*I*cos(d*x+c)-715*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^8/a^2","A"
355,1,144,92,1.755000," ","int(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \left(512 i \left(\cos^{7}\left(d x +c \right)\right)+512 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-64 i \left(\cos^{5}\left(d x +c \right)\right)+192 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-20 i \left(\cos^{3}\left(d x +c \right)\right)+140 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-225 i \cos \left(d x +c \right)-99 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{1287 d \cos \left(d x +c \right)^{6} a^{2}}"," ",0,"2/1287/d*(512*I*cos(d*x+c)^7+512*sin(d*x+c)*cos(d*x+c)^6-64*I*cos(d*x+c)^5+192*sin(d*x+c)*cos(d*x+c)^4-20*I*cos(d*x+c)^3+140*cos(d*x+c)^2*sin(d*x+c)-225*I*cos(d*x+c)-99*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^6/a^2","A"
356,1,117,61,1.218000," ","int(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \left(32 i \left(\cos^{5}\left(d x +c \right)\right)+32 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-4 i \left(\cos^{3}\left(d x +c \right)\right)+12 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-17 i \cos \left(d x +c \right)-7 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{63 d \cos \left(d x +c \right)^{4} a^{2}}"," ",0,"2/63/d*(32*I*cos(d*x+c)^5+32*sin(d*x+c)*cos(d*x+c)^4-4*I*cos(d*x+c)^3+12*cos(d*x+c)^2*sin(d*x+c)-17*I*cos(d*x+c)-7*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4/a^2","A"
357,1,90,29,1.146000," ","int(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \left(4 i \left(\cos^{3}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-3 i \cos \left(d x +c \right)-\sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{5 d \cos \left(d x +c \right)^{2} a^{2}}"," ",0,"2/5/d*(4*I*cos(d*x+c)^3+4*cos(d*x+c)^2*sin(d*x+c)-3*I*cos(d*x+c)-sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/a^2","B"
358,1,157,71,1.154000," ","int(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-\sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right)}{d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) a^{2}}"," ",0,"2/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+I*cos(d*x+c)-I+sin(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/a^2","B"
359,1,318,68,1.004000," ","int(sec(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+\sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+8 i \left(\cos^{3}\left(d x +c \right)\right)+8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 i \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{8 d \,a^{2}}"," ",0,"1/8/d*(I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)+2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+8*I*cos(d*x+c)^3+8*cos(d*x+c)^2*sin(d*x+c)-4*I*cos(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/a^2","B"
360,1,346,126,1.045000," ","int(cos(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(64 i \left(\cos^{5}\left(d x +c \right)\right)+15 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+64 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+8 i \left(\cos^{3}\left(d x +c \right)\right)+15 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+15 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+40 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-60 i \cos \left(d x +c \right)\right)}{128 d \,a^{2}}"," ",0,"1/128/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(64*I*cos(d*x+c)^5+15*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)+64*sin(d*x+c)*cos(d*x+c)^4+8*I*cos(d*x+c)^3+15*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+15*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+40*cos(d*x+c)^2*sin(d*x+c)-60*I*cos(d*x+c))/a^2","B"
361,1,373,190,1.160000," ","int(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1024 i \left(\cos^{7}\left(d x +c \right)\right)+1024 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+64 i \left(\cos^{5}\left(d x +c \right)\right)+315 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+576 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+168 i \left(\cos^{3}\left(d x +c \right)\right)+315 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+315 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+840 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-1260 i \cos \left(d x +c \right)\right)}{3072 d \,a^{2}}"," ",0,"1/3072/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(1024*I*cos(d*x+c)^7+1024*sin(d*x+c)*cos(d*x+c)^6+64*I*cos(d*x+c)^5+315*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)+576*sin(d*x+c)*cos(d*x+c)^4+168*I*cos(d*x+c)^3+315*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+315*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+840*cos(d*x+c)^2*sin(d*x+c)-1260*I*cos(d*x+c))/a^2","A"
362,1,127,116,1.828000," ","int(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(-4096 i \left(\cos^{6}\left(d x +c \right)\right)+4096 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-512 i \left(\cos^{4}\left(d x +c \right)\right)+2560 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-6230 i \left(\cos^{2}\left(d x +c \right)\right)-3990 \cos \left(d x +c \right) \sin \left(d x +c \right)+1155 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{15015 d \cos \left(d x +c \right)^{6} a^{3}}"," ",0,"2/15015/d*(-4096*I*cos(d*x+c)^6+4096*cos(d*x+c)^5*sin(d*x+c)-512*I*cos(d*x+c)^4+2560*cos(d*x+c)^3*sin(d*x+c)-6230*I*cos(d*x+c)^2-3990*cos(d*x+c)*sin(d*x+c)+1155*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^6/a^3","A"
363,1,100,93,1.267000," ","int(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 \left(128 i \left(\cos^{4}\left(d x +c \right)\right)-128 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+226 i \left(\cos^{2}\left(d x +c \right)\right)+130 \cos \left(d x +c \right) \sin \left(d x +c \right)-35 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{315 d \cos \left(d x +c \right)^{4} a^{3}}"," ",0,"-2/315/d*(128*I*cos(d*x+c)^4-128*cos(d*x+c)^3*sin(d*x+c)+226*I*cos(d*x+c)^2+130*cos(d*x+c)*sin(d*x+c)-35*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4/a^3","A"
364,1,73,70,1.175000," ","int(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 \left(46 i \left(\cos^{2}\left(d x +c \right)\right)+14 \cos \left(d x +c \right) \sin \left(d x +c \right)-3 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{15 d \cos \left(d x +c \right)^{2} a^{3}}"," ",0,"-2/15/d*(46*I*cos(d*x+c)^2+14*cos(d*x+c)*sin(d*x+c)-3*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/a^3","A"
365,1,65,47,1.160000," ","int(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(2 \cos \left(d x +c \right) \sin \left(d x +c \right)+i+2 i \left(\cos^{2}\left(d x +c \right)\right)\right)}{d \,a^{3}}"," ",0,"2/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(2*cos(d*x+c)*sin(d*x+c)+I+2*I*cos(d*x+c)^2)/a^3","A"
366,1,24,23,0.186000," ","int(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 i}{3 a d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"2/3*I/a/d/(a+I*a*tan(d*x+c))^(3/2)","A"
367,1,395,160,1.188000," ","int(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(2560 i \left(\cos^{8}\left(d x +c \right)\right)+2560 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-768 i \left(\cos^{6}\left(d x +c \right)\right)+512 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+96 i \left(\cos^{4}\left(d x +c \right)\right)+315 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+315 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+672 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+315 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+420 i \left(\cos^{2}\left(d x +c \right)\right)+1260 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{4480 d \,a^{3}}"," ",0,"1/4480/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(2560*I*cos(d*x+c)^8+2560*sin(d*x+c)*cos(d*x+c)^7-768*I*cos(d*x+c)^6+512*cos(d*x+c)^5*sin(d*x+c)+96*I*cos(d*x+c)^4+315*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)+315*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+672*cos(d*x+c)^3*sin(d*x+c)+315*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+420*I*cos(d*x+c)^2+1260*cos(d*x+c)*sin(d*x+c))/a^3","B"
368,1,422,220,1.371000," ","int(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(286720 i \left(\cos^{10}\left(d x +c \right)\right)+286720 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-81920 i \left(\cos^{8}\left(d x +c \right)\right)+61440 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+6656 i \left(\cos^{6}\left(d x +c \right)\right)+73216 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+13728 i \left(\cos^{4}\left(d x +c \right)\right)+45045 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+45045 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+96096 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+45045 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+60060 i \left(\cos^{2}\left(d x +c \right)\right)+180180 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{645120 d \,a^{3}}"," ",0,"1/645120/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(286720*I*cos(d*x+c)^10+286720*sin(d*x+c)*cos(d*x+c)^9-81920*I*cos(d*x+c)^8+61440*sin(d*x+c)*cos(d*x+c)^7+6656*I*cos(d*x+c)^6+73216*cos(d*x+c)^5*sin(d*x+c)+13728*I*cos(d*x+c)^4+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+96096*cos(d*x+c)^3*sin(d*x+c)+45045*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+60060*I*cos(d*x+c)^2+180180*cos(d*x+c)*sin(d*x+c))/a^3","A"
369,1,181,123,19.234000," ","int(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(8192 i \left(\cos^{10}\left(d x +c \right)\right)+8192 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-1024 i \left(\cos^{8}\left(d x +c \right)\right)+3072 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-320 i \left(\cos^{6}\left(d x +c \right)\right)+2240 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-168 i \left(\cos^{4}\left(d x +c \right)\right)+1848 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-5356 i \left(\cos^{2}\left(d x +c \right)\right)-3640 \cos \left(d x +c \right) \sin \left(d x +c \right)+1105 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{20995 d \cos \left(d x +c \right)^{9} a^{3}}"," ",0,"2/20995/d*(8192*I*cos(d*x+c)^10+8192*sin(d*x+c)*cos(d*x+c)^9-1024*I*cos(d*x+c)^8+3072*sin(d*x+c)*cos(d*x+c)^7-320*I*cos(d*x+c)^6+2240*cos(d*x+c)^5*sin(d*x+c)-168*I*cos(d*x+c)^4+1848*cos(d*x+c)^3*sin(d*x+c)-5356*I*cos(d*x+c)^2-3640*cos(d*x+c)*sin(d*x+c)+1105*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^9/a^3","A"
370,1,154,92,2.898000," ","int(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(1024 i \left(\cos^{8}\left(d x +c \right)\right)+1024 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)-128 i \left(\cos^{6}\left(d x +c \right)\right)+384 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-40 i \left(\cos^{4}\left(d x +c \right)\right)+280 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-736 i \left(\cos^{2}\left(d x +c \right)\right)-484 \cos \left(d x +c \right) \sin \left(d x +c \right)+143 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2145 d \cos \left(d x +c \right)^{7} a^{3}}"," ",0,"2/2145/d*(1024*I*cos(d*x+c)^8+1024*sin(d*x+c)*cos(d*x+c)^7-128*I*cos(d*x+c)^6+384*cos(d*x+c)^5*sin(d*x+c)-40*I*cos(d*x+c)^4+280*cos(d*x+c)^3*sin(d*x+c)-736*I*cos(d*x+c)^2-484*cos(d*x+c)*sin(d*x+c)+143*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^7/a^3","A"
371,1,127,61,1.451000," ","int(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(64 i \left(\cos^{6}\left(d x +c \right)\right)+64 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-8 i \left(\cos^{4}\left(d x +c \right)\right)+24 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-52 i \left(\cos^{2}\left(d x +c \right)\right)-32 \cos \left(d x +c \right) \sin \left(d x +c \right)+9 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{99 d \cos \left(d x +c \right)^{5} a^{3}}"," ",0,"2/99/d*(64*I*cos(d*x+c)^6+64*cos(d*x+c)^5*sin(d*x+c)-8*I*cos(d*x+c)^4+24*cos(d*x+c)^3*sin(d*x+c)-52*I*cos(d*x+c)^2-32*cos(d*x+c)*sin(d*x+c)+9*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^5/a^3","B"
372,1,100,29,1.172000," ","int(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(8 i \left(\cos^{4}\left(d x +c \right)\right)+8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-8 i \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right) \sin \left(d x +c \right)+i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{7 d \cos \left(d x +c \right)^{3} a^{3}}"," ",0,"2/7/d*(8*I*cos(d*x+c)^4+8*cos(d*x+c)^3*sin(d*x+c)-8*I*cos(d*x+c)^2-4*cos(d*x+c)*sin(d*x+c)+I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/a^3","B"
373,1,281,102,1.212000," ","int(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(3 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+3 \sqrt{2}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+8 i \left(\cos^{2}\left(d x +c \right)\right)+8 \cos \left(d x +c \right) \sin \left(d x +c \right)-7 i \cos \left(d x +c \right)-\sin \left(d x +c \right)-i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right) a^{3}}"," ",0,"2/3/d*(3*cos(d*x+c)*sin(d*x+c)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)+3*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+8*I*cos(d*x+c)^2+8*cos(d*x+c)*sin(d*x+c)-7*I*cos(d*x+c)-sin(d*x+c)-I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)/a^3","B"
374,1,443,71,1.189000," ","int(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{\sin \left(d x +c \right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+8 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-i \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-8 \left(\cos^{4}\left(d x +c \right)\right)-4 i \cos \left(d x +c \right) \sin \left(d x +c \right)-\sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+8 \left(\cos^{2}\left(d x +c \right)\right)\right)}{4 d \left(\cos^{2}\left(d x +c \right)-1\right) a^{3}}"," ",0,"-1/4/d*sin(d*x+c)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-I*sin(d*x+c)*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+8*I*cos(d*x+c)^3*sin(d*x+c)-I*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+cos(d*x+c)^2*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-8*cos(d*x+c)^4-4*I*cos(d*x+c)*sin(d*x+c)-2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+8*cos(d*x+c)^2)/(cos(d*x+c)^2-1)/a^3","B"
375,1,346,97,1.067000," ","int(sec(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(64 i \left(\cos^{5}\left(d x +c \right)\right)+3 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+64 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+3 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-24 i \left(\cos^{3}\left(d x +c \right)\right)+8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-12 i \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{64 d \,a^{3}}"," ",0,"1/64/d*(64*I*cos(d*x+c)^5+3*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+64*sin(d*x+c)*cos(d*x+c)^4+3*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-24*I*cos(d*x+c)^3+8*cos(d*x+c)^2*sin(d*x+c)-12*I*cos(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/a^3","B"
376,1,373,155,1.094000," ","int(cos(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1024 i \left(\cos^{7}\left(d x +c \right)\right)+1024 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-320 i \left(\cos^{5}\left(d x +c \right)\right)+105 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+192 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+105 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+56 i \left(\cos^{3}\left(d x +c \right)\right)+105 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+280 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-420 i \cos \left(d x +c \right)\right)}{1536 d \,a^{3}}"," ",0,"1/1536/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(1024*I*cos(d*x+c)^7+1024*sin(d*x+c)*cos(d*x+c)^6-320*I*cos(d*x+c)^5+105*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+192*sin(d*x+c)*cos(d*x+c)^4+105*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+56*I*cos(d*x+c)^3+105*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+280*cos(d*x+c)^2*sin(d*x+c)-420*I*cos(d*x+c))/a^3","B"
377,1,400,221,1.250000," ","int(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(24576 i \left(\cos^{9}\left(d x +c \right)\right)+24576 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)-7168 i \left(\cos^{7}\left(d x +c \right)\right)+5120 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+704 i \left(\cos^{5}\left(d x +c \right)\right)+3465 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+6336 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+3465 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+1848 i \left(\cos^{3}\left(d x +c \right)\right)+3465 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+9240 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-13860 i \cos \left(d x +c \right)\right)}{49152 d \,a^{3}}"," ",0,"1/49152/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(24576*I*cos(d*x+c)^9+24576*sin(d*x+c)*cos(d*x+c)^8-7168*I*cos(d*x+c)^7+5120*sin(d*x+c)*cos(d*x+c)^6+704*I*cos(d*x+c)^5+3465*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)+6336*sin(d*x+c)*cos(d*x+c)^4+3465*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+1848*I*cos(d*x+c)^3+3465*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+9240*cos(d*x+c)^2*sin(d*x+c)-13860*I*cos(d*x+c))/a^3","A"
378,1,117,116,1.456000," ","int(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \left(-2048 i \left(\cos^{5}\left(d x +c \right)\right)+2048 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-4876 i \left(\cos^{3}\left(d x +c \right)\right)-3340 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+1505 i \cos \left(d x +c \right)+315 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3465 d \cos \left(d x +c \right)^{5} a^{4}}"," ",0,"2/3465/d*(-2048*I*cos(d*x+c)^5+2048*sin(d*x+c)*cos(d*x+c)^4-4876*I*cos(d*x+c)^3-3340*cos(d*x+c)^2*sin(d*x+c)+1505*I*cos(d*x+c)+315*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^5/a^4","A"
379,1,90,93,1.211000," ","int(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{2 \left(204 i \left(\cos^{3}\left(d x +c \right)\right)+76 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-27 i \cos \left(d x +c \right)-5 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{35 d \cos \left(d x +c \right)^{3} a^{4}}"," ",0,"-2/35/d*(204*I*cos(d*x+c)^3+76*cos(d*x+c)^2*sin(d*x+c)-27*I*cos(d*x+c)-5*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/a^4","A"
380,1,88,70,1.185000," ","int(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(12 i \left(\cos^{3}\left(d x +c \right)\right)+12 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+11 i \cos \left(d x +c \right)+\sin \left(d x +c \right)\right)}{3 d \cos \left(d x +c \right) a^{4}}"," ",0,"2/3/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(12*I*cos(d*x+c)^3+12*cos(d*x+c)^2*sin(d*x+c)+11*I*cos(d*x+c)+sin(d*x+c))/cos(d*x+c)/a^4","A"
381,1,88,47,1.147000," ","int(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \cos \left(d x +c \right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(4 i \left(\cos^{3}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-5 i \cos \left(d x +c \right)-3 \sin \left(d x +c \right)\right)}{3 d \,a^{4}}"," ",0,"2/3/d*cos(d*x+c)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(4*I*cos(d*x+c)^3+4*cos(d*x+c)^2*sin(d*x+c)-5*I*cos(d*x+c)-3*sin(d*x+c))/a^4","A"
382,1,24,23,0.184000," ","int(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 i}{5 a d \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"2/5*I/a/d/(a+I*a*tan(d*x+c))^(5/2)","A"
383,1,422,183,1.242000," ","int(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(71680 i \left(\cos^{10}\left(d x +c \right)\right)+71680 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)-43520 i \left(\cos^{8}\left(d x +c \right)\right)-7680 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+512 i \left(\cos^{6}\left(d x +c \right)\right)+5632 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+3465 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1056 i \left(\cos^{4}\left(d x +c \right)\right)+3465 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3465 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+7392 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+4620 i \left(\cos^{2}\left(d x +c \right)\right)+13860 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{80640 d \,a^{4}}"," ",0,"1/80640/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(71680*I*cos(d*x+c)^10+71680*sin(d*x+c)*cos(d*x+c)^9-43520*I*cos(d*x+c)^8-7680*sin(d*x+c)*cos(d*x+c)^7+512*I*cos(d*x+c)^6+5632*cos(d*x+c)^5*sin(d*x+c)+3465*I*2^(1/2)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+1056*I*cos(d*x+c)^4+3465*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3465*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+7392*cos(d*x+c)^3*sin(d*x+c)+4620*I*cos(d*x+c)^2+13860*cos(d*x+c)*sin(d*x+c))/a^4","B"
384,1,449,243,1.701000," ","int(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(688128 i \left(\cos^{12}\left(d x +c \right)\right)+688128 \sin \left(d x +c \right) \left(\cos^{11}\left(d x +c \right)\right)-401408 i \left(\cos^{10}\left(d x +c \right)\right)-57344 \sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)+4096 i \left(\cos^{8}\left(d x +c \right)\right)+61440 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)+6656 i \left(\cos^{6}\left(d x +c \right)\right)+73216 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+13728 i \left(\cos^{4}\left(d x +c \right)\right)+45045 i \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+45045 i \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+96096 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+45045 \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+60060 i \left(\cos^{2}\left(d x +c \right)\right)+180180 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{946176 d \,a^{4}}"," ",0,"1/946176/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(688128*I*cos(d*x+c)^12+688128*sin(d*x+c)*cos(d*x+c)^11-401408*I*cos(d*x+c)^10-57344*sin(d*x+c)*cos(d*x+c)^9+4096*I*cos(d*x+c)^8+61440*sin(d*x+c)*cos(d*x+c)^7+6656*I*cos(d*x+c)^6+73216*cos(d*x+c)^5*sin(d*x+c)+13728*I*cos(d*x+c)^4+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+96096*cos(d*x+c)^3*sin(d*x+c)+45045*arctan(1/2*(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+60060*I*cos(d*x+c)^2+180180*cos(d*x+c)*sin(d*x+c))/a^4","A"
385,1,171,92,6.861000," ","int(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \left(2048 i \left(\cos^{9}\left(d x +c \right)\right)+2048 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)-256 i \left(\cos^{7}\left(d x +c \right)\right)+768 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-80 i \left(\cos^{5}\left(d x +c \right)\right)+560 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-2252 i \left(\cos^{3}\left(d x +c \right)\right)-1748 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+871 i \cos \left(d x +c \right)+195 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3315 d \cos \left(d x +c \right)^{8} a^{4}}"," ",0,"2/3315/d*(2048*I*cos(d*x+c)^9+2048*sin(d*x+c)*cos(d*x+c)^8-256*I*cos(d*x+c)^7+768*sin(d*x+c)*cos(d*x+c)^6-80*I*cos(d*x+c)^5+560*sin(d*x+c)*cos(d*x+c)^4-2252*I*cos(d*x+c)^3-1748*cos(d*x+c)^2*sin(d*x+c)+871*I*cos(d*x+c)+195*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^8/a^4","A"
386,1,144,61,1.779000," ","int(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \left(128 i \left(\cos^{7}\left(d x +c \right)\right)+128 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-16 i \left(\cos^{5}\left(d x +c \right)\right)+48 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-148 i \left(\cos^{3}\left(d x +c \right)\right)-108 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+51 i \cos \left(d x +c \right)+11 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{143 d \cos \left(d x +c \right)^{6} a^{4}}"," ",0,"2/143/d*(128*I*cos(d*x+c)^7+128*sin(d*x+c)*cos(d*x+c)^6-16*I*cos(d*x+c)^5+48*sin(d*x+c)*cos(d*x+c)^4-148*I*cos(d*x+c)^3-108*cos(d*x+c)^2*sin(d*x+c)+51*I*cos(d*x+c)+11*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^6/a^4","B"
387,1,115,29,1.204000," ","int(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \left(16 i \left(\cos^{5}\left(d x +c \right)\right)+16 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-20 i \left(\cos^{3}\left(d x +c \right)\right)-12 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 i \cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{9 d \cos \left(d x +c \right)^{4} a^{4}}"," ",0,"2/9/d*(16*I*cos(d*x+c)^5+16*sin(d*x+c)*cos(d*x+c)^4-20*I*cos(d*x+c)^3-12*cos(d*x+c)^2*sin(d*x+c)+5*I*cos(d*x+c)+sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4/a^4","B"
388,1,399,133,1.265000," ","int(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{2 \left(-15 \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}-30 \cos \left(d x +c \right) \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}\, \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}-15 \sqrt{2}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)+92 i \left(\cos^{3}\left(d x +c \right)\right)-76 i \left(\cos^{2}\left(d x +c \right)\right)+92 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-19 i \cos \left(d x +c \right)-16 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 i-3 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{15 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right)^{2} a^{4}}"," ",0,"2/15/d*(-15*cos(d*x+c)^2*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-30*cos(d*x+c)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-15*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)+92*I*cos(d*x+c)^3-76*I*cos(d*x+c)^2+92*cos(d*x+c)^2*sin(d*x+c)-19*I*cos(d*x+c)-16*cos(d*x+c)*sin(d*x+c)+3*I-3*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)^2/a^4","B"
389,1,318,102,1.205000," ","int(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(7/2),x)","-\frac{\left(3 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-8 i \left(\cos^{3}\left(d x +c \right)\right)-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \,a^{4}}"," ",0,"-1/2/d*(3*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)*2^(1/2)+3*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-8*I*cos(d*x+c)^3-8*cos(d*x+c)^2*sin(d*x+c)-4*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/a^4","B"
390,1,346,100,1.250000," ","int(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{\left(64 i \left(\cos^{5}\left(d x +c \right)\right)+64 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-56 i \left(\cos^{3}\left(d x +c \right)\right)-i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-\sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-24 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 i \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{32 d \,a^{4}}"," ",0,"1/32/d*(64*I*cos(d*x+c)^5+64*sin(d*x+c)*cos(d*x+c)^4-I*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-56*I*cos(d*x+c)^3-I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-24*cos(d*x+c)^2*sin(d*x+c)+4*I*cos(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/a^4","B"
391,1,373,126,0.941000," ","int(sec(d*x+c)/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{\left(1024 i \left(\cos^{7}\left(d x +c \right)\right)+1024 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-704 i \left(\cos^{5}\left(d x +c \right)\right)+15 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-192 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+15 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+8 i \left(\cos^{3}\left(d x +c \right)\right)+15 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+40 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-60 i \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{768 d \,a^{4}}"," ",0,"1/768/d*(1024*I*cos(d*x+c)^7+1024*sin(d*x+c)*cos(d*x+c)^6-704*I*cos(d*x+c)^5+15*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)-192*sin(d*x+c)*cos(d*x+c)^4+15*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+8*I*cos(d*x+c)^3+15*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+40*cos(d*x+c)^2*sin(d*x+c)-60*I*cos(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/a^4","B"
392,1,400,184,1.168000," ","int(cos(d*x+c)/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(8192 i \left(\cos^{9}\left(d x +c \right)\right)+8192 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)-5120 i \left(\cos^{7}\left(d x +c \right)\right)-1024 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+64 i \left(\cos^{5}\left(d x +c \right)\right)+315 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+576 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+168 i \left(\cos^{3}\left(d x +c \right)\right)+315 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+315 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+840 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-1260 i \cos \left(d x +c \right)\right)}{8192 d \,a^{4}}"," ",0,"1/8192/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(8192*I*cos(d*x+c)^9+8192*sin(d*x+c)*cos(d*x+c)^8-5120*I*cos(d*x+c)^7-1024*sin(d*x+c)*cos(d*x+c)^6+64*I*cos(d*x+c)^5+315*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)+576*sin(d*x+c)*cos(d*x+c)^4+168*I*cos(d*x+c)^3+315*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+315*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+840*cos(d*x+c)^2*sin(d*x+c)-1260*I*cos(d*x+c))/a^4","B"
393,1,427,252,1.451000," ","int(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(7/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(786432 i \left(\cos^{11}\left(d x +c \right)\right)+786432 \sin \left(d x +c \right) \left(\cos^{10}\left(d x +c \right)\right)-466944 i \left(\cos^{9}\left(d x +c \right)\right)-73728 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)+5120 i \left(\cos^{7}\left(d x +c \right)\right)+66560 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+9152 i \left(\cos^{5}\left(d x +c \right)\right)+45045 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+82368 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+45045 i \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+24024 i \left(\cos^{3}\left(d x +c \right)\right)+45045 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\left(i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)\right) \sqrt{2}}{2 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+120120 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-180180 i \cos \left(d x +c \right)\right)}{983040 d \,a^{4}}"," ",0,"1/983040/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(786432*I*cos(d*x+c)^11+786432*sin(d*x+c)*cos(d*x+c)^10-466944*I*cos(d*x+c)^9-73728*sin(d*x+c)*cos(d*x+c)^8+5120*I*cos(d*x+c)^7+66560*sin(d*x+c)*cos(d*x+c)^6+9152*I*cos(d*x+c)^5+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)+82368*sin(d*x+c)*cos(d*x+c)^4+45045*I*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+24024*I*cos(d*x+c)^3+45045*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+120120*cos(d*x+c)^2*sin(d*x+c)-180180*I*cos(d*x+c))/a^4","A"
394,1,309,416,1.371000," ","int((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+2 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-2 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{2 d \sin \left(d x +c \right)^{3} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/2/d*(e/cos(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*(I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+2*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-2*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-2*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^3/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(3/2)","A"
395,1,230,249,1.330000," ","int((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right) \left(i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)\right)}{d \sin \left(d x +c \right) \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/d*(e/cos(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))*(I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))))/sin(d*x+c)/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(1/2)","A"
396,1,56,30,1.247000," ","int((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(1/2),x)","-\frac{2 i \cos \left(d x +c \right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{e}{\cos \left(d x +c \right)}}}{d e}"," ",0,"-2*I/d*cos(d*x+c)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(1/2)/e","A"
397,1,75,65,1.301000," ","int((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(3/2),x)","\frac{2 \left(i \cos \left(d x +c \right)+2 \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \,e^{3}}"," ",0,"2/3/d*(I*cos(d*x+c)+2*sin(d*x+c))*cos(d*x+c)^2*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(3/2)/e^3","A"
398,1,85,98,1.303000," ","int((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(5/2),x)","\frac{2 \left(i \left(\cos^{2}\left(d x +c \right)\right)+4 \cos \left(d x +c \right) \sin \left(d x +c \right)-8 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(d x +c \right)\right)}{15 d \,e^{5}}"," ",0,"2/15/d*(I*cos(d*x+c)^2+4*cos(d*x+c)*sin(d*x+c)-8*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(5/2)*cos(d*x+c)^3/e^5","A"
399,1,102,132,1.374000," ","int((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(7/2),x)","\frac{2 \left(i \left(\cos^{3}\left(d x +c \right)\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 i \cos \left(d x +c \right)+16 \sin \left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{35 d \,e^{7}}"," ",0,"2/35/d*(I*cos(d*x+c)^3+6*cos(d*x+c)^2*sin(d*x+c)+8*I*cos(d*x+c)+16*sin(d*x+c))*cos(d*x+c)^4*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(7/2)/e^7","A"
400,1,414,347,1.255000," ","int((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{3} \left(21 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-21 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+42 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+28 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+42 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-21 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-21 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-16 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+14 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-44 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-16 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) a}{48 d \sin \left(d x +c \right)^{5} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/48/d*(e/cos(d*x+c))^(5/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^3*(21*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-21*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+42*I*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+28*I*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+42*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)-21*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-21*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-16*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+14*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)-44*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-16*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^5/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(5/2)*a","A"
401,1,363,449,1.291000," ","int((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x)","\frac{\left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-5 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+10 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+5 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-14 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) a}{8 d \sin \left(d x +c \right)^{3} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/8/d*(e/cos(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(5*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-5*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+10*I*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+5*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+5*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-10*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)-4*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-14*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-4*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^3/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(3/2)*a","A"
402,1,304,280,1.303000," ","int((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(3 i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-3 i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-2 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-3 \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-2 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) a}{2 d \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right)}"," ",0,"-1/2/d*(e/cos(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(3*I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-3*I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-2*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-3*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-3*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-2*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-2*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)/(1/(1+cos(d*x+c)))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)*a","A"
403,1,286,416,1.237000," ","int((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(1/2),x)","-\frac{\left(i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 i \cos \left(d x +c \right)-4 i-4 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}}"," ",0,"-1/d*(I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*I*cos(d*x+c)-4*I-4*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/(e/cos(d*x+c))^(1/2)*a","A"
404,1,76,30,1.198000," ","int((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(3/2),x)","-\frac{2 \left(i \cos \left(d x +c \right)-\sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) a}{3 d \,e^{3}}"," ",0,"-2/3/d*(I*cos(d*x+c)-sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(3/2)*cos(d*x+c)^2/e^3*a","B"
405,1,86,65,1.194000," ","int((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(5/2),x)","-\frac{2 \left(i \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right) \sin \left(d x +c \right)+2 i\right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a}{5 d \,e^{5}}"," ",0,"-2/5/d*(I*cos(d*x+c)^2-cos(d*x+c)*sin(d*x+c)+2*I)*cos(d*x+c)^3*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(5/2)/e^5*a","A"
406,1,103,101,1.282000," ","int((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(7/2),x)","-\frac{2 \left(3 i \left(\cos^{3}\left(d x +c \right)\right)-3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 i \cos \left(d x +c \right)-8 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{4}\left(d x +c \right)\right) a}{21 d \,e^{7}}"," ",0,"-2/21/d*(3*I*cos(d*x+c)^3-3*cos(d*x+c)^2*sin(d*x+c)-4*I*cos(d*x+c)-8*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(7/2)*cos(d*x+c)^4/e^7*a","A"
407,1,113,135,1.328000," ","int((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(9/2),x)","-\frac{2 \left(5 i \left(\cos^{4}\left(d x +c \right)\right)-5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-2 i \left(\cos^{2}\left(d x +c \right)\right)-8 \cos \left(d x +c \right) \sin \left(d x +c \right)+16 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{5}\left(d x +c \right)\right) a}{45 d \,e^{9}}"," ",0,"-2/45/d*(5*I*cos(d*x+c)^4-5*cos(d*x+c)^3*sin(d*x+c)-2*I*cos(d*x+c)^2-8*cos(d*x+c)*sin(d*x+c)+16*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(9/2)*cos(d*x+c)^5/e^9*a","A"
408,1,424,482,1.185000," ","int((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(45 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-45 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+90 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-68 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-90 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+45 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+45 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-16 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-158 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-52 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+16 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a^{2}}{48 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right)^{3} \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/48/d*(-1+cos(d*x+c))^2*(45*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-45*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+90*I*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-68*I*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-90*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)+45*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+45*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-16*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-158*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)-52*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+16*(1/(1+cos(d*x+c)))^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(3/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)/sin(d*x+c)^3/(1/(1+cos(d*x+c)))^(3/2)*a^2","A"
409,1,371,313,1.285000," ","int((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(21 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-21 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+22 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+22 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+21 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+21 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+18 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, a^{2}}{8 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}"," ",0,"1/8/d*(-1+cos(d*x+c))*(21*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-21*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+22*I*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+4*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+22*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)+21*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+21*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+18*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-4*(1/(1+cos(d*x+c)))^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)/sin(d*x+c)/(1/(1+cos(d*x+c)))^(1/2)*a^2","A"
410,1,347,449,1.257000," ","int((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-5 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+5 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+16 i \left(\cos^{2}\left(d x +c \right)\right)-18 i \cos \left(d x +c \right)-16 \cos \left(d x +c \right) \sin \left(d x +c \right)+2 i-2 \sin \left(d x +c \right)\right) a^{2}}{2 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}}"," ",0,"-1/2/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-5*I*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+5*I*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+5*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+5*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+16*I*cos(d*x+c)^2-18*I*cos(d*x+c)-16*cos(d*x+c)*sin(d*x+c)+2*I-2*sin(d*x+c))/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)/(e/cos(d*x+c))^(1/2)*a^2","A"
411,1,323,280,1.224000," ","int((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-3 i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 i \left(\cos^{2}\left(d x +c \right)\right)-3 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \cos \left(d x +c \right) \sin \left(d x +c \right)-4 i \cos \left(d x +c \right)+4 \sin \left(d x +c \right)-4 i\right) a^{2}}{3 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/3/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-3*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*I*cos(d*x+c)^2-3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*cos(d*x+c)*sin(d*x+c)-4*I*cos(d*x+c)+4*sin(d*x+c)-4*I)/(I*sin(d*x+c)+cos(d*x+c)-1)/cos(d*x+c)/(e/cos(d*x+c))^(3/2)*a^2","A"
412,1,88,30,1.207000," ","int((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(5/2),x)","-\frac{2 \left(2 i \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right)-i\right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a^{2}}{5 d \,e^{5}}"," ",0,"-2/5/d*(2*I*cos(d*x+c)^2-2*cos(d*x+c)*sin(d*x+c)-I)*cos(d*x+c)^3*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(5/2)/e^5*a^2","B"
413,1,105,65,1.211000," ","int((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(7/2),x)","-\frac{2 \left(6 i \left(\cos^{3}\left(d x +c \right)\right)-6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-i \cos \left(d x +c \right)-2 \sin \left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} a^{2}}{21 d \,e^{7}}"," ",0,"-2/21/d*(6*I*cos(d*x+c)^3-6*cos(d*x+c)^2*sin(d*x+c)-I*cos(d*x+c)-2*sin(d*x+c))*cos(d*x+c)^4*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(7/2)/e^7*a^2","A"
414,1,115,101,1.273000," ","int((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(9/2),x)","-\frac{2 \left(10 i \left(\cos^{4}\left(d x +c \right)\right)-10 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-i \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right) \sin \left(d x +c \right)+8 i\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{5}\left(d x +c \right)\right) a^{2}}{45 d \,e^{9}}"," ",0,"-2/45/d*(10*I*cos(d*x+c)^4-10*cos(d*x+c)^3*sin(d*x+c)-I*cos(d*x+c)^2-4*cos(d*x+c)*sin(d*x+c)+8*I)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(9/2)*cos(d*x+c)^5/e^9*a^2","A"
415,1,132,137,1.417000," ","int((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(11/2),x)","-\frac{2 \left(14 i \left(\cos^{5}\left(d x +c \right)\right)-14 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-i \left(\cos^{3}\left(d x +c \right)\right)-6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-8 i \cos \left(d x +c \right)-16 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \left(\cos^{6}\left(d x +c \right)\right) a^{2}}{77 d \,e^{11}}"," ",0,"-2/77/d*(14*I*cos(d*x+c)^5-14*sin(d*x+c)*cos(d*x+c)^4-I*cos(d*x+c)^3-6*cos(d*x+c)^2*sin(d*x+c)-8*I*cos(d*x+c)-16*sin(d*x+c))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(11/2)*cos(d*x+c)^6/e^11*a^2","A"
416,1,316,285,1.330000," ","int((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{3} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+2 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+2 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{2 d \sin \left(d x +c \right)^{5} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a}"," ",0,"-1/2/d*(e/cos(d*x+c))^(5/2)*cos(d*x+c)^2*(-1+cos(d*x+c))^3*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+2*I*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+2*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+2*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^5/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(5/2)/a","A"
417,1,232,385,1.254000," ","int((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)\right)}{d \sin \left(d x +c \right)^{3} \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) a}"," ",0,"1/d*(e/cos(d*x+c))^(3/2)*cos(d*x+c)^2*(-1+cos(d*x+c))^2*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))))/sin(d*x+c)^3/(1/(1+cos(d*x+c)))^(3/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/a","A"
418,1,72,30,1.162000," ","int((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 i \cos \left(d x +c \right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{d a}"," ",0,"2*I/d*cos(d*x+c)*(e/cos(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(-I*sin(d*x+c)+cos(d*x+c))/a","B"
419,1,85,64,1.164000," ","int(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(i \cos \left(d x +c \right)-2 \sin \left(d x +c \right)\right)}{3 d \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, a}"," ",0,"-2/3/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(I*cos(d*x+c)-2*sin(d*x+c))/(I*sin(d*x+c)+cos(d*x+c))/(e/cos(d*x+c))^(1/2)/a","A"
420,1,105,97,1.169000," ","int(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 i \left(\cos^{3}\left(d x +c \right)\right)+3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 i \cos \left(d x +c \right)+8 \sin \left(d x +c \right)\right)}{15 d \,e^{3} a}"," ",0,"2/15/d*cos(d*x+c)^2*(e/cos(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*I*cos(d*x+c)^3+3*cos(d*x+c)^2*sin(d*x+c)+4*I*cos(d*x+c)+8*sin(d*x+c))/e^3/a","A"
421,1,115,133,1.194000," ","int(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(5 i \left(\cos^{4}\left(d x +c \right)\right)+5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 i \left(\cos^{2}\left(d x +c \right)\right)+8 \cos \left(d x +c \right) \sin \left(d x +c \right)-16 i\right)}{35 d \,e^{5} a}"," ",0,"2/35/d*cos(d*x+c)^3*(e/cos(d*x+c))^(5/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(5*I*cos(d*x+c)^4+5*cos(d*x+c)^3*sin(d*x+c)+2*I*cos(d*x+c)^2+8*cos(d*x+c)*sin(d*x+c)-16*I)/e^5/a","A"
422,1,132,166,1.247000," ","int(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(35 i \left(\cos^{5}\left(d x +c \right)\right)+35 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+8 i \left(\cos^{3}\left(d x +c \right)\right)+48 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+64 i \cos \left(d x +c \right)+128 \sin \left(d x +c \right)\right)}{315 d \,e^{7} a}"," ",0,"2/315/d*(e/cos(d*x+c))^(7/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(35*I*cos(d*x+c)^5+35*sin(d*x+c)*cos(d*x+c)^4+8*I*cos(d*x+c)^3+48*cos(d*x+c)^2*sin(d*x+c)+64*I*cos(d*x+c)+128*sin(d*x+c))/e^7/a","A"
423,1,1022,421,1.162000," ","int((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-3 i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-6 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-3 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+3 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-6 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-6 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+6 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-6 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-6 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+3 i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-4 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+3 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+3 \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+3 \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+4 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{4 d \left(2 i \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \sin \left(d x +c \right)^{7} \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} a^{2}}"," ",0,"-1/4/d*(-1+cos(d*x+c))^3*(6*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+3*I*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+3*I*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-6*I*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+3*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-6*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-3*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+3*I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-3*I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-6*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-6*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-6*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+6*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-4*I*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-6*I*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-4*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)+3*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+3*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+3*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-3*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+3*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+3*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+4*(1/(1+cos(d*x+c)))^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(e/cos(d*x+c))^(7/2)/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/sin(d*x+c)^7/(1/(1+cos(d*x+c)))^(7/2)/a^2","B"
424,1,957,285,1.320000," ","int((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(2 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right) \sin \left(d x +c \right)+2 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-8 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+2 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-2 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+2 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right) \sin \left(d x +c \right)-8 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right) \sin \left(d x +c \right)+i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right) \sin \left(d x +c \right)+i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+8 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{2 d \left(2 i \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{5} a^{2}}"," ",0,"-1/2/d*(-1+cos(d*x+c))^2*(-I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))*sin(d*x+c)-8*I*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+2*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*cos(d*x+c)*sin(d*x+c)+2*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))*cos(d*x+c)*sin(d*x+c)-2*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*cos(d*x+c)^2+2*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-2*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+2*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))*cos(d*x+c)^2-I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+2*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+2*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*sin(d*x+c)-8*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)-cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))*sin(d*x+c)-I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*sin(d*x+c)+I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+8*(1/(1+cos(d*x+c)))^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(e/cos(d*x+c))^(5/2)/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/(1/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^5/a^2","B"
425,1,87,30,1.111000," ","int((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 i \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{3 d \left(2 i \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) a^{2}}"," ",0,"2/3*I/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e/cos(d*x+c))^(3/2)*cos(d*x+c)^2/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/a^2","B"
426,1,101,64,1.213000," ","int((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 i \cos \left(d x +c \right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(2 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2 \left(\cos^{3}\left(d x +c \right)\right)+2 i \sin \left(d x +c \right)-\cos \left(d x +c \right)\right)}{5 d \,a^{2}}"," ",0,"-2/5*I/d*cos(d*x+c)*(e/cos(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(2*I*cos(d*x+c)^2*sin(d*x+c)-2*cos(d*x+c)^3+2*I*sin(d*x+c)-cos(d*x+c))/a^2","A"
427,1,106,97,1.234000," ","int(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x)","-\frac{2 \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(9 i \left(\cos^{2}\left(d x +c \right)\right)-12 \cos \left(d x +c \right) \sin \left(d x +c \right)-8 i\right)}{21 d \left(2 i \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, a^{2}}"," ",0,"-2/21/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(9*I*cos(d*x+c)^2-12*cos(d*x+c)*sin(d*x+c)-8*I)/(2*I*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-1)/(e/cos(d*x+c))^(1/2)/a^2","A"
428,1,132,133,1.185000," ","int(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(10 i \left(\cos^{5}\left(d x +c \right)\right)+10 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+i \left(\cos^{3}\left(d x +c \right)\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 i \cos \left(d x +c \right)+16 \sin \left(d x +c \right)\right)}{45 d \,e^{3} a^{2}}"," ",0,"2/45/d*cos(d*x+c)^2*(e/cos(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(10*I*cos(d*x+c)^5+10*sin(d*x+c)*cos(d*x+c)^4+I*cos(d*x+c)^3+6*cos(d*x+c)^2*sin(d*x+c)+8*I*cos(d*x+c)+16*sin(d*x+c))/e^3/a^2","A"
429,1,142,169,1.174000," ","int(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x)","\frac{2 \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(70 i \left(\cos^{6}\left(d x +c \right)\right)+70 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 i \left(\cos^{4}\left(d x +c \right)\right)+40 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+16 i \left(\cos^{2}\left(d x +c \right)\right)+64 \cos \left(d x +c \right) \sin \left(d x +c \right)-128 i\right)}{385 d \,e^{5} a^{2}}"," ",0,"2/385/d*cos(d*x+c)^3*(e/cos(d*x+c))^(5/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(70*I*cos(d*x+c)^6+70*cos(d*x+c)^5*sin(d*x+c)+5*I*cos(d*x+c)^4+40*cos(d*x+c)^3*sin(d*x+c)+16*I*cos(d*x+c)^2+64*cos(d*x+c)*sin(d*x+c)-128*I)/e^5/a^2","A"
430,1,1439,321,1.148000," ","int((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{4} \left(15 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+4 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+10 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+10 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-44 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-5 \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+5 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+5 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-20 i \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+20 i \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+10 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+10 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-84 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-20 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+20 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+80 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-20 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-20 i \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-15 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+15 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-20 \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-20 \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+80 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+10 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-10 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+10 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-10 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+5 i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-5 i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-5 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+15 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}}}{4 d \left(4 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \left(\cos^{3}\left(d x +c \right)\right)-i \sin \left(d x +c \right)-3 \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{9} \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} a^{3}}"," ",0,"1/4/d*(-1+cos(d*x+c))^4*(-20*I*cos(d*x+c)^3*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-44*I*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+5*I*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+10*I*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+10*I*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+5*I*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+80*I*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-20*I*cos(d*x+c)^3*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+4*(1/(1+cos(d*x+c)))^(1/2)-10*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+10*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-5*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+5*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+20*I*cos(d*x+c)^4*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-20*I*cos(d*x+c)^4*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-10*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+10*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-15*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+15*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+5*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*cos(d*x+c)-5*I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+20*cos(d*x+c)^3*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-20*cos(d*x+c)^3*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+10*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+10*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-84*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)+15*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+15*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-5*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-5*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-20*cos(d*x+c)^4*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-20*cos(d*x+c)^4*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+80*cos(d*x+c)^4*(1/(1+cos(d*x+c)))^(1/2))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(e/cos(d*x+c))^(9/2)/(4*I*sin(d*x+c)*cos(d*x+c)^2+4*cos(d*x+c)^3-I*sin(d*x+c)-3*cos(d*x+c))/sin(d*x+c)^9/(1/(1+cos(d*x+c)))^(9/2)/a^3","B"
431,1,1324,421,1.186000," ","int((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(-6 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+8 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-12 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-12 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-8 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+9 \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+9 \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+6 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+6 i \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+3 i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right) \sin \left(d x +c \right)+3 i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right) \sin \left(d x +c \right)-3 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-3 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-12 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-12 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-8 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+6 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+12 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-12 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+12 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-12 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+3 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right) \sin \left(d x +c \right)-3 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right) \sin \left(d x +c \right)-3 i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+3 i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+9 i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-9 i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)-6 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right)}{2}\right)\right) \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{6 d \left(4 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \left(\cos^{3}\left(d x +c \right)\right)-i \sin \left(d x +c \right)-3 \cos \left(d x +c \right)\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{7} a^{3}}"," ",0,"1/6/d*(-1+cos(d*x+c))^3*(-3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+8*(1/(1+cos(d*x+c)))^(1/2)-3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-12*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+12*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+6*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-6*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-12*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-12*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-8*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)-8*I*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-12*I*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-12*I*cos(d*x+c)^2*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+6*I*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+6*I*cos(d*x+c)*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+6*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+6*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+9*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+9*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+12*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-12*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-6*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+6*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-9*I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+9*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*cos(d*x+c)+3*I*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))+3*I*sin(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))*sin(d*x+c)-3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))*sin(d*x+c)+3*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c)))-3*I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))))*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(e/cos(d*x+c))^(7/2)/(4*I*sin(d*x+c)*cos(d*x+c)^2+4*cos(d*x+c)^3-I*sin(d*x+c)-3*cos(d*x+c))/(1/(1+cos(d*x+c)))^(7/2)/sin(d*x+c)^7/a^3","B"
432,1,103,30,1.116000," ","int((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 i \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(-4 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \left(\cos^{3}\left(d x +c \right)\right)+i \sin \left(d x +c \right)-3 \cos \left(d x +c \right)\right)}{5 d \,a^{3}}"," ",0,"2/5*I/d*(e/cos(d*x+c))^(5/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(-4*I*cos(d*x+c)^2*sin(d*x+c)+4*cos(d*x+c)^3+I*sin(d*x+c)-3*cos(d*x+c))/a^3","B"
433,1,112,64,1.108000," ","int((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 i \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(12 i \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-12 \left(\cos^{4}\left(d x +c \right)\right)+i \cos \left(d x +c \right) \sin \left(d x +c \right)+5 \left(\cos^{2}\left(d x +c \right)\right)+2\right)}{21 d \,a^{3}}"," ",0,"-2/21*I/d*(e/cos(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(12*I*cos(d*x+c)^3*sin(d*x+c)-12*cos(d*x+c)^4+I*sin(d*x+c)*cos(d*x+c)+5*cos(d*x+c)^2+2)/a^3","A"
434,1,128,97,1.168000," ","int((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x)","-\frac{2 i \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(20 i \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)-20 \left(\cos^{5}\left(d x +c \right)\right)+3 i \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+7 \left(\cos^{3}\left(d x +c \right)\right)+8 i \sin \left(d x +c \right)-4 \cos \left(d x +c \right)\right)}{45 d \,a^{3}}"," ",0,"-2/45*I/d*(e/cos(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(20*I*cos(d*x+c)^4*sin(d*x+c)-20*cos(d*x+c)^5+3*I*cos(d*x+c)^2*sin(d*x+c)+7*cos(d*x+c)^3+8*I*sin(d*x+c)-4*cos(d*x+c))/a^3","A"
435,1,140,130,1.186000," ","int(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \cos \left(d x +c \right) \sqrt{\frac{e}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(28 i \left(\cos^{6}\left(d x +c \right)\right)+28 \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)-9 i \left(\cos^{4}\left(d x +c \right)\right)+5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 i \left(\cos^{2}\left(d x +c \right)\right)+8 \cos \left(d x +c \right) \sin \left(d x +c \right)-16 i\right)}{77 d e \,a^{3}}"," ",0,"2/77/d*cos(d*x+c)*(e/cos(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(28*I*cos(d*x+c)^6+28*cos(d*x+c)^5*sin(d*x+c)-9*I*cos(d*x+c)^4+5*cos(d*x+c)^3*sin(d*x+c)+2*I*cos(d*x+c)^2+8*cos(d*x+c)*sin(d*x+c)-16*I)/e/a^3","A"
436,1,159,166,1.176000," ","int(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x)","\frac{2 \left(\frac{e}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(180 i \left(\cos^{7}\left(d x +c \right)\right)+180 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)-55 i \left(\cos^{5}\left(d x +c \right)\right)+35 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+8 i \left(\cos^{3}\left(d x +c \right)\right)+48 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+64 i \cos \left(d x +c \right)+128 \sin \left(d x +c \right)\right)}{585 d \,e^{3} a^{3}}"," ",0,"2/585/d*(e/cos(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(180*I*cos(d*x+c)^7+180*sin(d*x+c)*cos(d*x+c)^6-55*I*cos(d*x+c)^5+35*sin(d*x+c)*cos(d*x+c)^4+8*I*cos(d*x+c)^3+48*cos(d*x+c)^2*sin(d*x+c)+64*I*cos(d*x+c)+128*sin(d*x+c))/e^3/a^3","A"
437,0,0,64,1.159000," ","int((e*sec(d*x+c))^(7/3)/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{\frac{7}{3}}}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int((e*sec(d*x+c))^(7/3)/(a+I*a*tan(d*x+c))^(1/2),x)","F"
438,0,0,64,1.158000," ","int((e*sec(d*x+c))^(5/3)/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{\frac{5}{3}}}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int((e*sec(d*x+c))^(5/3)/(a+I*a*tan(d*x+c))^(1/2),x)","F"
439,0,0,63,1.402000," ","int((e*sec(d*x+c))^(2/3)/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{\frac{2}{3}}}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int((e*sec(d*x+c))^(2/3)/(a+I*a*tan(d*x+c))^(1/2),x)","F"
440,0,0,63,1.346000," ","int((e*sec(d*x+c))^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{\frac{1}{3}}}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int((e*sec(d*x+c))^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x)","F"
441,0,0,63,1.365000," ","int(1/(e*sec(d*x+c))^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{1}{\left(e \sec \left(d x +c \right)\right)^{\frac{1}{3}} \sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int(1/(e*sec(d*x+c))^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x)","F"
442,0,0,66,1.260000," ","int(1/(e*sec(d*x+c))^(4/3)/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{1}{\left(e \sec \left(d x +c \right)\right)^{\frac{4}{3}} \sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int(1/(e*sec(d*x+c))^(4/3)/(a+I*a*tan(d*x+c))^(1/2),x)","F"
443,0,0,342,0.809000," ","int((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(7/3),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}}}{\left(a +i a \tan \left(f x +e \right)\right)^{\frac{7}{3}}}\, dx"," ",0,"int((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(7/3),x)","F"
444,0,0,294,0.776000," ","int((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(4/3),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}}}{\left(a +i a \tan \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(4/3),x)","F"
445,0,0,264,0.738000," ","int((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(1/3),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}}}{\left(a +i a \tan \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(1/3),x)","F"
446,0,0,31,0.710000," ","int((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(2/3),x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}} \left(a +i a \tan \left(f x +e \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(2/3),x)","F"
447,0,0,65,0.756000," ","int((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(5/3),x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}} \left(a +i a \tan \left(f x +e \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(5/3),x)","F"
448,0,0,98,0.778000," ","int((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(8/3),x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}} \left(a +i a \tan \left(f x +e \right)\right)^{\frac{8}{3}}\, dx"," ",0,"int((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(8/3),x)","F"
449,0,0,131,0.772000," ","int((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(11/3),x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{2}{3}} \left(a +i a \tan \left(f x +e \right)\right)^{\frac{11}{3}}\, dx"," ",0,"int((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(11/3),x)","F"
450,0,0,73,1.213000," ","int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^5,x)","\int \left(e \sec \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)^{5}\, dx"," ",0,"int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^5,x)","F"
451,0,0,73,1.420000," ","int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^3,x)","\int \left(e \sec \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^3,x)","F"
452,0,0,73,1.173000," ","int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x)","\int \left(e \sec \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x)","F"
453,0,0,69,1.426000," ","int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c)),x)","\int \left(e \sec \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)\, dx"," ",0,"int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c)),x)","F"
454,0,0,73,2.315000," ","int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c)),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{m}}{a +i a \tan \left(d x +c \right)}\, dx"," ",0,"int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c)),x)","F"
455,0,0,73,3.861000," ","int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{m}}{\left(a +i a \tan \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x)","F"
456,0,0,73,4.486000," ","int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^3,x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{m}}{\left(a +i a \tan \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^3,x)","F"
457,0,0,87,1.272000," ","int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(7/2),x)","\int \left(e \sec \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(7/2),x)","F"
458,0,0,87,1.212000," ","int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(5/2),x)","\int \left(e \sec \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(5/2),x)","F"
459,0,0,85,1.229000," ","int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(3/2),x)","\int \left(e \sec \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(3/2),x)","F"
460,0,0,85,1.512000," ","int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x)","\int \left(e \sec \left(d x +c \right)\right)^{m} \sqrt{a +i a \tan \left(d x +c \right)}\, dx"," ",0,"int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x)","F"
461,0,0,84,1.178000," ","int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{m}}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x)","F"
462,0,0,87,1.125000," ","int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(3/2),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{m}}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(3/2),x)","F"
463,0,0,87,1.135000," ","int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(5/2),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{m}}{\left(a +i a \tan \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(5/2),x)","F"
464,0,0,89,1.859000," ","int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x)","F"
465,1,3316,91,1.510000," ","int(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^n,x)","\text{output too large to display}"," ",0,"-32*I/(exp(2*I*(d*x+c))+1)^5/(n+4)/(5+n)/d/(3+n)*(2*2^n*a^n/((exp(2*I*(d*x+c))+1)^n)*(exp(I*(Re(d*x)+Re(c)))^n)^2*exp(-2*n*Im(d*x)-2*n*Im(c))*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n)*exp(I*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n)*exp(10*I*d*x)*exp(-1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n)*exp(10*I*c)+2*n*2^n*a^n/((exp(2*I*(d*x+c))+1)^n)*(exp(I*(Re(d*x)+Re(c)))^n)^2*exp(-2*n*Im(d*x)-2*n*Im(c))*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n)*exp(I*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n)*exp(8*I*d*x)*exp(-1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n)*exp(8*I*c)+n^2*2^n*a^n/((exp(2*I*(d*x+c))+1)^n)*(exp(I*(Re(d*x)+Re(c)))^n)^2*exp(-2*n*Im(d*x)-2*n*Im(c))*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n)*exp(I*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n)*exp(6*I*d*x)*exp(-1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n)*exp(6*I*c)+10*2^n*a^n/((exp(2*I*(d*x+c))+1)^n)*(exp(I*(Re(d*x)+Re(c)))^n)^2*exp(-2*n*Im(d*x)-2*n*Im(c))*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n)*exp(I*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n)*exp(8*I*d*x)*exp(-1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n)*exp(8*I*c)+9*n*2^n*a^n/((exp(2*I*(d*x+c))+1)^n)*(exp(I*(Re(d*x)+Re(c)))^n)^2*exp(-2*n*Im(d*x)-2*n*Im(c))*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n)*exp(I*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n)*exp(6*I*d*x)*exp(-1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n)*exp(6*I*c)+20*2^n*a^n/((exp(2*I*(d*x+c))+1)^n)*(exp(I*(Re(d*x)+Re(c)))^n)^2*exp(-2*n*Im(d*x)-2*n*Im(c))*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n)*exp(I*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n)*exp(6*I*d*x)*exp(-1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n)*exp(6*I*c))","C"
466,1,1668,61,0.925000," ","int(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^n,x)","-\frac{8 i \left(2^{n} a^{n} \left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)^{-n} \left({\mathrm e}^{i \left(\Re \left(d x \right)+\Re \left(c \right)\right)}\right)^{2 n} {\mathrm e}^{-2 n \Im \left(d x \right)-2 n \Im \left(c \right)} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right)^{3} \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} \pi  n}{2}} {\mathrm e}^{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) \pi  n} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i a \right) \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right)^{2} \pi  n}{2}} {\mathrm e}^{6 i d x} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(i a \right) \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \pi  n}{2}} {\mathrm e}^{6 i c}+n \left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)^{-n} \left({\mathrm e}^{i \left(\Re \left(d x \right)+\Re \left(c \right)\right)}\right)^{2 n} a^{n} 2^{n} {\mathrm e}^{-2 n \Im \left(d x \right)-2 n \Im \left(c \right)} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i a \right) \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(i a \right) \pi  n}{2}} {\mathrm e}^{4 i d x} {\mathrm e}^{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) \pi  n} {\mathrm e}^{\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right)^{2} \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \pi  n}{2}} {\mathrm e}^{4 i c} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right)^{3} \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} \pi  n}{2}}+3 \left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)^{-n} \left({\mathrm e}^{i \left(\Re \left(d x \right)+\Re \left(c \right)\right)}\right)^{2 n} a^{n} 2^{n} {\mathrm e}^{-2 n \Im \left(d x \right)-2 n \Im \left(c \right)} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i a \right) \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(i a \right) \pi  n}{2}} {\mathrm e}^{4 i d x} {\mathrm e}^{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) \pi  n} {\mathrm e}^{\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right)^{2} \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} \pi  n}{2}} {\mathrm e}^{\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \pi  n}{2}} {\mathrm e}^{4 i c} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right)^{3} \pi  n}{2}} {\mathrm e}^{-\frac{i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} \pi  n}{2}}\right)}{\left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)^{3} \left(3+n \right) d \left(2+n \right)}"," ",0,"-8*I/(exp(2*I*(d*x+c))+1)^3/(3+n)/d/(2+n)*(2^n*a^n/((exp(2*I*(d*x+c))+1)^n)*(exp(I*(Re(d*x)+Re(c)))^n)^2*exp(-2*n*Im(d*x)-2*n*Im(c))*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n)*exp(I*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n)*exp(6*I*d*x)*exp(-1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n)*exp(6*I*c)+n/((exp(2*I*(d*x+c))+1)^n)*(exp(I*(Re(d*x)+Re(c)))^n)^2*a^n*2^n*exp(-2*n*Im(d*x)-2*n*Im(c))*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n)*exp(1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n)*exp(4*I*d*x)*exp(I*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(-1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n)*exp(4*I*c)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n)+3/((exp(2*I*(d*x+c))+1)^n)*(exp(I*(Re(d*x)+Re(c)))^n)^2*a^n*2^n*exp(-2*n*Im(d*x)-2*n*Im(c))*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n)*exp(1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n)*exp(4*I*d*x)*exp(I*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n)*exp(-1/2*I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n)*exp(1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n)*exp(4*I*c)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c)))^3*Pi*n)*exp(-1/2*I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n))","C"
467,1,31,30,0.131000," ","int(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^n,x)","-\frac{i \left(a +i a \tan \left(d x +c \right)\right)^{1+n}}{a d \left(1+n \right)}"," ",0,"-I*(a+I*a*tan(d*x+c))^(1+n)/a/d/(1+n)","A"
468,0,0,49,4.388000," ","int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^n,x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^n,x)","F"
469,0,0,53,3.677000," ","int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^n,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^n,x)","F"
470,0,0,53,3.688000," ","int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^n,x)","\int \left(\cos^{6}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^n,x)","F"
471,0,0,76,1.050000," ","int(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x)","\int \left(\sec^{5}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x)","F"
472,0,0,74,1.459000," ","int(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x)","\int \left(\sec^{3}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x)","F"
473,0,0,72,1.230000," ","int(sec(d*x+c)*(a+I*a*tan(d*x+c))^n,x)","\int \sec \left(d x +c \right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)*(a+I*a*tan(d*x+c))^n,x)","F"
474,0,0,69,1.843000," ","int(cos(d*x+c)*(a+I*a*tan(d*x+c))^n,x)","\int \cos \left(d x +c \right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)*(a+I*a*tan(d*x+c))^n,x)","F"
475,0,0,76,7.958000," ","int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x)","\int \left(\cos^{3}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x)","F"
476,0,0,76,6.779000," ","int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x)","\int \left(\cos^{5}\left(d x +c \right)\right) \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x)","F"
477,0,0,76,0.852000," ","int((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{\frac{5}{2}} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^n,x)","F"
478,0,0,76,0.827000," ","int((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{\frac{3}{2}} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^n,x)","F"
479,0,0,76,0.870000," ","int((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^n,x)","\int \sqrt{e \sec \left(d x +c \right)}\, \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^n,x)","F"
480,0,0,73,0.881000," ","int((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(1/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n}}{\sqrt{e \sec \left(d x +c \right)}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(1/2),x)","F"
481,0,0,73,0.866000," ","int((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(3/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n}}{\left(e \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(3/2),x)","F"
482,0,0,78,0.826000," ","int((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(5/2),x)","\int \frac{\left(a +i a \tan \left(d x +c \right)\right)^{n}}{\left(e \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(5/2),x)","F"
483,1,5823,259,2.505000," ","int((e*sec(d*x+c))^(-4-n)*(a+I*a*tan(d*x+c))^n,x)","\text{output too large to display}"," ",0,"result too large to display","C"
484,1,4994,197,2.176000," ","int((e*sec(d*x+c))^(-3-n)*(a+I*a*tan(d*x+c))^n,x)","\text{output too large to display}"," ",0,"1/8/(-3*I*d+I*n*d)*exp(I*(d*x+c))^n*a^n/e^3*e^(-n)*exp(-1/2*I*(6*c+6*d*x-2*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+n*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-3*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n-n*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3+3*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3+csgn(I*exp(2*I*(d*x+c)))^3*Pi*n-3*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3+3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+3*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n))+1/8/(I*n*d+3*I*d)*exp(I*(d*x+c))^n*a^n/e^3*e^(-n)*exp(1/2*I*(6*c+6*d*x+2*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-n*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+3*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n+n*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-3*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-csgn(I*exp(2*I*(d*x+c)))^3*Pi*n+3*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3+3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)-3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-3*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n))+3/8/(-I*d+I*n*d)*exp(I*(d*x+c))^n*a^n/e^3*e^(-n)*exp(-1/2*I*(2*c+2*d*x-2*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+n*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-3*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n-n*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3+3*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3+csgn(I*exp(2*I*(d*x+c)))^3*Pi*n-3*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3+3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+3*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n))+3/8/(I*d+I*n*d)*exp(I*(d*x+c))^n*a^n/e^3*e^(-n)*exp(1/2*I*(2*c+2*d*x+2*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-n*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+3*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n+n*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-3*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-csgn(I*exp(2*I*(d*x+c)))^3*Pi*n+3*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3+3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)-3*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-3*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n))","C"
485,1,3327,142,1.845000," ","int((e*sec(d*x+c))^(-2-n)*(a+I*a*tan(d*x+c))^n,x)","\text{output too large to display}"," ",0,"1/4/(-2*I*d+I*n*d)*exp(I*(d*x+c))^n*a^n/e^2*e^(-n)*exp(-1/2*I*(4*c+4*d*x-2*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+n*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-2*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-2*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n-n*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3+2*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3+csgn(I*exp(2*I*(d*x+c)))^3*Pi*n-2*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-2*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3+2*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+2*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+2*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n))+1/4/(2*I*d+I*n*d)*exp(I*(d*x+c))^n*a^n/e^2*e^(-n)*exp(1/2*I*(4*c+4*d*x+2*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-n*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+2*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+2*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n+n*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-2*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-csgn(I*exp(2*I*(d*x+c)))^3*Pi*n+2*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3+2*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-2*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)-2*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-2*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n))-1/2*I/d/n/e^2/(e^n)*a^n*exp(I*(d*x+c))^n*exp(1/2*I*n*Pi*(-csgn(I*exp(2*I*(d*x+c)))^3+2*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)-csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3+csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)+csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3))","C"
486,1,2490,90,1.857000," ","int((e*sec(d*x+c))^(-1-n)*(a+I*a*tan(d*x+c))^n,x)","\text{Expression too large to display}"," ",0,"1/2/(I*d+I*n*d)*exp(I*(d*x+c))^n*a^n/e*e^(-n)*exp(1/2*I*(2*c+2*d*x+2*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-n*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n+n*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-csgn(I*exp(2*I*(d*x+c)))^3*Pi*n+Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3+Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)-Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n))+1/2/(-I*d+I*n*d)*exp(I*(d*x+c))^n*a^n/e*e^(-n)*exp(-1/2*I*(2*c+2*d*x-2*csgn(I*exp(2*I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c)))*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+n*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi*n-csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*n+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(I*(d*x+c)))^2*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n-csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi*n+n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-n*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I/(exp(2*I*(d*x+c))+1))*Pi*n+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi*n-n*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3+Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi*n-n*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3+csgn(I*exp(2*I*(d*x+c)))^3*Pi*n-Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3+Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))+Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2+csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi*n))","C"
487,1,874,35,1.000000," ","int((a+I*a*tan(d*x+c))^n/((e*sec(d*x+c))^n),x)","-\frac{i {\mathrm e}^{\frac{n \left(i \pi  \,\mathrm{csgn}\left(\frac{i e \,{\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)-i \pi  \mathrm{csgn}\left(\frac{i e \,{\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)-i \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2}-i \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2}-i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i a \right) \pi +i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3}-i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)-i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} \pi -i \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} \pi +i \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)-i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right)^{3} \pi -i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \pi  \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right)^{2}+i \pi  \mathrm{csgn}\left(\frac{i e \,{\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3}-i \pi  \mathrm{csgn}\left(\frac{i e \,{\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(i e \right)+i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \pi +i \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)+i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \pi +2 i \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(d x +c \right)}\right)^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right)+i \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(i a \right) \pi +2 \ln \left(a \right)-2 \ln \left(e \right)+2 \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)\right)}{2}}}{n d}"," ",0,"-I/n/d*exp(1/2*n*(I*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))*csgn(I*e)*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-I*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-I*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-I*Pi*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2-I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))*csgn(I*a)*Pi+I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*Pi*csgn(I/(exp(2*I*(d*x+c))+1))-I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*Pi-I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^3*Pi+I*Pi*csgn(I/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))-I*csgn(I*exp(2*I*(d*x+c)))^3*Pi-I*csgn(I*exp(2*I*(d*x+c)))*Pi*csgn(I*exp(I*(d*x+c)))^2+I*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^3-I*Pi*csgn(I*e/(exp(2*I*(d*x+c))+1)*exp(I*(d*x+c)))^2*csgn(I*e)+I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*Pi+I*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi*csgn(I/(exp(2*I*(d*x+c))+1))+I*csgn(I*exp(2*I*(d*x+c)))*csgn(I*exp(2*I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*Pi+2*I*csgn(I*exp(2*I*(d*x+c)))^2*Pi*csgn(I*exp(I*(d*x+c)))+I*csgn(I*a/(exp(2*I*(d*x+c))+1)*exp(2*I*(d*x+c)))^2*csgn(I*a)*Pi+2*ln(a)-2*ln(e)+2*ln(exp(I*(d*x+c)))))","C"
488,0,0,94,2.080000," ","int((e*sec(d*x+c))^(-n+1)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{-n +1} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(-n+1)*(a+I*a*tan(d*x+c))^n,x)","F"
489,0,0,95,2.053000," ","int((e*sec(d*x+c))^(2-n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{2-n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(2-n)*(a+I*a*tan(d*x+c))^n,x)","F"
490,0,0,97,2.085000," ","int((e*sec(d*x+c))^(3-n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{3-n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(3-n)*(a+I*a*tan(d*x+c))^n,x)","F"
491,0,0,150,2.233000," ","int((e*sec(d*x+c))^(6-2*n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{6-2 n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(6-2*n)*(a+I*a*tan(d*x+c))^n,x)","F"
492,0,0,75,2.115000," ","int((e*sec(d*x+c))^(5-2*n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{5-2 n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(5-2*n)*(a+I*a*tan(d*x+c))^n,x)","F"
493,0,0,94,2.039000," ","int((e*sec(d*x+c))^(4-2*n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{4-2 n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(4-2*n)*(a+I*a*tan(d*x+c))^n,x)","F"
494,0,0,75,2.001000," ","int((e*sec(d*x+c))^(3-2*n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{3-2 n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(3-2*n)*(a+I*a*tan(d*x+c))^n,x)","F"
495,0,0,44,2.076000," ","int((e*sec(d*x+c))^(2-2*n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{2-2 n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(2-2*n)*(a+I*a*tan(d*x+c))^n,x)","F"
496,0,0,75,1.957000," ","int((e*sec(d*x+c))^(1-2*n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{1-2 n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(1-2*n)*(a+I*a*tan(d*x+c))^n,x)","F"
497,0,0,60,1.359000," ","int((a+I*a*tan(d*x+c))^n/((e*sec(d*x+c))^(2*n)),x)","\int \left(a +i a \tan \left(d x +c \right)\right)^{n} \left(e \sec \left(d x +c \right)\right)^{-2 n}\, dx"," ",0,"int((a+I*a*tan(d*x+c))^n/((e*sec(d*x+c))^(2*n)),x)","F"
498,0,0,75,2.835000," ","int((e*sec(d*x+c))^(-1-2*n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{-1-2 n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(-1-2*n)*(a+I*a*tan(d*x+c))^n,x)","F"
499,0,0,69,2.666000," ","int((e*sec(d*x+c))^(-2-2*n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{-2-2 n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(-2-2*n)*(a+I*a*tan(d*x+c))^n,x)","F"
500,0,0,75,2.994000," ","int((e*sec(d*x+c))^(-3-2*n)*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \sec \left(d x +c \right)\right)^{-3-2 n} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*sec(d*x+c))^(-3-2*n)*(a+I*a*tan(d*x+c))^n,x)","F"
501,0,0,59,4.827000," ","int((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-2-n),x)","\int \left(d \sec \left(f x +e \right)\right)^{2 n} \left(a +i a \tan \left(f x +e \right)\right)^{-2-n}\, dx"," ",0,"int((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-2-n),x)","F"
502,0,0,59,4.734000," ","int((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-1-n),x)","\int \left(d \sec \left(f x +e \right)\right)^{2 n} \left(a +i a \tan \left(f x +e \right)\right)^{-1-n}\, dx"," ",0,"int((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-1-n),x)","F"
503,0,0,56,1.410000," ","int((d*sec(f*x+e))^(2*n)/((a+I*a*tan(f*x+e))^n),x)","\int \left(d \sec \left(f x +e \right)\right)^{2 n} \left(a +i a \tan \left(f x +e \right)\right)^{-n}\, dx"," ",0,"int((d*sec(f*x+e))^(2*n)/((a+I*a*tan(f*x+e))^n),x)","F"
504,1,1291,38,1.663000," ","int((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-n+1),x)","\frac{i a 2^{n} a^{-n} d^{2 n} {\mathrm e}^{-\frac{i \pi  \left(2 n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)-n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)-n \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)+2 n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(\frac{i d \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)-2 n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i d \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-2 n \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(\frac{i d \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-2 n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-2 n \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+n \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)+n \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)+n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-n \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right)+2 n \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right)^{2}+\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}+\mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}+\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right)^{3}-2 \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right)^{2}-n \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}+2 n \mathrm{csgn}\left(\frac{i d \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}-\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+2 n \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}-\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+\mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right)-\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-n \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(f x +e \right)}\right)^{3}-n \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}\right)}{2}} \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n}}{f n}"," ",0,"I/f*a*2^n*a^(-n)*d^(2*n)*exp(-1/2*I*Pi*(-2*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*d/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2-2*n*csgn(I*d)*csgn(I*d/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^2-2*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-2*n*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-2*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(2*I*(f*x+e)))^2+2*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))-n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(2*I*(f*x+e)))*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))-n*csgn(I*a)*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*a/(exp(2*I*(f*x+e))+1)*exp(2*I*(f*x+e)))+2*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*d)*csgn(I*d/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))+csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3-n*csgn(I*a/(exp(2*I*(f*x+e))+1)*exp(2*I*(f*x+e)))^3+2*n*csgn(I*d/(exp(2*I*(f*x+e))+1)*exp(I*(f*x+e)))^3-csgn(I*a)*csgn(I*a/(exp(2*I*(f*x+e))+1)*exp(2*I*(f*x+e)))^2+2*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3+csgn(I*a/(exp(2*I*(f*x+e))+1)*exp(2*I*(f*x+e)))^3+n*csgn(I*a)*csgn(I*a/(exp(2*I*(f*x+e))+1)*exp(2*I*(f*x+e)))^2+csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(2*I*(f*x+e)))*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))+n*csgn(I*exp(2*I*(f*x+e)))*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2+n*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*a/(exp(2*I*(f*x+e))+1)*exp(2*I*(f*x+e)))^2+csgn(I*a)*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*a/(exp(2*I*(f*x+e))+1)*exp(2*I*(f*x+e)))+n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-n*csgn(I*exp(I*(f*x+e)))^2*csgn(I*exp(2*I*(f*x+e)))+2*n*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(2*I*(f*x+e)))^2+csgn(I*exp(2*I*(f*x+e)))^3-csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*a/(exp(2*I*(f*x+e))+1)*exp(2*I*(f*x+e)))^2+csgn(I*exp(I*(f*x+e)))^2*csgn(I*exp(2*I*(f*x+e)))-csgn(I*exp(2*I*(f*x+e)))*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-n*csgn(I*exp(2*I*(f*x+e)))^3-n*csgn(I*exp(2*I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3))/n*(exp(2*I*(f*x+e))+1)^(-n)","C"
505,0,0,88,3.617000," ","int((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(2-n),x)","\int \left(d \sec \left(f x +e \right)\right)^{2 n} \left(a +i a \tan \left(f x +e \right)\right)^{2-n}\, dx"," ",0,"int((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(2-n),x)","F"
506,0,0,142,3.781000," ","int((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(3-n),x)","\int \left(d \sec \left(f x +e \right)\right)^{2 n} \left(a +i a \tan \left(f x +e \right)\right)^{3-n}\, dx"," ",0,"int((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(3-n),x)","F"
507,1,48,54,0.370000," ","int(sec(d*x+c)^6*(a+b*tan(d*x+c)),x)","\frac{-a \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{b}{6 \cos \left(d x +c \right)^{6}}}{d}"," ",0,"1/d*(-a*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+1/6*b/cos(d*x+c)^6)","A"
508,1,74,66,0.378000," ","int(sec(d*x+c)^5*(a+b*tan(d*x+c)),x)","\frac{a \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b}{5 d \cos \left(d x +c \right)^{5}}"," ",0,"1/4*a*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/5/d*b/cos(d*x+c)^5","A"
509,1,38,40,0.365000," ","int(sec(d*x+c)^4*(a+b*tan(d*x+c)),x)","\frac{-a \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{b}{4 \cos \left(d x +c \right)^{4}}}{d}"," ",0,"1/d*(-a*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+1/4*b/cos(d*x+c)^4)","A"
510,1,54,46,0.375000," ","int(sec(d*x+c)^3*(a+b*tan(d*x+c)),x)","\frac{a \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{b}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"1/2*a*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b/cos(d*x+c)^3","A"
511,1,25,26,0.361000," ","int(sec(d*x+c)^2*(a+b*tan(d*x+c)),x)","\frac{a \tan \left(d x +c \right)+\frac{b}{2 \cos \left(d x +c \right)^{2}}}{d}"," ",0,"1/d*(a*tan(d*x+c)+1/2*b/cos(d*x+c)^2)","A"
512,1,34,24,0.086000," ","int(sec(d*x+c)*(a+b*tan(d*x+c)),x)","\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b}{d \cos \left(d x +c \right)}"," ",0,"1/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/d*b/cos(d*x+c)","A"
513,1,23,24,0.237000," ","int(cos(d*x+c)*(a+b*tan(d*x+c)),x)","\frac{a \sin \left(d x +c \right)-b \cos \left(d x +c \right)}{d}"," ",0,"1/d*(a*sin(d*x+c)-b*cos(d*x+c))","A"
514,1,41,37,0.291000," ","int(cos(d*x+c)^2*(a+b*tan(d*x+c)),x)","\frac{-\frac{\left(\cos^{2}\left(d x +c \right)\right) b}{2}+a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(-1/2*cos(d*x+c)^2*b+a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
515,1,36,40,0.389000," ","int(cos(d*x+c)^3*(a+b*tan(d*x+c)),x)","\frac{-\frac{\left(\cos^{3}\left(d x +c \right)\right) b}{3}+\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/3*cos(d*x+c)^3*b+1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
516,1,52,57,0.391000," ","int(cos(d*x+c)^4*(a+b*tan(d*x+c)),x)","\frac{-\frac{\left(\cos^{4}\left(d x +c \right)\right) b}{4}+a \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(-1/4*b*cos(d*x+c)^4+a*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
517,1,138,109,0.406000," ","int(sec(d*x+c)^8*(a+b*tan(d*x+c))^2,x)","\frac{-a^{2} \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)+\frac{a b}{4 \cos \left(d x +c \right)^{8}}+b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(-a^2*(-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)+1/4*a*b/cos(d*x+c)^8+b^2*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3))","A"
518,1,110,89,0.409000," ","int(sec(d*x+c)^6*(a+b*tan(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{a b}{3 \cos \left(d x +c \right)^{6}}+b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(-a^2*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+1/3*a*b/cos(d*x+c)^6+b^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3))","A"
519,1,82,69,0.408000," ","int(sec(d*x+c)^4*(a+b*tan(d*x+c))^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)+\frac{a b}{2 \cos \left(d x +c \right)^{4}}+b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(-a^2*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+1/2*a*b/cos(d*x+c)^4+b^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3))","A"
520,1,48,20,0.396000," ","int(sec(d*x+c)^2*(a+b*tan(d*x+c))^2,x)","\frac{a^{2} \tan \left(d x +c \right)+\frac{a b}{\cos \left(d x +c \right)^{2}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^2*tan(d*x+c)+a*b/cos(d*x+c)^2+1/3*b^2*sin(d*x+c)^3/cos(d*x+c)^3)","B"
521,1,70,45,0.297000," ","int(cos(d*x+c)^2*(a+b*tan(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\left(\cos^{2}\left(d x +c \right)\right) a b +a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(b^2*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-cos(d*x+c)^2*a*b+a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
522,1,97,82,0.436000," ","int(cos(d*x+c)^4*(a+b*tan(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{a b \left(\cos^{4}\left(d x +c \right)\right)}{2}+a^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b^2*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-1/2*a*b*cos(d*x+c)^4+a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
523,1,235,151,0.448000," ","int(sec(d*x+c)^7*(a+b*tan(d*x+c))^2,x)","\frac{a^{2} \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{5 a^{2} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{24 d}+\frac{5 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{5 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{2 a b}{7 d \cos \left(d x +c \right)^{7}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}+\frac{5 b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{6}}+\frac{5 b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{4}}+\frac{5 b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{2}}+\frac{5 b^{2} \sin \left(d x +c \right)}{128 d}-\frac{5 b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{128 d}"," ",0,"1/6/d*a^2*tan(d*x+c)*sec(d*x+c)^5+5/24*a^2*sec(d*x+c)^3*tan(d*x+c)/d+5/16*a^2*sec(d*x+c)*tan(d*x+c)/d+5/16/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/7/d*a*b/cos(d*x+c)^7+1/8/d*b^2*sin(d*x+c)^3/cos(d*x+c)^8+5/48/d*b^2*sin(d*x+c)^3/cos(d*x+c)^6+5/64/d*b^2*sin(d*x+c)^3/cos(d*x+c)^4+5/128/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+5/128*b^2*sin(d*x+c)/d-5/128/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
524,1,189,121,0.416000," ","int(sec(d*x+c)^5*(a+b*tan(d*x+c))^2,x)","\frac{a^{2} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 a b}{5 d \cos \left(d x +c \right)^{5}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{16 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}"," ",0,"1/4*a^2*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^2*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/5/d*a*b/cos(d*x+c)^5+1/6/d*b^2*sin(d*x+c)^3/cos(d*x+c)^6+1/8/d*b^2*sin(d*x+c)^3/cos(d*x+c)^4+1/16/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/16*b^2*sin(d*x+c)/d-1/16/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
525,1,143,91,0.418000," ","int(sec(d*x+c)^3*(a+b*tan(d*x+c))^2,x)","\frac{a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 a b}{3 d \cos \left(d x +c \right)^{3}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{8 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/2*a^2*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a*b/cos(d*x+c)^3+1/4/d*b^2*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/8*b^2*sin(d*x+c)/d-1/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
526,1,98,59,0.142000," ","int(sec(d*x+c)*(a+b*tan(d*x+c))^2,x)","\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 a b}{d \cos \left(d x +c \right)}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{2 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*a*b/cos(d*x+c)+1/2/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/2*b^2*sin(d*x+c)/d-1/2/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
527,1,63,47,0.273000," ","int(cos(d*x+c)*(a+b*tan(d*x+c))^2,x)","\frac{a^{2} \sin \left(d x +c \right)}{d}-\frac{b^{2} \sin \left(d x +c \right)}{d}-\frac{2 a b \cos \left(d x +c \right)}{d}+\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"a^2*sin(d*x+c)/d-b^2*sin(d*x+c)/d-2*a*b*cos(d*x+c)/d+1/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
528,1,52,82,0.423000," ","int(cos(d*x+c)^3*(a+b*tan(d*x+c))^2,x)","\frac{\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right) a b}{3}+\frac{a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/3*b^2*sin(d*x+c)^3-2/3*cos(d*x+c)^3*a*b+1/3*a^2*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
529,1,88,104,0.498000," ","int(cos(d*x+c)^5*(a+b*tan(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{2 a b \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a^{2} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(b^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-2/5*a*b*cos(d*x+c)^5+1/5*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
530,1,108,126,0.500000," ","int(cos(d*x+c)^7*(a+b*tan(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{2 a b \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{2} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(b^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-2/7*a*b*cos(d*x+c)^7+1/7*a^2*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
531,1,219,178,0.464000," ","int(sec(d*x+c)^8*(a+b*tan(d*x+c))^3,x)","\frac{-a^{3} \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)+\frac{3 a^{2} b}{8 \cos \left(d x +c \right)^{8}}+3 b^{2} a \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{40 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{40 \cos \left(d x +c \right)^{4}}\right)}{d}"," ",0,"1/d*(-a^3*(-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)+3/8*a^2*b/cos(d*x+c)^8+3*b^2*a*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+b^3*(1/10*sin(d*x+c)^4/cos(d*x+c)^10+3/40*sin(d*x+c)^4/cos(d*x+c)^8+1/20*sin(d*x+c)^4/cos(d*x+c)^6+1/40*sin(d*x+c)^4/cos(d*x+c)^4))","A"
532,1,173,128,0.460000," ","int(sec(d*x+c)^6*(a+b*tan(d*x+c))^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)+\frac{a^{2} b}{2 \cos \left(d x +c \right)^{6}}+3 b^{2} a \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{4}}\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)+1/2*a^2*b/cos(d*x+c)^6+3*b^2*a*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+b^3*(1/8*sin(d*x+c)^4/cos(d*x+c)^8+1/12*sin(d*x+c)^4/cos(d*x+c)^6+1/24*sin(d*x+c)^4/cos(d*x+c)^4))","A"
533,1,127,69,0.431000," ","int(sec(d*x+c)^4*(a+b*tan(d*x+c))^3,x)","\frac{-a^{3} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{3 a^{2} b}{4 \cos \left(d x +c \right)^{4}}+3 b^{2} a \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{6 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{4}}\right)}{d}"," ",0,"1/d*(-a^3*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+3/4*a^2*b/cos(d*x+c)^4+3*b^2*a*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+b^3*(1/6*sin(d*x+c)^4/cos(d*x+c)^6+1/12*sin(d*x+c)^4/cos(d*x+c)^4))","A"
534,1,72,20,0.431000," ","int(sec(d*x+c)^2*(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \tan \left(d x +c \right)+\frac{3 a^{2} b}{2 \cos \left(d x +c \right)^{2}}+\frac{b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{3}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 \cos \left(d x +c \right)^{4}}}{d}"," ",0,"1/d*(a^3*tan(d*x+c)+3/2*a^2*b/cos(d*x+c)^2+b^2*a*sin(d*x+c)^3/cos(d*x+c)^3+1/4*b^3*sin(d*x+c)^4/cos(d*x+c)^4)","B"
535,1,123,80,0.313000," ","int(cos(d*x+c)^2*(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{3} x}{2}+\frac{a^{3} c}{2 d}-\frac{3 a^{2} \left(\cos^{2}\left(d x +c \right)\right) b}{2 d}-\frac{3 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 a \,b^{2} x}{2}+\frac{3 a \,b^{2} c}{2 d}-\frac{\left(\sin^{2}\left(d x +c \right)\right) b^{3}}{2 d}-\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^3*cos(d*x+c)*sin(d*x+c)/d+1/2*a^3*x+1/2/d*a^3*c-3/2/d*a^2*cos(d*x+c)^2*b-3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d+3/2*a*b^2*x+3/2/d*a*b^2*c-1/2/d*sin(d*x+c)^2*b^3-b^3*ln(cos(d*x+c))/d","A"
536,1,114,78,0.471000," ","int(cos(d*x+c)^4*(a+b*tan(d*x+c))^3,x)","\frac{\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4}+3 b^{2} a \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{3 a^{2} b \left(\cos^{4}\left(d x +c \right)\right)}{4}+a^{3} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(1/4*b^3*sin(d*x+c)^4+3*b^2*a*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-3/4*a^2*b*cos(d*x+c)^4+a^3*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
537,1,328,146,0.536000," ","int(sec(d*x+c)^5*(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a^{2} b}{5 d \cos \left(d x +c \right)^{5}}+\frac{b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{6}}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \sin \left(d x +c \right)}{16 d}-\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}+\frac{3 b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{5}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{3}}-\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)}-\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{35 d}-\frac{2 b^{3} \cos \left(d x +c \right)}{35 d}"," ",0,"1/4*a^3*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^3*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/5/d*a^2*b/cos(d*x+c)^5+1/2/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^6+3/8/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^4+3/16/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^2+3/16*a*b^2*sin(d*x+c)/d-3/16/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/7/d*b^3*sin(d*x+c)^4/cos(d*x+c)^7+3/35/d*b^3*sin(d*x+c)^4/cos(d*x+c)^5+1/35/d*b^3*sin(d*x+c)^4/cos(d*x+c)^3-1/35/d*b^3*sin(d*x+c)^4/cos(d*x+c)-1/35/d*b^3*cos(d*x+c)*sin(d*x+c)^2-2/35/d*b^3*cos(d*x+c)","B"
538,1,256,115,0.534000," ","int(sec(d*x+c)^3*(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a^{2} b}{d \cos \left(d x +c \right)^{3}}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \sin \left(d x +c \right)}{8 d}-\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}-\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)}-\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{2 b^{3} \cos \left(d x +c \right)}{15 d}"," ",0,"1/2*a^3*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2*b/cos(d*x+c)^3+3/4/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^4+3/8/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^2+3/8*a*b^2*sin(d*x+c)/d-3/8/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/5/d*b^3*sin(d*x+c)^4/cos(d*x+c)^5+1/15/d*b^3*sin(d*x+c)^4/cos(d*x+c)^3-1/15/d*b^3*sin(d*x+c)^4/cos(d*x+c)-1/15/d*b^3*cos(d*x+c)*sin(d*x+c)^2-2/15/d*b^3*cos(d*x+c)","B"
539,1,187,82,0.295000," ","int(sec(d*x+c)*(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b}{d \cos \left(d x +c \right)}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \sin \left(d x +c \right)}{2 d}-\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 b^{3} \cos \left(d x +c \right)}{3 d}"," ",0,"1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^2*b/cos(d*x+c)+3/2/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^2+3/2*a*b^2*sin(d*x+c)/d-3/2/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^3*sin(d*x+c)^4/cos(d*x+c)^3-1/3/d*b^3*sin(d*x+c)^4/cos(d*x+c)-1/3/d*b^3*cos(d*x+c)*sin(d*x+c)^2-2/3/d*b^3*cos(d*x+c)","B"
540,1,126,83,0.372000," ","int(cos(d*x+c)*(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \sin \left(d x +c \right)}{d}-\frac{3 a^{2} b \cos \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \sin \left(d x +c \right)}{d}+\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{2 b^{3} \cos \left(d x +c \right)}{d}"," ",0,"a^3*sin(d*x+c)/d-3/d*a^2*b*cos(d*x+c)-3*a*b^2*sin(d*x+c)/d+3/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^3*sin(d*x+c)^4/cos(d*x+c)+1/d*b^3*cos(d*x+c)*sin(d*x+c)^2+2/d*b^3*cos(d*x+c)","A"
541,1,75,66,0.489000," ","int(cos(d*x+c)^3*(a+b*tan(d*x+c))^3,x)","\frac{-\frac{b^{3} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+b^{2} a \left(\sin^{3}\left(d x +c \right)\right)-a^{2} b \left(\cos^{3}\left(d x +c \right)\right)+\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/3*b^3*(2+sin(d*x+c)^2)*cos(d*x+c)+b^2*a*sin(d*x+c)^3-a^2*b*cos(d*x+c)^3+1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
542,1,125,99,0.562000," ","int(cos(d*x+c)^5*(a+b*tan(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+3 b^{2} a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a^{3} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(b^3*(-1/5*cos(d*x+c)^3*sin(d*x+c)^2-2/15*cos(d*x+c)^3)+3*b^2*a*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-3/5*a^2*b*cos(d*x+c)^5+1/5*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
543,1,145,134,0.569000," ","int(cos(d*x+c)^7*(a+b*tan(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+3 b^{2} a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{3 a^{2} b \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{3} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(b^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+3*b^2*a*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-3/7*a^2*b*cos(d*x+c)^7+1/7*a^3*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
544,1,162,110,0.464000," ","int(sec(d*x+c)^6/(a+b*tan(d*x+c)),x)","\frac{\tan^{4}\left(d x +c \right)}{4 b d}-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 b^{2} d}+\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d \,b^{3}}+\frac{\tan^{2}\left(d x +c \right)}{b d}-\frac{a^{3} \tan \left(d x +c \right)}{d \,b^{4}}-\frac{2 a \tan \left(d x +c \right)}{b^{2} d}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) a^{4}}{d \,b^{5}}+\frac{2 \ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \,b^{3}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right)}{b d}"," ",0,"1/4*tan(d*x+c)^4/b/d-1/3*a*tan(d*x+c)^3/b^2/d+1/2/d/b^3*a^2*tan(d*x+c)^2+tan(d*x+c)^2/b/d-1/d/b^4*a^3*tan(d*x+c)-2*a*tan(d*x+c)/b^2/d+1/d/b^5*ln(a+b*tan(d*x+c))*a^4+2/d/b^3*ln(a+b*tan(d*x+c))*a^2+ln(a+b*tan(d*x+c))/b/d","A"
545,1,72,57,0.434000," ","int(sec(d*x+c)^4/(a+b*tan(d*x+c)),x)","\frac{\tan^{2}\left(d x +c \right)}{2 b d}-\frac{a \tan \left(d x +c \right)}{b^{2} d}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \,b^{3}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right)}{b d}"," ",0,"1/2*tan(d*x+c)^2/b/d-a*tan(d*x+c)/b^2/d+1/d/b^3*ln(a+b*tan(d*x+c))*a^2+ln(a+b*tan(d*x+c))/b/d","A"
546,1,19,18,0.326000," ","int(sec(d*x+c)^2/(a+b*tan(d*x+c)),x)","\frac{\ln \left(a +b \tan \left(d x +c \right)\right)}{b d}"," ",0,"ln(a+b*tan(d*x+c))/b/d","A"
547,1,236,89,0.563000," ","int(cos(d*x+c)^2/(a+b*tan(d*x+c)),x)","\frac{b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\tan \left(d x +c \right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{\tan \left(d x +c \right) b^{2} a}{2 d \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{b^{3}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{b^{3} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) b^{2} a}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d*b^3/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)^2/(1+tan(d*x+c)^2)*tan(d*x+c)*a^3+1/2/d/(a^2+b^2)^2/(1+tan(d*x+c)^2)*tan(d*x+c)*b^2*a+1/2/d/(a^2+b^2)^2/(1+tan(d*x+c)^2)*a^2*b+1/2/d/(a^2+b^2)^2/(1+tan(d*x+c)^2)*b^3-1/2/d/(a^2+b^2)^2*b^3*ln(1+tan(d*x+c)^2)+3/2/d/(a^2+b^2)^2*arctan(tan(d*x+c))*b^2*a+1/2/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^3","B"
548,1,524,146,0.543000," ","int(cos(d*x+c)^4/(a+b*tan(d*x+c)),x)","\frac{b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \left(\tan^{3}\left(d x +c \right)\right) a^{5}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \left(\tan^{3}\left(d x +c \right)\right) b^{2} a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{7 \left(\tan^{3}\left(d x +c \right)\right) a \,b^{4}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{\left(\tan^{2}\left(d x +c \right)\right) a^{2} b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{\left(\tan^{2}\left(d x +c \right)\right) b^{5}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{7 \tan \left(d x +c \right) b^{2} a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{9 \tan \left(d x +c \right) a \,b^{4}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \tan \left(d x +c \right) a^{5}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{a^{4} b}{4 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{a^{2} b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 b^{5}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{b^{5} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{15 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{4}}{8 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{5}}{8 d \left(a^{2}+b^{2}\right)^{3}}+\frac{5 \arctan \left(\tan \left(d x +c \right)\right) b^{2} a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/d*b^5/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+3/8/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^5+5/4/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^2*a^3+7/8/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a*b^4+1/2/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^2*b^3+1/2/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*b^5+7/4/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^2*a^3+9/8/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a*b^4+5/8/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^5+1/4/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*a^4*b+1/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*a^2*b^3+3/4/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*b^5-1/2/d/(a^2+b^2)^3*b^5*ln(1+tan(d*x+c)^2)+15/8/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a*b^4+3/8/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^5+5/4/d/(a^2+b^2)^3*arctan(tan(d*x+c))*b^2*a^3","B"
549,1,488,130,0.473000," ","int(sec(d*x+c)^5/(a+b*tan(d*x+c)),x)","\frac{2 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{4}}{d \,b^{4} \sqrt{a^{2}+b^{2}}}+\frac{4 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}+b^{2}}}+\frac{2 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \sqrt{a^{2}+b^{2}}}-\frac{1}{3 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a^{2}}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{4}}+\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{2}}+\frac{1}{3 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a^{2}}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{4}}-\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{2}}"," ",0,"2/d/b^4/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))*a^4+4/d/b^2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))*a^2+2/d/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-1/3/d/b/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2*a-1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^2-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a^2-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)*a-3/2/d/b/(tan(1/2*d*x+1/2*c)-1)+1/d*a^3/b^4*ln(tan(1/2*d*x+1/2*c)-1)+3/2/d*a/b^2*ln(tan(1/2*d*x+1/2*c)-1)+1/3/d/b/(tan(1/2*d*x+1/2*c)+1)^3+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2*a-1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^2+1/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a^2-1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)*a+3/2/d/b/(tan(1/2*d*x+1/2*c)+1)-1/d*a^3/b^4*ln(tan(1/2*d*x+1/2*c)+1)-3/2/d*a/b^2*ln(tan(1/2*d*x+1/2*c)+1)","B"
550,1,174,75,0.449000," ","int(sec(d*x+c)^3/(a+b*tan(d*x+c)),x)","\frac{2 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}+b^{2}}}+\frac{2 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \sqrt{a^{2}+b^{2}}}-\frac{1}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{2}}+\frac{1}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{2}}"," ",0,"2/d/b^2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))*a^2+2/d/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-1/d/b/(tan(1/2*d*x+1/2*c)-1)+1/d*a/b^2*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b/(tan(1/2*d*x+1/2*c)+1)-1/d*a/b^2*ln(tan(1/2*d*x+1/2*c)+1)","B"
551,1,43,42,0.243000," ","int(sec(d*x+c)/(a+b*tan(d*x+c)),x)","\frac{2 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \sqrt{a^{2}+b^{2}}}"," ",0,"2/d/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))","A"
552,1,90,86,0.536000," ","int(cos(d*x+c)/(a+b*tan(d*x+c)),x)","\frac{\frac{2 b^{2} \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{2 \left(-a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-b \right)}{\left(a^{2}+b^{2}\right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{d}"," ",0,"1/d*(2*b^2/(a^2+b^2)^(3/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-2/(a^2+b^2)*(-a*tan(1/2*d*x+1/2*c)-b)/(1+tan(1/2*d*x+1/2*c)^2))","A"
553,1,221,157,0.541000," ","int(cos(d*x+c)^3/(a+b*tan(d*x+c)),x)","\frac{\frac{2 b^{4} \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}+b^{2}}}-\frac{2 \left(\left(-a^{3}-2 b^{2} a \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-a^{2} b -2 b^{3}\right) \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-\frac{2}{3} a^{3}-\frac{8}{3} b^{2} a \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-a^{3}-2 b^{2} a \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{a^{2} b}{3}-\frac{4 b^{3}}{3}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}}{d}"," ",0,"1/d*(2*b^4/(a^4+2*a^2*b^2+b^4)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-2/(a^4+2*a^2*b^2+b^4)*((-a^3-2*a*b^2)*tan(1/2*d*x+1/2*c)^5+(-a^2*b-2*b^3)*tan(1/2*d*x+1/2*c)^4+(-2/3*a^3-8/3*b^2*a)*tan(1/2*d*x+1/2*c)^3-2*b^3*tan(1/2*d*x+1/2*c)^2+(-a^3-2*a*b^2)*tan(1/2*d*x+1/2*c)-1/3*a^2*b-4/3*b^3)/(1+tan(1/2*d*x+1/2*c)^2)^3)","A"
554,1,305,174,0.489000," ","int(sec(d*x+c)^8/(a+b*tan(d*x+c))^2,x)","\frac{\tan^{5}\left(d x +c \right)}{5 b^{2} d}-\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{2 b^{3} d}+\frac{\left(\tan^{3}\left(d x +c \right)\right) a^{2}}{d \,b^{4}}+\frac{\tan^{3}\left(d x +c \right)}{b^{2} d}-\frac{2 a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d \,b^{5}}-\frac{3 a \left(\tan^{2}\left(d x +c \right)\right)}{b^{3} d}+\frac{5 a^{4} \tan \left(d x +c \right)}{d \,b^{6}}+\frac{9 a^{2} \tan \left(d x +c \right)}{d \,b^{4}}+\frac{3 \tan \left(d x +c \right)}{b^{2} d}-\frac{6 a^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{7}}-\frac{12 a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{5}}-\frac{6 a \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{3} d}-\frac{a^{6}}{d \,b^{7} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{4}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 a^{2}}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{1}{b d \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"1/5*tan(d*x+c)^5/b^2/d-1/2*a*tan(d*x+c)^4/b^3/d+1/d/b^4*tan(d*x+c)^3*a^2+tan(d*x+c)^3/b^2/d-2/d/b^5*a^3*tan(d*x+c)^2-3*a*tan(d*x+c)^2/b^3/d+5/d/b^6*a^4*tan(d*x+c)+9/d/b^4*a^2*tan(d*x+c)+3*tan(d*x+c)/b^2/d-6/d*a^5/b^7*ln(a+b*tan(d*x+c))-12/d*a^3/b^5*ln(a+b*tan(d*x+c))-6*a*ln(a+b*tan(d*x+c))/b^3/d-1/d/b^7/(a+b*tan(d*x+c))*a^6-3/d/b^5/(a+b*tan(d*x+c))*a^4-3/d/b^3/(a+b*tan(d*x+c))*a^2-1/b/d/(a+b*tan(d*x+c))","A"
555,1,174,114,0.465000," ","int(sec(d*x+c)^6/(a+b*tan(d*x+c))^2,x)","\frac{\tan^{3}\left(d x +c \right)}{3 b^{2} d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{b^{3} d}+\frac{3 a^{2} \tan \left(d x +c \right)}{d \,b^{4}}+\frac{2 \tan \left(d x +c \right)}{b^{2} d}-\frac{4 a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{5}}-\frac{4 a \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{3} d}-\frac{a^{4}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 a^{2}}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{1}{b d \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"1/3*tan(d*x+c)^3/b^2/d-a*tan(d*x+c)^2/b^3/d+3/d/b^4*a^2*tan(d*x+c)+2*tan(d*x+c)/b^2/d-4/d*a^3/b^5*ln(a+b*tan(d*x+c))-4*a*ln(a+b*tan(d*x+c))/b^3/d-1/d/b^5/(a+b*tan(d*x+c))*a^4-2/d/b^3/(a+b*tan(d*x+c))*a^2-1/b/d/(a+b*tan(d*x+c))","A"
556,1,78,64,0.475000," ","int(sec(d*x+c)^4/(a+b*tan(d*x+c))^2,x)","\frac{\tan \left(d x +c \right)}{b^{2} d}-\frac{2 a \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{3} d}-\frac{a^{2}}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{1}{b d \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"tan(d*x+c)/b^2/d-2*a*ln(a+b*tan(d*x+c))/b^3/d-1/d/b^3/(a+b*tan(d*x+c))*a^2-1/b/d/(a+b*tan(d*x+c))","A"
557,1,21,20,0.333000," ","int(sec(d*x+c)^2/(a+b*tan(d*x+c))^2,x)","-\frac{1}{b d \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"-1/b/d/(a+b*tan(d*x+c))","A"
558,1,292,146,0.470000," ","int(cos(d*x+c)^2/(a+b*tan(d*x+c))^2,x)","-\frac{b^{3}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 b^{3} a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\tan \left(d x +c \right) a^{4}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{\tan \left(d x +c \right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{a^{3} b}{d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{2 a \,b^{3} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{2 d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/d*b^3/(a^2+b^2)^2/(a+b*tan(d*x+c))+4/d*b^3/(a^2+b^2)^3*a*ln(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)*tan(d*x+c)*a^4-1/2/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)*tan(d*x+c)*b^4+1/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)*a^3*b+1/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)*a*b^3-2/d/(a^2+b^2)^3*a*b^3*ln(1+tan(d*x+c)^2)+3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^2*b^2-3/2/d/(a^2+b^2)^3*arctan(tan(d*x+c))*b^4+1/2/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^4","A"
559,1,661,227,0.477000," ","int(cos(d*x+c)^4/(a+b*tan(d*x+c))^2,x)","-\frac{b^{5}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{6 b^{5} a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{3 \left(\tan^{3}\left(d x +c \right)\right) a^{6}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{15 \left(\tan^{3}\left(d x +c \right)\right) b^{2} a^{4}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \left(\tan^{3}\left(d x +c \right)\right) b^{4} a^{2}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{7 \left(\tan^{3}\left(d x +c \right)\right) b^{6}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{2 \left(\tan^{2}\left(d x +c \right)\right) a^{3} b^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{2 \left(\tan^{2}\left(d x +c \right)\right) a \,b^{5}}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{17 \tan \left(d x +c \right) b^{2} a^{4}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 \tan \left(d x +c \right) b^{4} a^{2}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{9 \tan \left(d x +c \right) b^{6}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \tan \left(d x +c \right) a^{6}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{a^{5} b}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 a^{3} b^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 a \,b^{5}}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 a \,b^{5} \ln \left(1+\tan^{2}\left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{45 \arctan \left(\tan \left(d x +c \right)\right) b^{4} a^{2}}{8 d \left(a^{2}+b^{2}\right)^{4}}-\frac{15 \arctan \left(\tan \left(d x +c \right)\right) b^{6}}{8 d \left(a^{2}+b^{2}\right)^{4}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{6}}{8 d \left(a^{2}+b^{2}\right)^{4}}+\frac{15 \arctan \left(\tan \left(d x +c \right)\right) b^{2} a^{4}}{8 d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/d*b^5/(a^2+b^2)^3/(a+b*tan(d*x+c))+6/d*b^5/(a^2+b^2)^4*a*ln(a+b*tan(d*x+c))+3/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^6+15/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^2*a^4+5/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^4*a^2-7/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^6+2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^3*b^3+2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a*b^5+17/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^2*a^4+3/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^4*a^2-9/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^6+5/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^6+1/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*a^5*b+3/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*a^3*b^3+5/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*a*b^5-3/d/(a^2+b^2)^4*a*b^5*ln(1+tan(d*x+c)^2)+45/8/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^4*a^2-15/8/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^6+3/8/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^6+15/8/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^2*a^4","B"
560,1,989,219,0.476000," ","int(sec(d*x+c)^7/(a+b*tan(d*x+c))^2,x)","-\frac{5 a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{4 a^{3}}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a}{3 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{3 a^{2}}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{4}}{d \,b^{6}}-\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2}}{2 d \,b^{4}}+\frac{4 a^{3}}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 a^{2}}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{5 a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 a}{3 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{3 a^{2}}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3 a^{2}}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{4}}{d \,b^{6}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{2 d \,b^{4}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right) a}+\frac{4 a^{2}}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)}+\frac{2 a^{4}}{d \,b^{5} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)}-\frac{11}{8 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 d \,b^{2}}+\frac{9}{8 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{11}{8 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 d \,b^{2}}+\frac{9}{8 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{4 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{4 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{2}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)}+\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)}+\frac{4 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)}-\frac{10 a^{5} \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \,b^{6} \sqrt{a^{2}+b^{2}}}-\frac{20 a^{3} \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \,b^{4} \sqrt{a^{2}+b^{2}}}-\frac{10 a \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}+b^{2}}}"," ",0,"-5/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a-4/d/b^5/(tan(1/2*d*x+1/2*c)+1)*a^3+2/d/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)/a*tan(1/2*d*x+1/2*c)+2/3/d/b^3/(tan(1/2*d*x+1/2*c)-1)^3*a+3/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)^2*a^2+1/d/b^3/(tan(1/2*d*x+1/2*c)-1)^2*a-5/d/b^6*ln(tan(1/2*d*x+1/2*c)-1)*a^4-15/2/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)*a^2+4/d/b^5/(tan(1/2*d*x+1/2*c)-1)*a^3+3/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)*a^2+5/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a-2/3/d/b^3/(tan(1/2*d*x+1/2*c)+1)^3*a-3/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)^2*a^2+1/d/b^3/(tan(1/2*d*x+1/2*c)+1)^2*a+4/d/b^3/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)*a^2+3/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)*a^2+5/d/b^6*ln(tan(1/2*d*x+1/2*c)+1)*a^4+15/2/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)*a^2+2/d/b^5/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)*a^4+2/d/b^4/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)*a^3*tan(1/2*d*x+1/2*c)-11/8/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2+15/8/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)+9/8/d/b^2/(tan(1/2*d*x+1/2*c)+1)+1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^3+11/8/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2-15/8/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)+9/8/d/b^2/(tan(1/2*d*x+1/2*c)-1)-1/4/d/b^2/(tan(1/2*d*x+1/2*c)+1)^4+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^3+2/d/b/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)+1/4/d/b^2/(tan(1/2*d*x+1/2*c)-1)^4+4/d/b^2/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)*a*tan(1/2*d*x+1/2*c)-10/d/b^6*a^5/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-20/d/b^4*a^3/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-10/d/b^2*a/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))","B"
561,1,440,162,0.452000," ","int(sec(d*x+c)^5/(a+b*tan(d*x+c))^2,x)","\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right) a}+\frac{2 a^{2}}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)}+\frac{2}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)}-\frac{6 \sqrt{a^{2}+b^{2}}\, a \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \,b^{4}}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{2 a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2}}{d \,b^{4}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{2}}-\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2 a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{d \,b^{4}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{2}}"," ",0,"2/d/b^2/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)*a*tan(1/2*d*x+1/2*c)+2/d/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)/a*tan(1/2*d*x+1/2*c)+2/d/b^3/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)*a^2+2/d/b/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)-6/d/b^4*(a^2+b^2)^(1/2)*a*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))+1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2+2/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a+1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)-3/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)*a^2-3/2/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2-2/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)+3/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)*a^2+3/2/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)","B"
562,1,174,87,0.471000," ","int(sec(d*x+c)^3/(a+b*tan(d*x+c))^2,x)","\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right) a}+\frac{2}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)}-\frac{2 a \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}+b^{2}}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{2}}"," ",0,"2/d/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)/a*tan(1/2*d*x+1/2*c)+2/d/b/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)-2/d/b^2*a/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-1/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)","A"
563,1,118,78,0.256000," ","int(sec(d*x+c)/(a+b*tan(d*x+c))^2,x)","\frac{-\frac{2 \left(-\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(a^{2}+b^{2}\right) a}-\frac{b}{a^{2}+b^{2}}\right)}{a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a}+\frac{2 a \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{\frac{3}{2}}}}{d}"," ",0,"1/d*(-2*(-b^2/(a^2+b^2)/a*tan(1/2*d*x+1/2*c)-b/(a^2+b^2))/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)+2*a/(a^2+b^2)^(3/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))","A"
564,1,172,149,0.496000," ","int(cos(d*x+c)/(a+b*tan(d*x+c))^2,x)","\frac{-\frac{2 b^{2} \left(\frac{-\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a}-b}{a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a}-\frac{3 a \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{2}}-\frac{2 \left(\left(-a^{2}+b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 a b \right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{d}"," ",0,"1/d*(-2*b^2/(a^2+b^2)^2*((-b^2/a*tan(1/2*d*x+1/2*c)-b)/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)-3*a/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))-2/(a^4+2*a^2*b^2+b^4)*((-a^2+b^2)*tan(1/2*d*x+1/2*c)-2*a*b)/(1+tan(1/2*d*x+1/2*c)^2))","A"
565,1,320,227,0.518000," ","int(cos(d*x+c)^3/(a+b*tan(d*x+c))^2,x)","\frac{-\frac{2 b^{4} \left(\frac{-\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a}-b}{a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a}-\frac{5 a \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a^{2}+b^{2}\right)}-\frac{2 \left(\left(-a^{4}-3 a^{2} b^{2}+2 b^{4}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-2 a^{3} b -6 a \,b^{3}\right) \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-\frac{2}{3} a^{4}-6 a^{2} b^{2}+\frac{8}{3} b^{4}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 a \,b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-a^{4}-3 a^{2} b^{2}+2 b^{4}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{2 a^{3} b}{3}-\frac{14 a \,b^{3}}{3}\right)}{\left(a^{2}+b^{2}\right) \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}}{d}"," ",0,"1/d*(-2*b^4/(a^4+2*a^2*b^2+b^4)/(a^2+b^2)*((-b^2/a*tan(1/2*d*x+1/2*c)-b)/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)-5*a/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))-2/(a^2+b^2)/(a^4+2*a^2*b^2+b^4)*((-a^4-3*a^2*b^2+2*b^4)*tan(1/2*d*x+1/2*c)^5+(-2*a^3*b-6*a*b^3)*tan(1/2*d*x+1/2*c)^4+(-2/3*a^4-6*a^2*b^2+8/3*b^4)*tan(1/2*d*x+1/2*c)^3-8*a*b^3*tan(1/2*d*x+1/2*c)^2+(-a^4-3*a^2*b^2+2*b^4)*tan(1/2*d*x+1/2*c)-2/3*a^3*b-14/3*a*b^3)/(1+tan(1/2*d*x+1/2*c)^2)^3)","A"
566,1,321,179,0.526000," ","int(sec(d*x+c)^8/(a+b*tan(d*x+c))^3,x)","\frac{\tan^{4}\left(d x +c \right)}{4 b^{3} d}-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{b^{4} d}+\frac{3 a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d \,b^{5}}+\frac{3 \left(\tan^{2}\left(d x +c \right)\right)}{2 b^{3} d}-\frac{10 a^{3} \tan \left(d x +c \right)}{d \,b^{6}}-\frac{9 a \tan \left(d x +c \right)}{b^{4} d}+\frac{15 \ln \left(a +b \tan \left(d x +c \right)\right) a^{4}}{d \,b^{7}}+\frac{18 \ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \,b^{5}}+\frac{3 \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{3} d}+\frac{6 a^{5}}{d \,b^{7} \left(a +b \tan \left(d x +c \right)\right)}+\frac{12 a^{3}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)}+\frac{6 a}{b^{3} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{6}}{2 d \,b^{7} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 a^{4}}{2 d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 a^{2}}{2 d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{1}{2 b d \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"1/4*tan(d*x+c)^4/b^3/d-a*tan(d*x+c)^3/b^4/d+3/d/b^5*a^2*tan(d*x+c)^2+3/2*tan(d*x+c)^2/b^3/d-10/d/b^6*a^3*tan(d*x+c)-9*a*tan(d*x+c)/b^4/d+15/d/b^7*ln(a+b*tan(d*x+c))*a^4+18/d/b^5*ln(a+b*tan(d*x+c))*a^2+3*ln(a+b*tan(d*x+c))/b^3/d+6/d*a^5/b^7/(a+b*tan(d*x+c))+12/d*a^3/b^5/(a+b*tan(d*x+c))+6*a/b^3/d/(a+b*tan(d*x+c))-1/2/d/b^7/(a+b*tan(d*x+c))^2*a^6-3/2/d/b^5/(a+b*tan(d*x+c))^2*a^4-3/2/d/b^3/(a+b*tan(d*x+c))^2*a^2-1/2/b/d/(a+b*tan(d*x+c))^2","A"
567,1,184,117,0.503000," ","int(sec(d*x+c)^6/(a+b*tan(d*x+c))^3,x)","\frac{\tan^{2}\left(d x +c \right)}{2 b^{3} d}-\frac{3 a \tan \left(d x +c \right)}{b^{4} d}+\frac{6 \ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \,b^{5}}+\frac{2 \ln \left(a +b \tan \left(d x +c \right)\right)}{b^{3} d}+\frac{4 a^{3}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 a}{b^{3} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{4}}{2 d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{2}}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{1}{2 b d \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"1/2*tan(d*x+c)^2/b^3/d-3*a*tan(d*x+c)/b^4/d+6/d/b^5*ln(a+b*tan(d*x+c))*a^2+2*ln(a+b*tan(d*x+c))/b^3/d+4/d*a^3/b^5/(a+b*tan(d*x+c))+4*a/b^3/d/(a+b*tan(d*x+c))-1/2/d/b^5/(a+b*tan(d*x+c))^2*a^4-1/d/b^3/(a+b*tan(d*x+c))^2*a^2-1/2/b/d/(a+b*tan(d*x+c))^2","A"
568,1,84,71,0.512000," ","int(sec(d*x+c)^4/(a+b*tan(d*x+c))^3,x)","\frac{\ln \left(a +b \tan \left(d x +c \right)\right)}{b^{3} d}+\frac{2 a}{b^{3} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{2}}{2 d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{1}{2 b d \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"ln(a+b*tan(d*x+c))/b^3/d+2*a/b^3/d/(a+b*tan(d*x+c))-1/2/d/b^3/(a+b*tan(d*x+c))^2*a^2-1/2/b/d/(a+b*tan(d*x+c))^2","A"
569,1,21,20,0.339000," ","int(sec(d*x+c)^2/(a+b*tan(d*x+c))^3,x)","-\frac{1}{2 b d \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"-1/2/b/d/(a+b*tan(d*x+c))^2","A"
570,1,453,194,0.522000," ","int(cos(d*x+c)^2/(a+b*tan(d*x+c))^3,x)","-\frac{b^{3}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{4 b^{3} a}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{10 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\tan \left(d x +c \right) a^{5}}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{\tan \left(d x +c \right) b^{2} a^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{3 \tan \left(d x +c \right) a \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{3 a^{4} b}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{a^{2} b^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{b^{5}}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{5 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{5}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{5 \arctan \left(\tan \left(d x +c \right)\right) b^{2} a^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{15 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{5}}{2 d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/2/d*b^3/(a^2+b^2)^2/(a+b*tan(d*x+c))^2-4/d*b^3/(a^2+b^2)^3*a/(a+b*tan(d*x+c))+10/d*b^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*a^2-2/d*b^5/(a^2+b^2)^4*ln(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*tan(d*x+c)*a^5-1/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*tan(d*x+c)*b^2*a^3-3/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*tan(d*x+c)*a*b^4+3/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*a^4*b+1/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*a^2*b^3-1/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*b^5-5/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^3+1/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*b^5+5/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^2*a^3-15/2/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a*b^4+1/2/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^5","B"
571,1,824,285,0.571000," ","int(cos(d*x+c)^4/(a+b*tan(d*x+c))^3,x)","-\frac{15 \left(\tan^{3}\left(d x +c \right)\right) a^{3} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{7}}{8 d \left(a^{2}+b^{2}\right)^{5}}-\frac{b^{5}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{21 \arctan \left(\tan \left(d x +c \right)\right) a^{5} b^{2}}{8 d \left(a^{2}+b^{2}\right)^{5}}-\frac{6 b^{5} a}{d \left(a^{2}+b^{2}\right)^{4} \left(a +b \tan \left(d x +c \right)\right)}+\frac{21 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{3 b^{7} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{5}}+\frac{105 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{5}}-\frac{105 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{6}}{8 d \left(a^{2}+b^{2}\right)^{5}}-\frac{5 b^{7}}{4 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{\left(\tan^{2}\left(d x +c \right)\right) b^{7}}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \tan \left(d x +c \right) a^{7}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 a^{6} b}{4 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{21 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{5}}{2 d \left(a^{2}+b^{2}\right)^{5}}+\frac{17 a^{2} b^{5}}{4 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{25 a^{4} b^{3}}{4 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 \left(\tan^{3}\left(d x +c \right)\right) a^{7}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{7}}{2 d \left(a^{2}+b^{2}\right)^{5}}+\frac{4 \left(\tan^{2}\left(d x +c \right)\right) a^{2} b^{5}}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{19 \tan \left(d x +c \right) a^{5} b^{2}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{39 \tan \left(d x +c \right) a \,b^{6}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{25 \tan \left(d x +c \right) a^{3} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \left(\tan^{2}\left(d x +c \right)\right) a^{4} b^{3}}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{33 \left(\tan^{3}\left(d x +c \right)\right) a \,b^{6}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{21 \left(\tan^{3}\left(d x +c \right)\right) a^{5} b^{2}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}"," ",0,"-15/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^3*b^4+4/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^2*b^5+19/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^5*b^2-39/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a*b^6-25/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^3*b^4+5/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^4*b^3-33/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a*b^6+3/8/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^7-1/2/d*b^5/(a^2+b^2)^3/(a+b*tan(d*x+c))^2+3/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^7-1/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*b^7+5/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^7+3/4/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*a^6*b+21/8/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^5*b^2-6/d*b^5/(a^2+b^2)^4*a/(a+b*tan(d*x+c))+21/d*b^5/(a^2+b^2)^5*ln(a+b*tan(d*x+c))*a^2-21/2/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*a^2*b^5-3/d*b^7/(a^2+b^2)^5*ln(a+b*tan(d*x+c))-5/4/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*b^7+3/2/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*b^7+105/8/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^3*b^4-105/8/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a*b^6+17/4/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*a^2*b^5+25/4/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*a^4*b^3+21/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^5*b^2","B"
572,1,1125,219,0.516000," ","int(sec(d*x+c)^7/(a+b*tan(d*x+c))^3,x)","-\frac{15 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{4}}-\frac{3 a}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{6 a^{2}}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 a}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{10 a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{6}}+\frac{15 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{4}}+\frac{3 a}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{6 a^{2}}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 a}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{10 a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{6}}+\frac{5 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}+b^{2}}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2} a}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2} a}+\frac{15 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{8 a^{4}}{d \,b^{5} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{7 a^{2}}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}-\frac{5 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{25 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{23 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{9 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}-\frac{7 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}-\frac{8 a^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{5} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}-\frac{2 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2} a^{2}}+\frac{20 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{4}}{d \,b^{6} \sqrt{a^{2}+b^{2}}}+\frac{25 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{d \,b^{4} \sqrt{a^{2}+b^{2}}}+\frac{5}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{3 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{5}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{3 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{1}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}"," ",0,"-15/2/d*a/b^4*ln(tan(1/2*d*x+1/2*c)+1)+2/d/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2/a*tan(1/2*d*x+1/2*c)^3-2/d/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2/a*tan(1/2*d*x+1/2*c)+15/d/b/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*tan(1/2*d*x+1/2*c)^2+8/d/b^5/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a^4+7/d/b^3/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a^2+5/d/b^2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-3/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)^2*a-6/d/b^5/(tan(1/2*d*x+1/2*c)-1)*a^2-3/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)*a+10/d*a^3/b^6*ln(tan(1/2*d*x+1/2*c)-1)+15/2/d*a/b^4*ln(tan(1/2*d*x+1/2*c)-1)+3/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)^2*a+6/d/b^5/(tan(1/2*d*x+1/2*c)+1)*a^2-3/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)*a-10/d*a^3/b^6*ln(tan(1/2*d*x+1/2*c)+1)-5/d/b^2/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a*tan(1/2*d*x+1/2*c)^3+25/d/b^4/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a^3*tan(1/2*d*x+1/2*c)+25/d/b^4/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))*a^2+23/d/b^2/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a*tan(1/2*d*x+1/2*c)+20/d/b^6/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))*a^4+9/d/b^3/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a^2*tan(1/2*d*x+1/2*c)^2-7/d/b^4/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a^3*tan(1/2*d*x+1/2*c)^3-1/d/b/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2+5/2/d/b^3/(tan(1/2*d*x+1/2*c)+1)-1/3/d/b^3/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/b^3/(tan(1/2*d*x+1/2*c)-1)^2-5/2/d/b^3/(tan(1/2*d*x+1/2*c)-1)+1/3/d/b^3/(tan(1/2*d*x+1/2*c)+1)^3-1/2/d/b^3/(tan(1/2*d*x+1/2*c)+1)^2-8/d/b^5/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a^4*tan(1/2*d*x+1/2*c)^2-2/d*b/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2/a^2*tan(1/2*d*x+1/2*c)^2","B"
573,1,611,138,0.495000," ","int(sec(d*x+c)^5/(a+b*tan(d*x+c))^3,x)","-\frac{3 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2} a}-\frac{4 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}-\frac{2 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2} a^{2}}+\frac{13 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2} a}+\frac{4 a^{2}}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}-\frac{1}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{6 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{d \,b^{4} \sqrt{a^{2}+b^{2}}}+\frac{3 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}+b^{2}}}-\frac{1}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{4}}+\frac{1}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{4}}"," ",0,"-3/d/b^2/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a*tan(1/2*d*x+1/2*c)^3+2/d/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2/a*tan(1/2*d*x+1/2*c)^3-4/d/b^3/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a^2*tan(1/2*d*x+1/2*c)^2+9/d/b/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*tan(1/2*d*x+1/2*c)^2-2/d*b/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2/a^2*tan(1/2*d*x+1/2*c)^2+13/d/b^2/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a*tan(1/2*d*x+1/2*c)-2/d/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2/a*tan(1/2*d*x+1/2*c)+4/d/b^3/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2*a^2-1/d/b/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2+6/d/b^4/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))*a^2+3/d/b^2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)+3/d*a/b^4*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b^3/(tan(1/2*d*x+1/2*c)+1)-3/d*a/b^4*ln(tan(1/2*d*x+1/2*c)+1)","B"
574,1,191,87,0.533000," ","int(sec(d*x+c)^3/(a+b*tan(d*x+c))^3,x)","\frac{-\frac{2 \left(-\frac{\left(a^{2}+2 b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a^{2}+b^{2}\right) a}-\frac{b \left(a^{2}-2 b^{2}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a^{2}+b^{2}\right) a^{2}}-\frac{\left(a^{2}-2 b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a^{2}+b^{2}\right) a}+\frac{b}{2 a^{2}+2 b^{2}}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{\arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{\frac{3}{2}}}}{d}"," ",0,"1/d*(-2*(-1/2*(a^2+2*b^2)/(a^2+b^2)/a*tan(1/2*d*x+1/2*c)^3-1/2*b*(a^2-2*b^2)/(a^2+b^2)/a^2*tan(1/2*d*x+1/2*c)^2-1/2*(a^2-2*b^2)/(a^2+b^2)/a*tan(1/2*d*x+1/2*c)+1/2*b/(a^2+b^2))/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2+1/(a^2+b^2)^(3/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))","B"
575,1,280,141,0.270000," ","int(sec(d*x+c)/(a+b*tan(d*x+c))^3,x)","\frac{-\frac{2 \left(-\frac{b^{2} \left(5 a^{2}+2 b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{b \left(4 a^{4}-7 a^{2} b^{2}-2 b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) a^{2}}+\frac{b^{2} \left(11 a^{2}+2 b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) a}+\frac{b \left(4 a^{2}+b^{2}\right)}{2 a^{4}+4 a^{2} b^{2}+2 b^{4}}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}+\frac{\left(2 a^{2}-b^{2}\right) \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}+b^{2}}}}{d}"," ",0,"1/d*(-2*(-1/2*b^2*(5*a^2+2*b^2)/a/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^3-1/2*b*(4*a^4-7*a^2*b^2-2*b^4)/(a^4+2*a^2*b^2+b^4)/a^2*tan(1/2*d*x+1/2*c)^2+1/2*b^2*(11*a^2+2*b^2)/(a^4+2*a^2*b^2+b^4)/a*tan(1/2*d*x+1/2*c)+1/2*b*(4*a^2+b^2)/(a^4+2*a^2*b^2+b^4))/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2+(2*a^2-b^2)/(a^4+2*a^2*b^2+b^4)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))","A"
576,1,283,207,0.531000," ","int(cos(d*x+c)/(a+b*tan(d*x+c))^3,x)","\frac{-\frac{2 b^{2} \left(\frac{-\frac{b^{2} \left(9 a^{2}+2 b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a}-\frac{b \left(8 a^{4}-15 a^{2} b^{2}-2 b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{2}}+\frac{b^{2} \left(23 a^{2}+2 b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a}+4 a^{2} b +\frac{b^{3}}{2}}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}-\frac{3 \left(4 a^{2}-b^{2}\right) \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{3}}-\frac{2 \left(\left(-a^{3}+3 b^{2} a \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-3 a^{2} b +b^{3}\right)}{\left(a^{6}+3 b^{2} a^{4}+3 b^{4} a^{2}+b^{6}\right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{d}"," ",0,"1/d*(-2*b^2/(a^2+b^2)^3*((-1/2*b^2*(9*a^2+2*b^2)/a*tan(1/2*d*x+1/2*c)^3-1/2*b*(8*a^4-15*a^2*b^2-2*b^4)/a^2*tan(1/2*d*x+1/2*c)^2+1/2*b^2*(23*a^2+2*b^2)/a*tan(1/2*d*x+1/2*c)+4*a^2*b+1/2*b^3)/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2-3/2*(4*a^2-b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))-2/(a^6+3*a^4*b^2+3*a^2*b^4+b^6)*((-a^3+3*a*b^2)*tan(1/2*d*x+1/2*c)-3*a^2*b+b^3)/(1+tan(1/2*d*x+1/2*c)^2))","A"
577,1,457,292,0.558000," ","int(cos(d*x+c)^3/(a+b*tan(d*x+c))^3,x)","\frac{-\frac{2 b^{4} \left(\frac{-\frac{b^{2} \left(13 a^{2}+2 b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a}-\frac{b \left(12 a^{4}-23 a^{2} b^{2}-2 b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{2}}+\frac{b^{2} \left(35 a^{2}+2 b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a}+6 a^{2} b +\frac{b^{3}}{2}}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b -a \right)^{2}}-\frac{5 \left(6 a^{2}-b^{2}\right) \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right) \left(a^{6}+3 b^{2} a^{4}+3 b^{4} a^{2}+b^{6}\right)}-\frac{2 \left(\left(-a^{5}-4 b^{2} a^{3}+9 a \,b^{4}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-3 a^{4} b -12 a^{2} b^{3}+3 b^{5}\right) \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-\frac{2}{3} a^{5}-\frac{32}{3} b^{2} a^{3}+14 a \,b^{4}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-20 a^{2} b^{3}+4 b^{5}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-a^{5}-4 b^{2} a^{3}+9 a \,b^{4}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a^{4} b -\frac{32 a^{2} b^{3}}{3}+\frac{7 b^{5}}{3}\right)}{\left(a^{6}+3 b^{2} a^{4}+3 b^{4} a^{2}+b^{6}\right) \left(a^{2}+b^{2}\right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}}{d}"," ",0,"1/d*(-2*b^4/(a^2+b^2)/(a^6+3*a^4*b^2+3*a^2*b^4+b^6)*((-1/2*b^2*(13*a^2+2*b^2)/a*tan(1/2*d*x+1/2*c)^3-1/2*b*(12*a^4-23*a^2*b^2-2*b^4)/a^2*tan(1/2*d*x+1/2*c)^2+1/2*b^2*(35*a^2+2*b^2)/a*tan(1/2*d*x+1/2*c)+6*a^2*b+1/2*b^3)/(a*tan(1/2*d*x+1/2*c)^2-2*tan(1/2*d*x+1/2*c)*b-a)^2-5/2*(6*a^2-b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))-2/(a^6+3*a^4*b^2+3*a^2*b^4+b^6)/(a^2+b^2)*((-a^5-4*a^3*b^2+9*a*b^4)*tan(1/2*d*x+1/2*c)^5+(-3*a^4*b-12*a^2*b^3+3*b^5)*tan(1/2*d*x+1/2*c)^4+(-2/3*a^5-32/3*b^2*a^3+14*a*b^4)*tan(1/2*d*x+1/2*c)^3+(-20*a^2*b^3+4*b^5)*tan(1/2*d*x+1/2*c)^2+(-a^5-4*a^3*b^2+9*a*b^4)*tan(1/2*d*x+1/2*c)-a^4*b-32/3*a^2*b^3+7/3*b^5)/(1+tan(1/2*d*x+1/2*c)^2)^3)","A"
578,1,371,129,0.922000," ","int((d*sec(f*x+e))^(7/2)*(a+b*tan(f*x+e)),x)","\frac{2 \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(21 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) a -21 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) a +21 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) a -21 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) a -21 a \left(\cos^{4}\left(f x +e \right)\right)+14 a \left(\cos^{3}\left(f x +e \right)\right)+7 a \cos \left(f x +e \right)+5 b \sin \left(f x +e \right)\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}}}{35 f \sin \left(f x +e \right)^{5}}"," ",0,"2/35/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(21*I*cos(f*x+e)^4*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*a-21*I*cos(f*x+e)^4*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*a+21*I*cos(f*x+e)^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*a-21*I*cos(f*x+e)^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*a-21*a*cos(f*x+e)^4+14*a*cos(f*x+e)^3+7*a*cos(f*x+e)+5*b*sin(f*x+e))*(d/cos(f*x+e))^(7/2)/sin(f*x+e)^5","C"
579,1,195,104,0.831000," ","int((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e)),x)","\frac{2 \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(5 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{3}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a +5 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a +5 \cos \left(f x +e \right) \sin \left(f x +e \right) a +3 b \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{15 f \sin \left(f x +e \right)^{4}}"," ",0,"2/15/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(5*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a+5*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a+5*cos(f*x+e)*sin(f*x+e)*a+3*b)*(d/cos(f*x+e))^(5/2)/sin(f*x+e)^4","C"
580,1,356,104,0.796000," ","int((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e)),x)","-\frac{2 \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(3 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a -3 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a +3 i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \sin \left(f x +e \right)-3 i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \sin \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right) a -3 a \cos \left(f x +e \right)-b \sin \left(f x +e \right)\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{3 f \sin \left(f x +e \right)^{5}}"," ",0,"-2/3/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(3*I*cos(f*x+e)^2*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a-3*I*cos(f*x+e)^2*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a+3*I*cos(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*sin(f*x+e)-3*I*cos(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*sin(f*x+e)+3*cos(f*x+e)^2*a-3*a*cos(f*x+e)-b*sin(f*x+e))*(d/cos(f*x+e))^(3/2)/sin(f*x+e)^5","C"
581,1,168,78,0.893000," ","int((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e)),x)","\frac{2 \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) a +i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a +b \right)}{f \sin \left(f x +e \right)^{4}}"," ",0,"2/f*(d/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*a+I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a+b)/sin(f*x+e)^4","C"
582,1,916,78,0.915000," ","int((a+b*tan(f*x+e))/(d*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(4 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a -4 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a +8 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a -8 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a +4 i a \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-4 i a \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-4 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a -4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b -4 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, b +b \ln \left(-\frac{2 \left(2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)^{2}}\right) \cos \left(f x +e \right) \sin \left(f x +e \right)-b \cos \left(f x +e \right) \ln \left(-\frac{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}+2 \cos \left(f x +e \right)-1}{\sin \left(f x +e \right)^{2}}\right) \sin \left(f x +e \right)+4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, a \right)}{2 f \sqrt{-\frac{\cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}}\, \cos \left(f x +e \right) \sin \left(f x +e \right)^{3} \sqrt{\frac{d}{\cos \left(f x +e \right)}}}"," ",0,"-1/2/f*(-1+cos(f*x+e))*(4*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a-4*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a+8*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a-8*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a+4*I*a*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-4*I*a*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-4*cos(f*x+e)^3*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*a-4*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*b-4*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*b+b*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*cos(f*x+e)*sin(f*x+e)-b*cos(f*x+e)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*sin(f*x+e)+4*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*a)/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/cos(f*x+e)/sin(f*x+e)^3/(d/cos(f*x+e))^(1/2)","C"
583,1,172,106,0.777000," ","int((a+b*tan(f*x+e))/(d*sec(f*x+e))^(3/2),x)","\frac{\frac{2 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) a}{3}+\frac{2 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a}{3}-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) b}{3}+\frac{2 \cos \left(f x +e \right) \sin \left(f x +e \right) a}{3}}{f \cos \left(f x +e \right)^{2} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"2/3/f*(I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*a+I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a-cos(f*x+e)^2*b+cos(f*x+e)*sin(f*x+e)*a)/cos(f*x+e)^2/(d/cos(f*x+e))^(3/2)","C"
584,1,345,106,0.811000," ","int((a+b*tan(f*x+e))/(d*sec(f*x+e))^(5/2),x)","-\frac{2 \left(-3 i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \sin \left(f x +e \right)+3 i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \sin \left(f x +e \right)-3 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a +3 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a +a \left(\cos^{4}\left(f x +e \right)\right)+\left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) b +2 \left(\cos^{2}\left(f x +e \right)\right) a -3 a \cos \left(f x +e \right)\right)}{5 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/5/f*(-3*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a+3*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a-3*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a+3*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a+a*cos(f*x+e)^4+cos(f*x+e)^3*sin(f*x+e)*b+2*cos(f*x+e)^2*a-3*a*cos(f*x+e))/cos(f*x+e)^3/sin(f*x+e)/(d/cos(f*x+e))^(5/2)","C"
585,1,190,131,0.822000," ","int((a+b*tan(f*x+e))/(d*sec(f*x+e))^(7/2),x)","\frac{\frac{10 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) a}{21}+\frac{10 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a}{21}-\frac{2 b \left(\cos^{4}\left(f x +e \right)\right)}{7}+\frac{2 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a}{7}+\frac{10 \cos \left(f x +e \right) \sin \left(f x +e \right) a}{21}}{f \cos \left(f x +e \right)^{4} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}}}"," ",0,"2/21/f*(5*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*a+5*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a-3*b*cos(f*x+e)^4+3*cos(f*x+e)^3*sin(f*x+e)*a+5*cos(f*x+e)*sin(f*x+e)*a)/cos(f*x+e)^4/(d/cos(f*x+e))^(7/2)","C"
586,1,382,151,0.953000," ","int((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e))^2,x)","\frac{2 \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(35 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-10 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+35 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{3}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-10 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{3}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+35 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}-10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}+42 \cos \left(f x +e \right) a b +15 \sin \left(f x +e \right) b^{2}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{105 f \sin \left(f x +e \right)^{4} \cos \left(f x +e \right)}"," ",0,"2/105/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(35*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-10*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+35*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-10*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+35*cos(f*x+e)^2*sin(f*x+e)*a^2-10*cos(f*x+e)^2*sin(f*x+e)*b^2+42*cos(f*x+e)*a*b+15*sin(f*x+e)*b^2)*(d/cos(f*x+e))^(5/2)/sin(f*x+e)^4/cos(f*x+e)","C"
587,1,712,151,0.914000," ","int((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e))^2,x)","-\frac{2 \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(15 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) a^{2}-6 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) b^{2}-15 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) a^{2}+6 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) b^{2}+15 i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) a^{2}-6 i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) b^{2}-15 i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) a^{2}+6 i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) b^{2}+15 \left(\cos^{3}\left(f x +e \right)\right) a^{2}-6 \left(\cos^{3}\left(f x +e \right)\right) b^{2}-15 a^{2} \left(\cos^{2}\left(f x +e \right)\right)+9 b^{2} \left(\cos^{2}\left(f x +e \right)\right)-10 a \cos \left(f x +e \right) b \sin \left(f x +e \right)-3 b^{2}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{15 f \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"-2/15/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(15*I*cos(f*x+e)^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*a^2-6*I*cos(f*x+e)^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*b^2-15*I*cos(f*x+e)^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*a^2+6*I*cos(f*x+e)^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*b^2+15*I*cos(f*x+e)^2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*a^2-6*I*cos(f*x+e)^2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*b^2-15*I*cos(f*x+e)^2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*a^2+6*I*cos(f*x+e)^2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*b^2+15*cos(f*x+e)^3*a^2-6*cos(f*x+e)^3*b^2-15*a^2*cos(f*x+e)^2+9*b^2*cos(f*x+e)^2-10*a*cos(f*x+e)*b*sin(f*x+e)-3*b^2)*(d/cos(f*x+e))^(3/2)/sin(f*x+e)^5/cos(f*x+e)","C"
588,1,339,115,0.904000," ","int((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2,x)","\frac{2 \sqrt{\frac{d}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right)^{2} \left(3 i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-2 i \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+3 i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-2 i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+6 \cos \left(f x +e \right) a b +\sin \left(f x +e \right) b^{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2}}{3 f \cos \left(f x +e \right) \sin \left(f x +e \right)^{4}}"," ",0,"2/3/f*(d/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))^2*(3*I*cos(f*x+e)^2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-2*I*cos(f*x+e)^2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+3*I*cos(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-2*I*cos(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+6*cos(f*x+e)*a*b+sin(f*x+e)*b^2)*(1+cos(f*x+e))^2/cos(f*x+e)/sin(f*x+e)^4","C"
589,1,2564,113,0.973000," ","int((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(1/2),x)","\text{Expression too large to display}"," ",0,"1/f*(-1+cos(f*x+e))*(2*I*cos(f*x+e)^4*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2+2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^2+16*I*cos(f*x+e)^3*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+12*I*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-24*I*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2-12*I*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2+24*I*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+8*I*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-16*I*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2-8*I*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2+16*I*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2-4*I*cos(f*x+e)^4*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2-2*I*cos(f*x+e)^4*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2+4*I*cos(f*x+e)^4*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+8*I*cos(f*x+e)^3*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-16*I*cos(f*x+e)^3*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2-8*I*cos(f*x+e)^3*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2+2*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2*sin(f*x+e)-4*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2*sin(f*x+e)-2*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2*sin(f*x+e)+4*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2*sin(f*x+e)-4*cos(f*x+e)^2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^2+4*cos(f*x+e)^2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^2-4*cos(f*x+e)^3*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^2+2*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^2+2*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^2-2*cos(f*x+e)^5*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^2+2*cos(f*x+e)^5*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^2-4*cos(f*x+e)^4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^2+2*cos(f*x+e)^4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^2-12*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b-4*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b-a*b*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*cos(f*x+e)^2*sin(f*x+e)+a*b*cos(f*x+e)^2*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*sin(f*x+e)-4*cos(f*x+e)^4*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b-12*cos(f*x+e)^3*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b)*(1+cos(f*x+e))^4*(d/cos(f*x+e))^(1/2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)/cos(f*x+e)^3/d/sin(f*x+e)^3","C"
590,1,320,149,0.877000," ","int((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(3/2),x)","-\frac{2 \left(-i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-2 i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}-i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a^{2}-2 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, b^{2}+2 \left(\cos^{2}\left(f x +e \right)\right) a b -\cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}+\cos \left(f x +e \right) \sin \left(f x +e \right) b^{2}\right)}{3 f \cos \left(f x +e \right)^{2} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/3/f*(-I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^2-2*I*cos(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2-I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^2-2*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*b^2+2*cos(f*x+e)^2*a*b-cos(f*x+e)*sin(f*x+e)*a^2+cos(f*x+e)*sin(f*x+e)*b^2)/cos(f*x+e)^2/(d/cos(f*x+e))^(3/2)","C"
591,1,670,153,0.883000," ","int((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(5/2),x)","-\frac{2 \left(-3 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+3 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}+2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}-3 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+3 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}+2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+\left(\cos^{4}\left(f x +e \right)\right) a^{2}-\left(\cos^{4}\left(f x +e \right)\right) b^{2}+2 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a b +2 a^{2} \left(\cos^{2}\left(f x +e \right)\right)+3 b^{2} \left(\cos^{2}\left(f x +e \right)\right)-3 \cos \left(f x +e \right) a^{2}-2 \cos \left(f x +e \right) b^{2}\right)}{5 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/5/f*(-3*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+3*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2+2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2-3*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+3*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2+2*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+cos(f*x+e)^4*a^2-cos(f*x+e)^4*b^2+2*cos(f*x+e)^3*sin(f*x+e)*a*b+2*a^2*cos(f*x+e)^2+3*b^2*cos(f*x+e)^2-3*cos(f*x+e)*a^2-2*cos(f*x+e)*b^2)/cos(f*x+e)^3/sin(f*x+e)/(d/cos(f*x+e))^(5/2)","C"
592,1,359,188,0.957000," ","int((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(7/2),x)","-\frac{2 \left(-5 i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-2 i \cos \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+6 \left(\cos^{4}\left(f x +e \right)\right) a b -3 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}+3 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{2}-5 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a^{2}-2 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, b^{2}-5 \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}-2 \cos \left(f x +e \right) \sin \left(f x +e \right) b^{2}\right)}{21 f \cos \left(f x +e \right)^{4} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}}}"," ",0,"-2/21/f*(-5*I*cos(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-2*I*cos(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*b^2+6*cos(f*x+e)^4*a*b-3*cos(f*x+e)^3*sin(f*x+e)*a^2+3*cos(f*x+e)^3*sin(f*x+e)*b^2-5*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^2-2*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*b^2-5*cos(f*x+e)*sin(f*x+e)*a^2-2*cos(f*x+e)*sin(f*x+e)*b^2)/cos(f*x+e)^4/(d/cos(f*x+e))^(7/2)","C"
593,1,697,188,1.000000," ","int((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(9/2),x)","-\frac{2 \left(5 \left(\cos^{6}\left(f x +e \right)\right) a^{2}-5 \left(\cos^{6}\left(f x +e \right)\right) b^{2}+10 \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) a b -21 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-6 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+6 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+21 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-21 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}+21 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{2}-6 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+6 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) b^{2}+2 \left(\cos^{4}\left(f x +e \right)\right) a^{2}+7 \left(\cos^{4}\left(f x +e \right)\right) b^{2}+14 a^{2} \left(\cos^{2}\left(f x +e \right)\right)+4 b^{2} \left(\cos^{2}\left(f x +e \right)\right)-21 \cos \left(f x +e \right) a^{2}-6 \cos \left(f x +e \right) b^{2}\right)}{45 f \cos \left(f x +e \right)^{5} \sin \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{9}{2}}}"," ",0,"-2/45/f*(5*cos(f*x+e)^6*a^2-5*cos(f*x+e)^6*b^2+10*cos(f*x+e)^5*sin(f*x+e)*a*b-6*I*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*b^2+21*I*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^2-6*I*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*b^2-21*I*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^2-21*I*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^2+21*I*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^2+6*I*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*b^2+6*I*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*b^2+2*cos(f*x+e)^4*a^2+7*cos(f*x+e)^4*b^2+14*a^2*cos(f*x+e)^2+4*b^2*cos(f*x+e)^2-21*cos(f*x+e)*a^2-6*cos(f*x+e)*b^2)/cos(f*x+e)^5/sin(f*x+e)/(d/cos(f*x+e))^(9/2)","C"
594,1,414,204,1.047000," ","int((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e))^3,x)","\frac{2 \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(105 i \left(\cos^{5}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a^{3}-90 i \left(\cos^{5}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a \,b^{2}+105 i \left(\cos^{4}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a^{3}-90 i \left(\cos^{4}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a \,b^{2}+105 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{3}-90 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a \,b^{2}+189 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b -63 b^{3} \left(\cos^{2}\left(f x +e \right)\right)+135 \cos \left(f x +e \right) \sin \left(f x +e \right) a \,b^{2}+35 b^{3}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{315 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{4}}"," ",0,"2/315/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(105*I*cos(f*x+e)^5*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-90*I*cos(f*x+e)^5*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+105*I*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-90*I*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+105*cos(f*x+e)^3*sin(f*x+e)*a^3-90*cos(f*x+e)^3*sin(f*x+e)*a*b^2+189*a^2*cos(f*x+e)^2*b-63*b^3*cos(f*x+e)^2+135*cos(f*x+e)*sin(f*x+e)*a*b^2+35*b^3)*(d/cos(f*x+e))^(5/2)/cos(f*x+e)^2/sin(f*x+e)^4","C"
595,1,759,182,1.010000," ","int((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e))^3,x)","-\frac{2 \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(105 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}-126 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}+126 i \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}-105 i \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}+126 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}-105 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}+105 i \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}-126 i \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}+105 \left(\cos^{4}\left(f x +e \right)\right) a^{3}-126 \left(\cos^{4}\left(f x +e \right)\right) a \,b^{2}-105 a^{3} \left(\cos^{3}\left(f x +e \right)\right)+189 a \,b^{2} \left(\cos^{3}\left(f x +e \right)\right)-105 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b \sin \left(f x +e \right)+35 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{3}-63 a \cos \left(f x +e \right) b^{2}-15 \sin \left(f x +e \right) b^{3}\right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{105 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{5}}"," ",0,"-2/105/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(-126*I*cos(f*x+e)^3*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2+126*I*cos(f*x+e)^4*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2-126*I*cos(f*x+e)^4*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2-105*I*cos(f*x+e)^4*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3+126*I*cos(f*x+e)^3*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2-105*I*cos(f*x+e)^3*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3+105*I*cos(f*x+e)^3*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3+105*I*cos(f*x+e)^4*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3+105*cos(f*x+e)^4*a^3-126*cos(f*x+e)^4*a*b^2-105*a^3*cos(f*x+e)^3+189*a*b^2*cos(f*x+e)^3-105*a^2*cos(f*x+e)^2*b*sin(f*x+e)+35*cos(f*x+e)^2*sin(f*x+e)*b^3-63*a*cos(f*x+e)*b^2-15*sin(f*x+e)*b^3)*(d/cos(f*x+e))^(3/2)/cos(f*x+e)^2/sin(f*x+e)^5","C"
596,1,373,141,1.004000," ","int((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3,x)","\frac{2 \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(5 i \left(\cos^{3}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a^{3}-10 i \left(\cos^{3}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a \,b^{2}+5 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a^{3}-10 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, a \,b^{2}+15 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b -5 b^{3} \left(\cos^{2}\left(f x +e \right)\right)+5 \cos \left(f x +e \right) \sin \left(f x +e \right) a \,b^{2}+b^{3}\right) \sqrt{\frac{d}{\cos \left(f x +e \right)}}}{5 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{4}}"," ",0,"2/5/f*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(5*I*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-10*I*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+5*I*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-10*I*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+15*a^2*cos(f*x+e)^2*b-5*b^3*cos(f*x+e)^2+5*cos(f*x+e)*sin(f*x+e)*a*b^2+b^3)*(d/cos(f*x+e))^(1/2)/cos(f*x+e)^2/sin(f*x+e)^4","C"
597,1,3065,190,1.076000," ","int((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"1/6/f*(-1+cos(f*x+e))^2*(36*cos(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b^2-72*cos(f*x+e)^3*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b^2+24*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^3+36*cos(f*x+e)^2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b^2+12*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^3-72*cos(f*x+e)^4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b^2+40*cos(f*x+e)^3*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^3+36*cos(f*x+e)^6*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b^2+12*cos(f*x+e)^5*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^3+3*cos(f*x+e)^3*sin(f*x+e)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*b^3-3*cos(f*x+e)^3*sin(f*x+e)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*b^3+72*I*cos(f*x+e)^3*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-72*I*cos(f*x+e)^3*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3+48*I*cos(f*x+e)^2*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-48*I*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3+12*I*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-12*I*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3+36*cos(f*x+e)^5*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a*b^2+36*cos(f*x+e)^4*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^3+12*I*cos(f*x+e)^5*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-12*I*cos(f*x+e)^5*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3+48*I*cos(f*x+e)^4*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-48*I*cos(f*x+e)^4*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-12*cos(f*x+e)^6*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^3+4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*b^3*sin(f*x+e)+12*cos(f*x+e)^2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^3+24*cos(f*x+e)^3*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^3-24*cos(f*x+e)^5*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^3-108*cos(f*x+e)^4*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^2*b-36*cos(f*x+e)^5*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^2*b-9*cos(f*x+e)^3*sin(f*x+e)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*a^2*b+9*cos(f*x+e)^3*sin(f*x+e)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*a^2*b-108*cos(f*x+e)^3*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^2*b-36*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*a^2*b-72*I*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+72*I*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2-72*I*cos(f*x+e)^5*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+72*I*cos(f*x+e)^5*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2-288*I*cos(f*x+e)^4*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+288*I*cos(f*x+e)^4*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2-432*I*cos(f*x+e)^3*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+432*I*cos(f*x+e)^3*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2-288*I*cos(f*x+e)^2*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+288*I*cos(f*x+e)^2*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2)/(1+cos(f*x+e))/cos(f*x+e)^2/sin(f*x+e)^5/(d/cos(f*x+e))^(1/2)/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(3/2)","C"
598,1,342,158,1.000000," ","int((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(3/2),x)","\frac{\frac{2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right) a^{3}}{3}+4 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right) a \,b^{2}+\frac{2 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}}{3}+4 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}-2 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b +\frac{2 b^{3} \left(\cos^{2}\left(f x +e \right)\right)}{3}+\frac{2 \cos \left(f x +e \right) \sin \left(f x +e \right) a^{3}}{3}-2 \cos \left(f x +e \right) \sin \left(f x +e \right) a \,b^{2}+2 b^{3}}{f \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2}}"," ",0,"2/3/f*(I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*a^3+6*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*a*b^2+I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3+6*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2-3*a^2*cos(f*x+e)^2*b+b^3*cos(f*x+e)^2+cos(f*x+e)*sin(f*x+e)*a^3-3*cos(f*x+e)*sin(f*x+e)*a*b^2+3*b^3)/(d/cos(f*x+e))^(3/2)/cos(f*x+e)^2","C"
599,1,1923,213,0.974000," ","int((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(5/2),x)","\text{Expression too large to display}"," ",0,"1/10/f*(1+cos(f*x+e))^3*(-1+cos(f*x+e))^2*(-12*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a^3+12*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3*sin(f*x+e)-12*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3*sin(f*x+e)+36*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^3*a*b^2+20*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2*sin(f*x+e)*b^3+12*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2*a*b^2+20*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*b^3-24*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)*a*b^2-12*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^5*a*b^2-4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^4*sin(f*x+e)*b^3-12*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^4*a*b^2-4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^3*sin(f*x+e)*b^3-5*cos(f*x+e)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*b^3*sin(f*x+e)+5*cos(f*x+e)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*b^3*sin(f*x+e)+4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^4*a^3+8*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^3*a^3-4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2*a^3+12*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-12*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3+24*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3-24*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a^3+24*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2*sin(f*x+e)-24*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2*sin(f*x+e)+4*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^5*a^3+12*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^4*sin(f*x+e)*a^2*b+12*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^3*sin(f*x+e)*a^2*b+24*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2*sin(f*x+e)*a*b^2-24*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2*sin(f*x+e)*a*b^2+48*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2-48*I*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*a*b^2)*cos(f*x+e)*(d/cos(f*x+e))^(5/2)*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/d^5/sin(f*x+e)^5","C"
600,1,391,183,0.982000," ","int((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(7/2),x)","-\frac{2 \left(-5 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right) a^{3}-6 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right) a \,b^{2}+9 \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -3 \left(\cos^{4}\left(f x +e \right)\right) b^{3}-3 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{3}+9 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a \,b^{2}-5 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}-6 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}+7 b^{3} \left(\cos^{2}\left(f x +e \right)\right)-5 \cos \left(f x +e \right) \sin \left(f x +e \right) a^{3}-6 \cos \left(f x +e \right) \sin \left(f x +e \right) a \,b^{2}\right)}{21 f \cos \left(f x +e \right)^{4} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}}}"," ",0,"-2/21/f*(-5*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*a^3-6*I*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+9*cos(f*x+e)^4*a^2*b-3*cos(f*x+e)^4*b^3-3*cos(f*x+e)^3*sin(f*x+e)*a^3+9*cos(f*x+e)^3*sin(f*x+e)*a*b^2-5*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3-6*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+7*b^3*cos(f*x+e)^2-5*cos(f*x+e)*sin(f*x+e)*a^3-6*cos(f*x+e)*sin(f*x+e)*a*b^2)/cos(f*x+e)^4/(d/cos(f*x+e))^(7/2)","C"
601,1,745,189,1.107000," ","int((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(9/2),x)","-\frac{2 \left(21 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}+21 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}-18 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}+18 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}+5 \left(\cos^{6}\left(f x +e \right)\right) a^{3}-15 \left(\cos^{6}\left(f x +e \right)\right) a \,b^{2}+15 \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{2} b -5 \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{3}-18 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}-21 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}-21 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}+18 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}+2 \left(\cos^{4}\left(f x +e \right)\right) a^{3}+21 \left(\cos^{4}\left(f x +e \right)\right) a \,b^{2}+9 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) b^{3}+14 \left(\cos^{2}\left(f x +e \right)\right) a^{3}+12 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-21 a^{3} \cos \left(f x +e \right)-18 a \cos \left(f x +e \right) b^{2}\right)}{45 f \cos \left(f x +e \right)^{5} \sin \left(f x +e \right) \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{9}{2}}}"," ",0,"-2/45/f*(18*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2+18*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2-21*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3-21*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3+5*cos(f*x+e)^6*a^3-15*cos(f*x+e)^6*a*b^2+15*cos(f*x+e)^5*sin(f*x+e)*a^2*b-5*cos(f*x+e)^5*sin(f*x+e)*b^3+21*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3-18*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2-18*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a*b^2+21*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3+2*cos(f*x+e)^4*a^3+21*cos(f*x+e)^4*a*b^2+9*cos(f*x+e)^3*sin(f*x+e)*b^3+14*cos(f*x+e)^2*a^3+12*cos(f*x+e)^2*a*b^2-21*a^3*cos(f*x+e)-18*a*cos(f*x+e)*b^2)/cos(f*x+e)^5/sin(f*x+e)/(d/cos(f*x+e))^(9/2)","C"
602,1,430,227,1.098000," ","int((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(11/2),x)","-\frac{2 \left(21 \left(\cos^{6}\left(f x +e \right)\right) a^{2} b -7 \left(\cos^{6}\left(f x +e \right)\right) b^{3}-7 \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{3}+21 \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) a \,b^{2}-15 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right) a^{3}-10 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right) a \,b^{2}+11 \left(\cos^{4}\left(f x +e \right)\right) b^{3}-9 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a^{3}-6 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) a \,b^{2}-15 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a^{3}-10 i \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) a \,b^{2}-15 \cos \left(f x +e \right) \sin \left(f x +e \right) a^{3}-10 \cos \left(f x +e \right) \sin \left(f x +e \right) a \,b^{2}\right)}{77 f \cos \left(f x +e \right)^{6} \left(\frac{d}{\cos \left(f x +e \right)}\right)^{\frac{11}{2}}}"," ",0,"-2/77/f*(21*cos(f*x+e)^6*a^2*b-7*cos(f*x+e)^6*b^3-7*cos(f*x+e)^5*sin(f*x+e)*a^3+21*cos(f*x+e)^5*sin(f*x+e)*a*b^2-15*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*a^3-10*I*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2+11*cos(f*x+e)^4*b^3-9*cos(f*x+e)^3*sin(f*x+e)*a^3-6*cos(f*x+e)^3*sin(f*x+e)*a*b^2-15*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*a^3-10*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*a*b^2-15*cos(f*x+e)*sin(f*x+e)*a^3-10*cos(f*x+e)*sin(f*x+e)*a*b^2)/cos(f*x+e)^6/(d/cos(f*x+e))^(11/2)","C"
603,1,26371,421,1.790000," ","int((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
604,1,10704,369,1.525000," ","int((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
605,1,3737,282,1.363000," ","int((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"1/2/f*(1+cos(f*x+e))^2*(-4*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(a^2+b^2)^(1/2)*a*b^3-4*I*b*a^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1/(-b+(a^2+b^2)^(1/2))^2*a^2,I)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(1/2)-4*I*b*a^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1/(b+(a^2+b^2)^(1/2))^2*a^2,I)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(1/2)+4*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(a^2+b^2)^(3/2)*a*b+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(3/2)*a^2-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(1/2)*a^2*b^2-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*(a^2+b^2)^(3/2)*a^2+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*(a^2+b^2)^(1/2)*a^2*b^2+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(3/2)*a^2-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(1/2)*a^2*b^2+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b-cos(f*x+e)*a^2-cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)+b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)/a^2)*(a^2+b^2)^(3/2)*b^2-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b-cos(f*x+e)*a^2-cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)+b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)/a^2)*(a^2+b^2)^(1/2)*b^4-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b-cos(f*x+e)*a^2-cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)+b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)/a^2)*a^4*b-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b-cos(f*x+e)*a^2-cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)+b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)/a^2)*a^2*b^3-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b+cos(f*x+e)*a^2+cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)-b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/a^2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(3/2)*b^2+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b+cos(f*x+e)*a^2+cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)-b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/a^2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(1/2)*b^4-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b+cos(f*x+e)*a^2+cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)-b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/a^2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*a^4*b-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b+cos(f*x+e)*a^2+cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)-b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/a^2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*a^2*b^3)*(-1+cos(f*x+e))*(d/cos(f*x+e))^(3/2)*cos(f*x+e)/sin(f*x+e)^2/b/a^2/(-b+(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2)/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/(b+(a^2+b^2)^(1/2))/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)","B"
606,1,3131,276,1.421000," ","int((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"1/2/f*(d/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))*(4*I*b*a^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1/(b+(a^2+b^2)^(1/2))^2*a^2,I)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(1/2)-4*I*b*a^3*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1/(-b+(a^2+b^2)^(1/2))^2*a^2,I)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(1/2)-4*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*a^5-4*I*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*a^3*b^2-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*a^4*b-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*ln(-(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*a^4*b+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*ln(-2*(2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*cos(f*x+e)^2-cos(f*x+e)^2-2*(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)+2*cos(f*x+e)-1)/sin(f*x+e)^2)*a^4*b+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b-cos(f*x+e)*a^2-cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)+b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)/a^2)*(a^2+b^2)^(3/2)*b^2-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b-cos(f*x+e)*a^2-cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)+b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)/a^2)*(a^2+b^2)^(1/2)*b^4-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b-cos(f*x+e)*a^2-cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)+b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)/a^2)*a^4*b-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b-cos(f*x+e)*a^2-cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)+b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)/a^2)*a^2*b^3+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b+cos(f*x+e)*a^2+cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)-b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/a^2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(3/2)*b^2-(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b+cos(f*x+e)*a^2+cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)-b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/a^2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*(a^2+b^2)^(1/2)*b^4+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b+cos(f*x+e)*a^2+cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)-b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/a^2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*a^4*b+(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)*arctanh(1/2*(-1+cos(f*x+e))*(cos(f*x+e)*(a^2+b^2)^(1/2)*b+cos(f*x+e)*a^2+cos(f*x+e)*b^2-b*(a^2+b^2)^(1/2)-b^2)/sin(f*x+e)^2/(-cos(f*x+e)/(1+cos(f*x+e))^2)^(1/2)/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/a^2)*(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)*a^2*b^3)/sin(f*x+e)^2/(a^2+b^2)/(b+(a^2+b^2)^(1/2))/a^2/(b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2+2*a^2*b+2*b^3)/a^4)^(1/2)/(-b+(a^2+b^2)^(1/2))/(-b*((a^2+b^2)^(1/2)*a^2+2*(a^2+b^2)^(1/2)*b^2-2*a^2*b-2*b^3)/a^4)^(1/2)","B"
607,1,8825,418,1.618000," ","int(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
608,1,6252,391,1.482000," ","int(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
609,1,14547,525,1.759000," ","int(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
610,1,44463,439,5.059000," ","int((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
611,1,5337,405,1.873000," ","int((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
612,1,25422,436,2.121000," ","int((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
613,1,14318,395,2.079000," ","int((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
614,1,38644,512,3.717000," ","int(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
615,1,15455,477,2.243000," ","int(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
616,1,44337,645,4.164000," ","int(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
617,1,101372,532,7.563000," ","int((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
618,1,45973,489,3.945000," ","int((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
619,1,80250,515,5.161000," ","int((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
620,1,82035,472,5.528000," ","int((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
621,1,100402,611,14.397000," ","int(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
622,1,82289,573,5.668000," ","int(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
623,1,114399,755,7.742000," ","int(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
624,0,0,64,0.583000," ","int((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e)),x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}} \left(a +b \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e)),x)","F"
625,0,0,64,0.578000," ","int((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e)),x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(a +b \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e)),x)","F"
626,0,0,64,0.584000," ","int((a+b*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x)","\int \frac{a +b \tan \left(f x +e \right)}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+b*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x)","F"
627,0,0,64,0.515000," ","int((a+b*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x)","\int \frac{a +b \tan \left(f x +e \right)}{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int((a+b*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x)","F"
628,0,0,101,0.676000," ","int((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e))^2,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}} \left(a +b \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e))^2,x)","F"
629,0,0,101,0.633000," ","int((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e))^2,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(a +b \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e))^2,x)","F"
630,0,0,101,0.593000," ","int((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{2}}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x)","F"
631,0,0,101,0.596000," ","int((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x)","\int \frac{\left(a +b \tan \left(f x +e \right)\right)^{2}}{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x)","F"
632,0,0,444,1.114000," ","int((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}}}{a +b \tan \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x)","F"
633,0,0,444,1.097000," ","int((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}{a +b \tan \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x)","F"
634,0,0,469,1.084000," ","int(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x)","\int \frac{1}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(a +b \tan \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x)","F"
635,0,0,469,1.071000," ","int(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x)","\int \frac{1}{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}} \left(a +b \tan \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x)","F"
636,0,0,563,1.375000," ","int((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}}}{\left(a +b \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x)","F"
637,0,0,563,1.372000," ","int((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}{\left(a +b \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x)","F"
638,0,0,589,1.375000," ","int(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x)","\int \frac{1}{\left(d \sec \left(f x +e \right)\right)^{\frac{1}{3}} \left(a +b \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x)","F"
639,0,0,589,1.397000," ","int(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x)","\int \frac{1}{\left(d \sec \left(f x +e \right)\right)^{\frac{5}{3}} \left(a +b \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x)","F"
640,0,0,169,1.421000," ","int((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^3,x)","\int \left(d \sec \left(f x +e \right)\right)^{m} \left(a +b \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^3,x)","F"
641,0,0,134,1.045000," ","int((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^2,x)","\int \left(d \sec \left(f x +e \right)\right)^{m} \left(a +b \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^2,x)","F"
642,0,0,83,1.597000," ","int((d*sec(f*x+e))^m*(a+b*tan(f*x+e)),x)","\int \left(d \sec \left(f x +e \right)\right)^{m} \left(a +b \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^m*(a+b*tan(f*x+e)),x)","F"
643,0,0,133,1.262000," ","int((d*sec(f*x+e))^m/(a+b*tan(f*x+e)),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{m}}{a +b \tan \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^m/(a+b*tan(f*x+e)),x)","F"
644,0,0,211,1.344000," ","int((d*sec(f*x+e))^m/(a+b*tan(f*x+e))^2,x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{m}}{\left(a +b \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*sec(f*x+e))^m/(a+b*tan(f*x+e))^2,x)","F"
645,0,0,171,0.926000," ","int((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^n,x)","\int \left(d \sec \left(f x +e \right)\right)^{m} \left(a +b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^n,x)","F"
646,0,0,161,0.873000," ","int(sec(d*x+c)^6*(a+b*tan(d*x+c))^n,x)","\int \left(\sec^{6}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)^6*(a+b*tan(d*x+c))^n,x)","F"
647,0,0,88,0.703000," ","int(sec(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","\int \left(\sec^{4}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","F"
648,1,27,26,0.146000," ","int(sec(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","\frac{\left(a +b \tan \left(d x +c \right)\right)^{1+n}}{b d \left(1+n \right)}"," ",0,"(a+b*tan(d*x+c))^(1+n)/b/d/(1+n)","A"
649,0,0,258,1.178000," ","int(cos(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","F"
650,0,0,418,1.278000," ","int(cos(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","F"
651,0,0,147,0.665000," ","int(sec(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","\int \left(\sec^{3}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","F"
652,0,0,147,0.928000," ","int(sec(d*x+c)*(a+b*tan(d*x+c))^n,x)","\int \sec \left(d x +c \right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)*(a+b*tan(d*x+c))^n,x)","F"
653,0,0,149,0.535000," ","int(cos(d*x+c)*(a+b*tan(d*x+c))^n,x)","\int \cos \left(d x +c \right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)*(a+b*tan(d*x+c))^n,x)","F"
654,0,0,149,2.066000," ","int(cos(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","\int \left(\cos^{3}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","F"
655,1,241,131,5.634000," ","int((e*cos(d*x+c))^(7/2)*(a+I*a*tan(d*x+c)),x)","-\frac{2 a \,e^{4} \left(48 i \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 i \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-24 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/21/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a*e^4*(48*I*sin(1/2*d*x+1/2*c)^9+48*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-96*I*sin(1/2*d*x+1/2*c)^7-72*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+72*I*sin(1/2*d*x+1/2*c)^5+56*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-24*I*sin(1/2*d*x+1/2*c)^3+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+3*I*sin(1/2*d*x+1/2*c))/d","A"
656,1,205,101,5.931000," ","int((e*cos(d*x+c))^(5/2)*(a+I*a*tan(d*x+c)),x)","\frac{2 a \,e^{3} \left(8 i \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+6 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/5/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a*e^3*(8*I*sin(1/2*d*x+1/2*c)^7+8*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*I*sin(1/2*d*x+1/2*c)^5-8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+6*I*sin(1/2*d*x+1/2*c)^3+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-I*sin(1/2*d*x+1/2*c))/d","B"
657,1,168,101,5.774000," ","int((e*cos(d*x+c))^(3/2)*(a+I*a*tan(d*x+c)),x)","-\frac{2 a \,e^{2} \left(4 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-4 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a*e^2*(4*I*sin(1/2*d*x+1/2*c)^5+4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-4*I*sin(1/2*d*x+1/2*c)^3+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+I*sin(1/2*d*x+1/2*c))/d","A"
658,1,108,79,3.523000," ","int((e*cos(d*x+c))^(1/2)*(a+I*a*tan(d*x+c)),x)","\frac{2 a e \left(2 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a*e*(2*I*sin(1/2*d*x+1/2*c)^3+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-I*sin(1/2*d*x+1/2*c))/d","A"
659,1,94,79,5.988000," ","int((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(1/2),x)","\frac{2 \left(-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"2/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)*(-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+I*sin(1/2*d*x+1/2*c))*a/d","A"
660,1,214,104,7.897000," ","int((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(6 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e d}"," ",0,"-2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e*(6*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-12*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+I*sin(1/2*d*x+1/2*c))*a/d","B"
661,1,283,107,10.038000," ","int((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(5/2),x)","\frac{2 \left(-20 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{15 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"2/15/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(-20*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4+20*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2-20*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+10*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+3*I*sin(1/2*d*x+1/2*c))*a/d","B"
662,1,396,137,16.457000," ","int((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(7/2),x)","-\frac{2 \left(168 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-336 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-252 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+504 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+126 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-280 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{35 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"-2/35/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(168*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^6-336*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-252*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+504*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+126*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-280*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+56*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*I*sin(1/2*d*x+1/2*c))*a/d","B"
663,1,387,192,6.931000," ","int((e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{2 e^{4} \left(-224 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3584 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{16}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15680 i \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12544 \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+1568 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-19264 \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25088 i \left(\sin^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+16800 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3584 i \left(\sin^{17}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-9104 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6272 i \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3128 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-14336 i \left(\sin^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-700 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-25088 i \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+90 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+14 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/105/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^4*(-224*I*sin(1/2*d*x+1/2*c)^3-3584*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^16+15680*I*sin(1/2*d*x+1/2*c)^9+12544*sin(1/2*d*x+1/2*c)^14*cos(1/2*d*x+1/2*c)+1568*I*sin(1/2*d*x+1/2*c)^5-19264*sin(1/2*d*x+1/2*c)^12*cos(1/2*d*x+1/2*c)+25088*I*sin(1/2*d*x+1/2*c)^13+16800*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+3584*I*sin(1/2*d*x+1/2*c)^17-9104*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-6272*I*sin(1/2*d*x+1/2*c)^7+3128*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-14336*I*sin(1/2*d*x+1/2*c)^15-700*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-25088*I*sin(1/2*d*x+1/2*c)^11-15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+90*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+14*I*sin(1/2*d*x+1/2*c))/d","B"
664,1,351,160,6.577000," ","int((e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 e^{3} \left(140 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1280 \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-5600 i \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3840 \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-4480 i \left(\sin^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4960 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-840 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3520 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2800 i \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1496 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1280 i \left(\sin^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+376 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-10 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-44 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+6720 i \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{65 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/65/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^3*(140*I*sin(1/2*d*x+1/2*c)^3-1280*sin(1/2*d*x+1/2*c)^14*cos(1/2*d*x+1/2*c)-5600*I*sin(1/2*d*x+1/2*c)^9+3840*sin(1/2*d*x+1/2*c)^12*cos(1/2*d*x+1/2*c)-4480*I*sin(1/2*d*x+1/2*c)^13-4960*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-840*I*sin(1/2*d*x+1/2*c)^5+3520*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+2800*I*sin(1/2*d*x+1/2*c)^7-1496*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+1280*I*sin(1/2*d*x+1/2*c)^15+376*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-10*I*sin(1/2*d*x+1/2*c)-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-44*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+6720*I*sin(1/2*d*x+1/2*c)^11)/d","B"
665,1,315,160,6.105000," ","int((e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{2 e^{2} \left(384 i \left(\sin^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-384 \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-1152 i \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+960 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+1440 i \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1008 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-960 i \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+552 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+360 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-176 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-72 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+28 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+6 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{33 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/33/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^2*(384*I*sin(1/2*d*x+1/2*c)^13-384*sin(1/2*d*x+1/2*c)^12*cos(1/2*d*x+1/2*c)-1152*I*sin(1/2*d*x+1/2*c)^11+960*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+1440*I*sin(1/2*d*x+1/2*c)^9-1008*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-960*I*sin(1/2*d*x+1/2*c)^7+552*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+360*I*sin(1/2*d*x+1/2*c)^5-176*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-72*I*sin(1/2*d*x+1/2*c)^3-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+28*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+6*I*sin(1/2*d*x+1/2*c))/d","A"
666,1,277,128,5.947000," ","int((e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 e \left(64 i \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-64 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-160 i \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 i \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-104 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+20 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/9/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e*(64*I*sin(1/2*d*x+1/2*c)^11-64*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-160*I*sin(1/2*d*x+1/2*c)^9+128*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+160*I*sin(1/2*d*x+1/2*c)^7-104*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-80*I*sin(1/2*d*x+1/2*c)^5+40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+20*I*sin(1/2*d*x+1/2*c)^3-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*I*sin(1/2*d*x+1/2*c))/d","B"
667,1,240,128,6.025000," ","int(1/(e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{\frac{64 i \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{64 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{128 i \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{96 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{96 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{32 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{7}+\frac{12 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{7}+\frac{4 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)}{7}}{a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/7/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(32*I*sin(1/2*d*x+1/2*c)^9-32*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-64*I*sin(1/2*d*x+1/2*c)^7+48*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+48*I*sin(1/2*d*x+1/2*c)^5-28*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-16*I*sin(1/2*d*x+1/2*c)^3-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*I*sin(1/2*d*x+1/2*c))/d","A"
668,1,207,106,5.715000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 \left(16 i \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+16 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+12 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 e \,a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/5/e/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(16*I*sin(1/2*d*x+1/2*c)^7-16*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-24*I*sin(1/2*d*x+1/2*c)^5+16*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+12*I*sin(1/2*d*x+1/2*c)^3-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-4*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*I*sin(1/2*d*x+1/2*c))/d","A"
669,1,170,106,5.382000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{\frac{16 i \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\frac{16 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{3}-\frac{16 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3}+\frac{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{3}+\frac{4 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)}{3}}{e^{2} a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/3/e^2/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(8*I*sin(1/2*d*x+1/2*c)^5-8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-8*I*sin(1/2*d*x+1/2*c)^3+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+4*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*I*sin(1/2*d*x+1/2*c))/d","A"
670,1,135,138,4.533000," ","int(1/(e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 \left(4 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{e^{3} a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/e^3/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(4*I*sin(1/2*d*x+1/2*c)^3-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*I*sin(1/2*d*x+1/2*c))/d","A"
671,1,208,138,7.144000," ","int(1/(e*cos(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^2,x)","-\frac{2 \left(10 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-6 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{4} d}"," ",0,"-2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^4*(10*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+12*I*sin(1/2*d*x+1/2*c)^3-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-6*I*sin(1/2*d*x+1/2*c))/d","A"
672,1,321,170,11.392000," ","int(1/(e*cos(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^2,x)","\frac{-\frac{56 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{112 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{56 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{112 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5}+\frac{8 i \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\frac{14 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{5}+\frac{24 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5}-\frac{4 i \sin \left(\frac{d x}{2}+\frac{c}{2}\right)}{3}}{\left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{5} d}"," ",0,"2/15/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^5*(-84*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+168*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+84*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-168*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+20*I*sin(1/2*d*x+1/2*c)^3-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+36*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-10*I*sin(1/2*d*x+1/2*c))/d","A"
673,1,97,147,1.497000," ","int((e*cos(d*x+c))^(7/2)*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(i \left(\cos^{3}\left(d x +c \right)\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 i \cos \left(d x +c \right)+16 \sin \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{35 d \cos \left(d x +c \right)^{3}}"," ",0,"2/35/d*(I*cos(d*x+c)^3+6*cos(d*x+c)^2*sin(d*x+c)+8*I*cos(d*x+c)+16*sin(d*x+c))*(e*cos(d*x+c))^(7/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3","A"
674,1,80,108,1.444000," ","int((e*cos(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(i \left(\cos^{2}\left(d x +c \right)\right)+4 \cos \left(d x +c \right) \sin \left(d x +c \right)-8 i\right) \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{15 d \cos \left(d x +c \right)^{2}}"," ",0,"2/15/d*(I*cos(d*x+c)^2+4*cos(d*x+c)*sin(d*x+c)-8*I)*(e*cos(d*x+c))^(5/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2","A"
675,1,70,69,1.439000," ","int((e*cos(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \left(i \cos \left(d x +c \right)+2 \sin \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3 d \cos \left(d x +c \right)}"," ",0,"2/3/d*(I*cos(d*x+c)+2*sin(d*x+c))*(e*cos(d*x+c))^(3/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)","A"
676,1,45,30,1.378000," ","int((e*cos(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 i \sqrt{e \cos \left(d x +c \right)}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d}"," ",0,"-2*I/d*(e*cos(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)","A"
677,1,226,257,1.541000," ","int((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right) \left(i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)-\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)\right)}{d \sin \left(d x +c \right) \sqrt{e \cos \left(d x +c \right)}\, \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))*(I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))-arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c))))/sin(d*x+c)/(e*cos(d*x+c))^(1/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(1/2)","A"
678,1,308,416,1.528000," ","int((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+2 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-2 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{2 d \sin \left(d x +c \right)^{3} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/2/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*(I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+2*I*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-2*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-2*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^3/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(3/2)/(e*cos(d*x+c))^(3/2)","A"
679,1,366,398,1.553000," ","int((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)^{3} \left(3 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+3 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+6 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+3 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+4 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{8 d \sin \left(d x +c \right)^{5} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"-1/8/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^3*(3*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+3*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+6*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)-3*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+3*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+4*I*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-4*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^5/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(5/2)/(e*cos(d*x+c))^(5/2)","A"
680,1,417,573,1.487000," ","int((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(7/2),x)","\frac{\sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)^{4} \left(15 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+15 i \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+30 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+20 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-15 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+15 \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-30 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+16 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-16 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{48 d \sin \left(d x +c \right)^{7} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}}}"," ",0,"1/48/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^4*(15*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+15*I*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+30*I*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+20*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-15*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+15*cos(d*x+c)^3*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-30*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)+16*I*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-10*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)+4*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-16*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^7/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(7/2)/(e*cos(d*x+c))^(7/2)","A"
681,1,110,143,1.391000," ","int((e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(5 i \left(\cos^{4}\left(d x +c \right)\right)+5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 i \left(\cos^{2}\left(d x +c \right)\right)+8 \cos \left(d x +c \right) \sin \left(d x +c \right)-16 i\right)}{35 d \cos \left(d x +c \right)^{2} a}"," ",0,"2/35/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e*cos(d*x+c))^(5/2)*(5*I*cos(d*x+c)^4+5*cos(d*x+c)^3*sin(d*x+c)+2*I*cos(d*x+c)^2+8*cos(d*x+c)*sin(d*x+c)-16*I)/cos(d*x+c)^2/a","A"
682,1,100,102,1.520000," ","int((e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(3 i \left(\cos^{3}\left(d x +c \right)\right)+3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 i \cos \left(d x +c \right)+8 \sin \left(d x +c \right)\right)}{15 d \cos \left(d x +c \right) a}"," ",0,"2/15/d*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(e*cos(d*x+c))^(3/2)*(3*I*cos(d*x+c)^3+3*cos(d*x+c)^2*sin(d*x+c)+4*I*cos(d*x+c)+8*sin(d*x+c))/cos(d*x+c)/a","A"
683,1,74,64,1.379000," ","int((e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{2 \sqrt{e \cos \left(d x +c \right)}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(i \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right) \sin \left(d x +c \right)-2 i\right)}{3 d a}"," ",0,"2/3/d*(e*cos(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(I*cos(d*x+c)^2+cos(d*x+c)*sin(d*x+c)-2*I)/a","A"
684,1,69,30,1.434000," ","int(1/(e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{2 i \sqrt{e \cos \left(d x +c \right)}\, \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(i \sin \left(d x +c \right)-\cos \left(d x +c \right)\right)}{d e a}"," ",0,"-2*I/d*(e*cos(d*x+c))^(1/2)*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(I*sin(d*x+c)-cos(d*x+c))/e/a","B"
685,1,232,393,1.402000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(\cos^{2}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+i \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)\right)}{d \sin \left(d x +c \right)^{3} \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) a}"," ",0,"1/d*cos(d*x+c)^2*(-1+cos(d*x+c))^2*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+I*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c))))/sin(d*x+c)^3/(e*cos(d*x+c))^(3/2)/(1/(1+cos(d*x+c)))^(3/2)/(I*sin(d*x+c)+cos(d*x+c)-1)/a","A"
686,1,313,370,1.518000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x)","-\frac{\left(\cos^{2}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{3} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+i \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+2 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+2 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-\cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+2 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{2 d \sin \left(d x +c \right)^{5} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} a}"," ",0,"-1/2/d*cos(d*x+c)^2*(-1+cos(d*x+c))^3*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+I*cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+2*I*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+2*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)-cos(d*x+c)*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+2*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^5/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(5/2)/(e*cos(d*x+c))^(5/2)/a","A"
687,1,371,544,1.515000," ","int(1/(e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x)","\frac{\left(\cos^{2}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{4} \sqrt{\frac{a \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+3 i \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)+6 i \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 i \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(-\cos \left(d x +c \right)-1+\sin \left(d x +c \right)\right)}{2}\right)+3 \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right)}{2}\right)-6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{8 d \sin \left(d x +c \right)^{7} \left(i \sin \left(d x +c \right)+\cos \left(d x +c \right)-1\right) \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}} a}"," ",0,"1/8/d*cos(d*x+c)^2*(-1+cos(d*x+c))^4*(a*(I*sin(d*x+c)+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+3*I*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))+6*I*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*I*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(-cos(d*x+c)-1+sin(d*x+c)))+3*cos(d*x+c)^2*arctanh(1/2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c)))-6*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)-2*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)+4*(1/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^7/(I*sin(d*x+c)+cos(d*x+c)-1)/(1/(1+cos(d*x+c)))^(7/2)/(e*cos(d*x+c))^(7/2)/a","A"
688,0,0,89,2.065000," ","int((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x)","\int \left(e \cos \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x)","F"
689,0,0,71,1.541000," ","int((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x)","\int \left(e \cos \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x)","F"
690,0,0,67,1.601000," ","int((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c)),x)","\int \left(e \cos \left(d x +c \right)\right)^{m} \left(a +i a \tan \left(d x +c \right)\right)\, dx"," ",0,"int((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c)),x)","F"
691,0,0,71,2.385000," ","int((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c)),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{m}}{a +i a \tan \left(d x +c \right)}\, dx"," ",0,"int((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c)),x)","F"
692,0,0,71,4.938000," ","int((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{m}}{\left(a +i a \tan \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x)","F"
693,0,0,85,1.468000," ","int((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x)","\int \left(e \cos \left(d x +c \right)\right)^{m} \sqrt{a +i a \tan \left(d x +c \right)}\, dx"," ",0,"int((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x)","F"
694,0,0,84,1.395000," ","int((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{m}}{\sqrt{a +i a \tan \left(d x +c \right)}}\, dx"," ",0,"int((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x)","F"
695,0,0,181,1.703000," ","int((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^3,x)","\int \left(d \cos \left(f x +e \right)\right)^{m} \left(a +b \tan \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^3,x)","F"
696,0,0,146,1.263000," ","int((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^2,x)","\int \left(d \cos \left(f x +e \right)\right)^{m} \left(a +b \tan \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^2,x)","F"
697,0,0,84,1.691000," ","int((d*cos(f*x+e))^m*(a+b*tan(f*x+e)),x)","\int \left(d \cos \left(f x +e \right)\right)^{m} \left(a +b \tan \left(f x +e \right)\right)\, dx"," ",0,"int((d*cos(f*x+e))^m*(a+b*tan(f*x+e)),x)","F"
698,0,0,130,1.217000," ","int((d*cos(f*x+e))^m/(a+b*tan(f*x+e)),x)","\int \frac{\left(d \cos \left(f x +e \right)\right)^{m}}{a +b \tan \left(f x +e \right)}\, dx"," ",0,"int((d*cos(f*x+e))^m/(a+b*tan(f*x+e)),x)","F"
699,0,0,207,1.694000," ","int((d*cos(f*x+e))^m/(a+b*tan(f*x+e))^2,x)","\int \frac{\left(d \cos \left(f x +e \right)\right)^{m}}{\left(a +b \tan \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*cos(f*x+e))^m/(a+b*tan(f*x+e))^2,x)","F"
700,0,0,175,0.824000," ","int((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^n,x)","\int \left(d \cos \left(f x +e \right)\right)^{m} \left(a +b \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^n,x)","F"